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This document, developed by the Rule Interchange Format (RIF) Working Group, specifies the production rule dialect of the W3C rule interchange format (RIF-PRD), a standard XML serialization format for production rule languages.
This section describes the status of this document at the time of its publication. Other documents may supersede this document. A list of current W3C publications and the latest revision of this technical report can be found in the W3C technical reports index at http://www.w3.org/TR/.
This document is being published as one of a set of 10 documents:
The Rule Interchange Format (RIF) Working Group seeks to gather experience from implementations in order to increase confidence in the language and meet specific exit criteria. This document will remain a Candidate Recommendation until at least 29 October 2009. After that date, when and if the exit criteria are met, the group intends to request Proposed Recommendation status.
Please send reports of implementation experience, and other feedback, to public-rif-comments@w3.org (public archive). Reports of any success or difficulty with the test cases are encouraged. Open discussion among developers is welcome at public-rif-dev@w3.org (public archive).
Publication as a Candidate Recommendation does not imply endorsement by the W3C Membership. This is a draft document and may be updated, replaced or obsoleted by other documents at any time. It is inappropriate to cite this document as other than work in progress.
This document was produced by a group operating under the 5 February 2004 W3C Patent Policy. W3C maintains a public list of any patent disclosures made in connection with the deliverables of the group; that page also includes instructions for disclosing a patent. An individual who has actual knowledge of a patent which the individual believes contains Essential Claim(s) must disclose the information in accordance with section 6 of the W3C Patent Policy.
This document specifies the production rule dialect of the W3C rule interchange format (RIF-PRD), a standard XML serialization format for production rule languages.
The production rule dialect is one of a set of rule interchange dialects that also includes the RIF Core dialect ([RIF-Core]) and the RIF basic logic dialect ([RIF-BLD]).
RIF-Core, the core dialect of the W3C rule interchange format, is designed to support the interchange of definite Horn rules without function symbols ("Datalog"). RIF-Core has both a standard first-order semantics and an operational semantics. Syntactically, RIF-Core has a number of extensions of Datalog:
RIF-Core is based on a rich set of datatypes and built-ins that are aligned with Web-aware rule system implementations [RIF-DTB]. In addition, the RIF RDF and OWL Compatibility document [RIF-RDF-OWL] specifies the syntax and semantics of combinations of RIF-Core, RDF, and OWL documents.
RIF-Core is intended to be the common core of all RIF dialects, and it has been designed, in particular, to be a useful common subset of RIF-BLD and RIF-PRD. RIF-PRD includes and extends RIF-Core, and, therefore, RIF-PRD inherits all RIF-Core features. These features make RIF-PRD a Web-aware (even a semantic Web-aware) language. However, it should be kept in mind that RIF is designed to enable interoperability among rule languages in general, and its uses are not limited to the Web.
This document targets designers and developers of RIF-PRD implementations. A RIF-PRD implementation is a software application that serializes production rules as RIF-PRD XML (producer application) and/or that deserializes RIF-PRD XML documents into production rules (consumer application).
Production rules have an if part, or condition, and a then part, or action. The condition is like the condition part of logic rules (as covered by RIF-Core and its basic logic dialect extension, RIF-BLD). The then part contains actions. An action can assert facts, modify facts, retract facts, and have other side-effects. In general, an action is different from the conclusion of a logic rule, which contains only a logical statement. However, the conclusion of rules interchanged using RIF-Core can be interpreted, according to RIF-PRD operational semantics, as actions that assert facts in the knowledge base.
Example 1.1. The following are examples of production rules:
Because RIF-PRD is a production rule interchange format, it specifies an abstract syntax that shares features with concrete production rule languages, and it associates the abstract constructs with normative semantics and a normative XML concrete syntax. Annotations (e.g. rule author) are the only constructs in RIF-PRD without a formal semantics.
The abstract syntax is specified in mathematical English, and the abstract syntactic constructs that are defined in the sections Abstract Syntax of Conditions, Abstract Syntax of Actions and Abstract Syntax of Rules and Rulesets, are mapped into the concrete XML constructs in the section XML syntax. A lightweight notation is used, instead of the XML syntax, to tie the abstract syntax to the specification of the semantics. A more complete presentation syntax is specified using an EBNF in Presentation Syntax. However, only the XML syntax and the associated semantics are normative. The normative XML schema is included in Appendix: XML Schema.
Example 1.2. In RIF-PRD presentation syntax, the first rule in example 1.1. can be represented as follows:
Prefix(ex <http://example.com/2008/prd1#>) (* ex:rule_1 *) Forall ?customer ?purchasesYTD ( If And( ?customer#ex:Customer ?customer[ex:purchasesYTD->?purchasesYTD] External(pred:numeric-greater-than(?purchasesYTD 5000)) ) Then Do( Modify(?customer[ex:status->"Gold"]) ) )
☐
Production rules are statements of programming logic that specify the execution of one or more actions when their conditions are satisfied. Production rules have an operational semantics, that the OMG Production Rule Representation specification [OMG-PRR] summarizes as follows:
In the section Operational semantics of rules and rule sets, the semantics for rules and rule sets is specified, accordingly, as a labeled terminal transition system (PLO04), where state transitions result from executing the action part of instantiated rules. When several rules are found to be executable at the same time, during the rule execution process, a conflict resolution strategy is used to select the rule to execute. The section Conflict resolution specifies how a conflict resolution strategy can be attached to a rule set. RIF-PRD defines a default conflict resolution strategy.
In the section Semantics of condition formulas, the semantics of the condition part of rules in RIF-PRD is specified operationally, in terms of matching substitutions. To emphasize the overlap between the rule conditions of RIF-BLD and RIF-PRD, and to share the same RIF definitions for datatypes and built-ins [RIF-DTB], an alternative, and equivalent, specification of the semantics of rule conditions in RIF-PRD, using a model theory, is provided in the appendix Model-theoretic semantics of RIF-PRD condition formulas.
The semantics of condition formulas and the semantics of rules and rule sets make no assumption regarding how condition formulas are evaluated. In particular, they do not require that condition formula be evaluated using pattern matching. However, RIF-PRD conformance, as defined in the section Conformance and interoperability, requires only support for safe rules, that is, forward-chaining rules where the conditions can be evaluated based on pattern matching only.
In the section Operational semantics of actions, the semantics of the action part of rules in RIF-PRD is specified using a transition relation between successive states of the data source, represented by ground condition formulas, thus making the link between the model-theoretic semantics of conditions and the operational semantics of rules and rule sets.
The abstract syntax of RIF-PRD documents, and the semantics of the combination of multiple RIF-PRD documents, is specified in the section Document and imports.
In addition to externally specified functions and predicates, and in particular, in addition to the functions and predicates built-ins defined in [RIF-DTB], RIF-PRD supports externally specified actions, and defines one action built-in, as specified in the section Built-in functions, predicates and actions.
The same example rules will be used throughout the document to illustrate the syntax and the semantics of RIF-PRD.
The rules are about the status of customers at a shop, and the discount awarded to them. The rule set contains four rules, to be applied when a customer checks out:
The Gold rule must be applied first; that is, e.g., a customer with "Silver" status and a shopping cart worth exactly $2,000 should be promoted to "Gold" status, before being given the 5% discount that would disallow the application of the Gold rule (since the total worth of his shopping cart would then be only $1,900).
In the remainder of this document, the prefix ex1 stands for the fictitious namespace of this example: http://example.com/2009/prd2#.
This section specifies the syntax and semantics of the condition language of RIF-PRD.
The RIF-PRD condition language specification depends on Section Constants, Symbol Spaces, and Datatypes, in the RIF data types and builtins specification [RIF-DTB].
The alphabet of the RIF-PRD condition language consists of:
For the sake of readability and simplicity, this specification introduces a notation for these constructs. The notation is not intended to be a concrete syntax, so it leaves out many details. The only concrete syntax for RIF-PRD is the XML syntax.
RIF-PRD supports externally defined functions only (including the built-in functions specified in [RIF-DTB]). RIF-PRD, unlike RIF-BLD, does not support uninterpreted function symbols (sometimes called logically defined functions).
RIF-PRD supports a form of negation. Neither RIF-Core nor RIF-BLD support negation, because logic rule languages use many different and incompatible kinds of negation. See also the RIF framework for logic dialects [RIF-FLD].
The most basic construct in the RIF-PRD condition language is the term. RIF-PRD defines several kinds of term: constants, variables, lists and positional terms.
Definition (Term).
To emphasize interoperability with RIF-BLD, positional terms may also be written: External(t(t1...tn)).
Example 2.1.
Atomic formulas are the basic tests of the RIF-PRD condition language.
Definition (Atomic formula). An atomic formula can have several different forms and is defined as follows:
Class membership, subclass, and frame atomic formulas are used to represent classifications, class hierarchies and object-attribute-value relations.
Externally defined atomic formulas are used, in particular, for representing built-in predicates.
In the RIF-BLD specification, as is common practice in logic languages, atomic formulas are also called terms.
Example 2.2.
Composite truth-valued constructs are called formulas, in RIF-PRD.
Note that terms (constants, variables, lists and functions) are not formulas.
More general formulas are constructed out of atomic formulas with the help of logical connectives.
Definition (Condition formula). A condition formula can have several different forms and is defined as follows:
In the definition of a formula, the component formulas φ and φi are said to be subformulas of the respective condition formulas that are built using these components.
Example 2.3.
And( ?customer # ex1:Customer ?customer[ex1:status->"New"] Exists ?shoppingCart ?item ( And ( ?customer[ex1:shoppingCart->?shoppingCart] ?shoppingCart[ex1:containsItem->?item] ?item # ex1:Widget) ) ) )
☐
The function Var, that maps a term, an atomic formula or a condition formula to the set of its free variables is defined as follows:
Definition (Ground formula). A condition formula φ is a ground formula if and only if Varφ = {} and φ does not contain any existential subformula. ☐
In other words, a ground formula does not contain any variable term.
Not all formulas are well-formed in RIF-PRD: it is required that no constant appear in more than one context. What this means precisely is explained below.
The set of all constant symbols, Const, is partitioned into the following subsets:
As seen from the following definitions, these subsets are not specified explicitly but, rather, are inferred from the occurrences of the symbols.
Definition (Context of a symbol).
The context of an occurrence of a symbol, s∈Const, in a formula, φ, is determined as follows:
Definition (Well-formed formula). A formula φ is well-formed iff:
Definition (RIF-PRD condition language). The RIF-PRD condition language consists of the set of all well-formed formulas. ☐
This section specifies the semantics of the condition formulas in a RIF-PRD document.
Informally, a condition formula is evaluated with respect to a state of facts and it is satisfied, or true, if and only if:
The semantics is specified in terms of matching substitutions in the sections below. The specification makes no assumption regarding how matching substitutions are determined. In particular, it does not require from well-formed condition formulas that they can be evaluated using pattern matching only. However, RIF-PRD requires safeness from well-formed rules, which implies that all the variables in the left-hand side can be bound by pattern matching.
For compatibility with other RIF specifications (in particular, RIF data types and built-ins [RIF-DTB] and RIF RDF and OWL compatibility [RIF-RDF-OWL]), and to make explicit the interoperability with RIF logic dialects (in particular RIF Core [RIF-Core] and RIF-BLD [RIF-BLD]), the semantics of RIF-PRD condition formulas is also specified using model theory, in appendix Model theoretic semantics of RIF-PRD condition formulas.
The two specifications are equivalent and normative.
Let Term be the set of the terms in the RIF-PRD condition language (as defined in section Terms).
Definition (Substitution). A substitution is a finitely non-identical assignment of terms to variables; i.e., a function σ from Var to Term such that the set {x ∈ Var | x ≠ σ(x)} is finite. This set is called the domain of σ and denoted by Dom(σ). Such a substitution is also written as a set such as σ = {ti/xi}i=1..n where Dom(σ) = {xi}i=1..n and σ(xi) = ti, i = 1..n. ☐
Definition (Ground Substitution). A ground substitution is a substitution σ that assigns only ground terms to the variables in Dom(σ): ∀ x ∈ Dom(σ), Var(σ(x)) = ∅ ☐
Because RIF-PRD covers only externally defined interpreted functions, a ground functional term can always be replaced by its value. As a consequence, a ground substitution can always be restricted, without loss of generality, to assign only constants to the variable in its domain. In the remainder of this document, it will always be assumed that a ground substitution assigns only constants to the variables in its domain.
If t is a term or a condition formula, and if σ is a ground substitution such that Var(t) ∈ Dom(σ), σ(t) denotes the ground term or the ground condition formula obtained by substituting, in t:
Definition (Matching substitution). Let ψ be a RIF-PRD condition formula; let σ be a ground substitution such that Var(ψ) ⊆ Dom(σ); and let Φ be a set of ground RIF-PRD atomic formulas.
We say that the ground substitution σ matches ψ to Φ if and only if one of the following is true:
We define, now, what it means for a state of the fact base to satisfy a condition formula. The satisfaction of condition formulas in a state of the fact base provides formal underpinning to the operational semantics of rule sets interchanged using RIF-PRD.
Definition (State of the fact base). A state of the fact base, wΦ, is associated to every set of ground atomic formulas, Φ, that satisfies, at least, the following conditions, for all triple of constants c1, c2, c3:
We say that wΦ is represented by Φ; or, equivalently, by the conjunction of all the ground atomic formulas in Φ. ☐
Each ground atomic formula in Φ represents a single fact, and, often, the ground atomic formulas, themselves, are called facts, as well.
Definition (Condition satisfaction). A RIF-PRD condition formula ψ is satisfied in a state of the fact base, w, if and only if w is represented by a set of ground atomic formulas Φ, and there is a ground substitution σ that matches ψ to Φ. ☐
Alternative, but equivalent, definitions of a state of the fact base and of the satisfaction of a condition are given in the appendix Model theoretic semantics of RIF-PRD condition formulas: they provide the formal link between the model theory of RIF-PRD condition formulas and the operational semantics of RIF-PRD documents.
This section specifies the syntax and semantics of the RIF-PRD action language. The conclusion of a production rule is often called the action part, the then part, or the right-hand side, or RHS.
The RIF-PRD action language is used to add, delete and modify facts in the fact base. As a rule interchange format, RIF-PRD does not make any assumption regarding the nature of the data sources that the producer or the consumer of a RIF-PRD document uses (e.g. a rule engine's working memory, an external data base, etc). As a consequence, the syntax of the actions that RIF-PRD supports are defined with respect to the RIF-PRD condition formulas that represent the facts that the actions affect. In the same way, the semantics of the actions is specified in terms of how their execution affects the evaluation of rule conditions.
The alphabet of the RIF-PRD action language includes symbols to denote:
Atomic action constructs take constructs from the RIF-PRD condition language as their arguments.
Definition (Atomic action). An atomic action can have several different forms and is defined as follows:
Definition (Ground atomic action). An atomic action with target t is a ground atomic action if and only if Var(t) = ∅. ☐
Example 3.1.
The action block is the top level construct to represent the conclusions of RIF-PRD rules. An action block contains a non-empty sequence of atomic actions. It may also include action variable declarations.
The action variable declaration construct is used to declare variables that are local to the action block, called action variables, and to assign them a value within the action block.
Definition (Action variable declaration). An action variable declaration is a pair, (v p) made of an action variable, v, and an action variable binding (or, simply, binding), p, where p has one of two forms:
Definition (Action block). If (v1 p1), ..., (vn pn), n ≥ 0, are action variable declarations, and if a1, ..., am, m ≥ 1, are atomic actions, then Do((v1 p1) ... (vn pn) a1 ... am) denotes an action block. ☐
Example 3.2. In the following action block, a local variable ?oldValue is bound to a value of the attribute value of the object bound to the variable ?shoppingCart. The ?oldValue is then used to compute a new value, and the Modify action is used to overwrite the old value with the new value in the fact base:
Do( (?oldValue ?shoppingCart[ex1:value->?oldValue]) Modify( ?shoppingCart[ex1:value->func:numeric-multiply(?oldValue 0.90)] ) )
☐
Not all action blocks are well-formed in RIF-PRD:
The notion of well-formedness, already defined for condition formulas, is extended to atomic actions, action variable declarations and action blocks.
Definition (Well-formed atomic action). An atomic action α is well-formed if and only if one of the following is true:
Definition (Well-formed action variable declaration). An action variable declaration (?v p) is well-formed if and only if one of the following is true:
For the definition of a well-formed action block, the function Var(f), that has been defined for condition formulas, is extended to atomic actions and frame object declarations as follows:
Definition (Well-formed action block). An action block is well-formed if and only if all of the following are true:
Definition (RIF-PRD action language). The RIF-PRD action language consists of the set of all the well-formed action blocks. ☐
This section specifies the semantics of the atomic actions in a RIF-PRD document.
The effect of the ground atomic actions in the RIF-PRD action language is to modify the state of the fact base, in such a way that it changes the set of conditions that are satisfied before and after each atomic action is performed.
As a consequence, the semantics of the ground atomic actions in the RIF-PRD action language determines a relation, called the RIF-PRD transition relation: →RIF-PRD ⊆ W × L × W, where W denotes the set of all the states of the fact base, and where L denotes the set of all the ground atomic actions in the RIF-PRD action language.
Individual states of the fact base are represented by sets of ground atomic formulas (Section Satisfaction of a condition). In the following, the operational semantics of RIF-PRD atomic actions, rules, and rule sets is specified by describing the changes they induce in the fact base.
Definition (RIF-PRD transition relation). The semantics of RIF-PRD atomic actions is specified by the transition relation →RIF-PRD ⊆ W × L × W. (w, α, w') ∈ →RIF-PRD if and only if w ∈ W, w' ∈ W, α is a ground atomic action, and one of the following is true:
Rule 1 says that all the condition formulas that were satisfied before an assertion will be satisfied after, and that, in addition, the condition formulas that are satisfied by the asserted ground formula will be satisfied after the assertion. No other condition formula will be satisfied after the execution of the action.
Rule 2 says that all the condition formulas that were satisfied before a retraction will be satisfied after, except if they are satisfied only by the retracted fact. No other condition formula will be satisfied after the execution of the action.
Rule 3 says that all the condition formulas that were satisfied before the removal of a frame object will be satisfied after, except if they are satisfied only by one of the frame or membership formulas about the removed object or a conjunction of such formulas. No other condition formula will be satisfied after the execution of the action.
Rule 4 says that all the condition formulas that were satisfied before the modification of a frame object will be satisfied after, except if they are satisfied only by one of the frame formulas about the modified slot of the modified object, with the exception of the frame that is asserted as the target of the action, or a conjunction of such formulas. No other condition formula will be satisfied after the execution of the action.
Rule 5 says that all the condition formulas that were satisfied before the execution of an action builtin will be satisfied after. No other condition formula will be satisfied after the execution of the action.
Example 3.3. Assume an initial state of the fact base that is represented by the following set, w0, of ground atomic formulas, where _c1, _v1 and _s1 denote individuals and where ex1:Customer, ex1:Voucher and ex1:ShoppingCart represent classes:
This section specifies the syntax and semantics of RIF-PRD rules and rule sets.
The alphabet of the RIF-PRD rule language includes the alphabets of the RIF-PRD condition language and the RIF-PRD action language and adds symbols for:
Definition (Rule). A rule can be one of:
Example 4.1. The Gold rule, from the running example: A "Silver" customer with a shopping cart worth at least $2,000 is awarded the "Gold" status, can be represented using the following rule with variable declaration:
Forall ?customer such that And( ?customer # ex1:Customer ?customer[ex1:status->"Silver"] ) (Forall ?shoppingCart such that And( ?shoppingCart # ex1:ShoppingCart ?customer[ex1:shoppingCart->?shoppingCart] ) (If Exists ?value (And( ?shoppingCart[ex1:value->?value] pred:numeric-greater-than-or-equal(?value 2000)) Then Do( Modify( ?customer[ex1:status->"Gold"] ) ) )
☐
The function Var(f), that has been defined for condition formulas and extended to actions, is further extended to rules, as follows:
As was already mentioned in the Overview, production rules have an operational semantics that can be described in terms of matching rules against states of the fact base, selecting rule instances to be executed, and executing rule instances' actions to transition to new states of the fact base.
When production rules are interchanged, the intended rule instance selection strategy, often called the conflict resolution strategy, needs to be interchanged along with the rules. In RIF-PRD, the group construct is used to group sets of rules and to associate them with a conflict resolution strategy. Many production rule systems use priorities associated with rules as part of their conflict resolution strategy. In RIF-PRD, the group is also used to carry the priority information that may be associated with the interchanged rules.
Definition (Group). A group consists of a, possibly empty, set of rules and groups, associated with a resolution conflict strategy and, a priority. If strategy is an IRI that identifies a conflict resolution strategy, if priority is an integer, and if each rgj, 0 ≤ j ≤ n, is either a rule or a group, then any of the following represents a group:
If a conflict resolution strategy is not explicitly attached to a group, the strategy defaults to rif:forwardChaining (specified below, in section Conflict resolution). ☐
The definitions in this section are unchanged from the definitions in the section Safeness in [RIF-Core], except for the definition of RIF-PRD rule safeness, that is extended from the definition of RIF-Core rule safeness. The definitions are reproduced for the reader's convenience.
Intuitively, safeness of rules guarantees that all the variables in a rule can be bound, using pattern matching only, before they are used, in a test or in an action.
To define safeness, we need to define, first, the notion of binding patterns for externally defined functions and predicates, as well as under what conditions variables are considered bound.
Definition (Binding pattern). (from [RIF-Core]) Binding patterns for externally defined functions and predicates are lists of the form (p1, ..., pn), such that pi=b or pi=u, for 1 ≤ i ≤ n: b stands for a "bound" and u stands for an "unbound" argument. ☐
Each external function or predicate has an associated list of valid binding patterns. We define here the binding patterns valid for the functions and predicates defined in [RIF-DTB].
Every function or predicate f defined in [RIF-DTB] has a valid binding pattern for each of its schemas with only the symbol b such that its length is the number of arguments in the schema. In addition,
The functions and predicates defined in [RIF-DTB] have no other valid binding patterns.
To keep the definitions concise and intuitive, boundedness and safeness are defined, in [RIF-Core], for condition formulas in disjunctive normal form, that can be existentially quantified themselves, but that contain, otherwise, no existential sub-formula. The definitions apply to any valid RIF-Core condition formula, because they can always, in principle, be put in that form, by applying the following syntactic transforms, in sequence:
In RIF-PRD, the definitions apply to conditions formulas in the same form as in [RIF-Core], with the exception that, in the disjunctive normal form, negated sub-formulas can be atomic formulas or existential formulas: in the latter case, the existentially quantified formula must be, itself, in disjunctive normal form, and contain no further existential sub-formulas. The definitions apply to any valid RIF-PRD condition formula, because they can always, in principle, be put in that form, by applying the above syntactic transform, modified as follows to take negation into account:
Definition (Boundedness). (from [RIF-Core]) An external term External(f(t1,...,tn)) is bound in a condition formula, if and only if f has a valid binding pattern (p1, ..., pn) and, for all j, 1 ≤ j ≤ n, such that pj=b, tj is bound in the formula.
A variable, v, is bound in an atomic formula, a, if and only if
A variable, v, is bound in a conjunction formula, f = And(c1...cn), n ≥ 1, if and only if, either
A variable, v, is bound in a disjunction formula, if and only if v is bound in every disjunct where it occurs;
A variable, v, is bound in an existential formula, Exists v1,...,vn (f'), n ≥ 1, if and only if v is bound in f'. ☐
Notice that the variables, v1,...,vn, that are existentially quantified in an existential formula f = Exists v1,...,vn (f'), are bound in any formula, F, that contains f as a sub-formula, if and only if they are bound in f, since they do not exist outside of f.
Definition (Variable safeness). (from [RIF-Core]) A variable, v, is safe in a condition formula, f, if and only if
Notice that the two definitions, above, are not extended for negation and, followingly, that an universally quantified (rule) variable is never bound or safe in a condition formula as a consequence of occurring in a negative formula.
The definition of rule safeness is replaced by the following one, that extends the one for RIF-Core rules.
Definition (RIF-PRD rule safeness). A RIF-PRD rule, r, is safe if and only if
Definition (Group safeness). (from [RIF-Core]) A group, Group (s1...sn), n ≥ 0, is safe if and only if
If f is a rule, Var(f) is the set of the free variables in f.
Definition (Well-formed rule). A rule, r, is a well-formed rule if and only if either
Definition (Well-formed group). A group is well-formed group if and only if it is safe and it contains only well-formed groups, g1...gn, n ≥ 0, and well-formed rules, r1...rm, m ≥ 0, such that Var(ri) = ∅ for all i, 0 ≤ i ≤ m. ☐
The set of the well-formed groups contains all the production rule sets that can be meaningfully interchanged using RIF-PRD.
As mentioned in the Overview, the description of a production rule system as a transition system is used to specify the semantics of production rules and rule sets interchanged using RIF-PRD.
The intuition of describing a production rule system as a transition system is that, given a set of production rules RS and a fact base w0, the rules in RS that are satisfied, in some sense, in w0 determine an action a1, whose execution results in a new fact base w1; the rules in RS that are satisfied in w1 determine an action a2 to execute in w1, and so on, until the system reaches a final state and stops. The result is the fact base wn when the system stops.
Example 4.2. The Rif Shop, Inc. is a rif-raf retail chain, with brick and mortar shops all over the world and virtual storefronts in many on-line shops. The Rif Shop, Inc. maintains its customer fidelity management policies in the form of production rule sets. The customer management department uses RIF-PRD to publish rule sets to all the shops and licensees so that everyone uses the latest version of the rules, even though several different rule engines are in use (in fact, some of the smallest shops actually run the rules by hand).
Here is a small rule set that governs discounts and customer status updates at checkout time (to keep the example short, this is a subset of the rules described in the running example):
(* ex1:CheckoutRuleset *) Group rif:forwardChaining ( (* ex1:GoldRule *) Group 10 ( Forall ?customer such that (And( ?customer # ex1:Customer ?customer[ex1:status->"Silver"] ) ) (Forall ?shoppingCart such that (?customer[ex1:shoppingCart->?shoppingCart]) (If Exists ?value (And( ?shoppingCart[ex1:value->?value] pred:numeric-greater-than-or-equal(?value 2000)) Then Do( Modify( ?customer[ex1:status->"Gold"] ) ) ) ) (* ex1:DiscountRule *) Group ( Forall ?customer such that (And( ?customer # ex1:Customer ) ) (If Or (?customer[ex1:status->"Silver"] ?customer[ex1:status->"Gold"] ) Then Do( (?s ?customer[ex1:shoppingCart->?s]) (?v ?s[ex1:value->?v]) Modify( ?s[ex1:value->func:numeric-multiply(?v 0.95)] ) ) ) )
To see how the rule set works, consider the case of a shop where the checkout processing of customer John is about to start. The initial state of the fact base can be represented as follows:
w0 = {_john#ex1:Customer _john[ex1:status->"Silver"] _s1#ex1:ShoppingCart _john[ex1:shoppingCart->_s1] _s1[ex1:value->2000]}
When instantiated against w0, the first pattern in the "Gold rule", And( ?customer#ex1:Customer ?customer[ex1:status->"Silver"] ), yields the single matching substitution: {(_john/?customer)}. The second pattern in the same rule also yields a single matching substitution: {(_john/?customer)(_s1/?shoppingCart)}, for which the existential condition is satisfied.
Likewise, the instantiation of the "Discount rule" yields a single matching substitution that satisfies the condition: {(_john/?customer)}. The conflict set is:
{ex1:GoldRule/{(_john/?customer)(_s1/?shoppingCart)}, ex1:DiscountRule/{(_john/?customer)}}
The instance ex1:GoldRule/{(_john/?customer)(_s1/?shoppingCart)} is selected because of its higher priority. The ground atomic action: Modify(_john[ex1:status->"Gold"]), is executed, resulting in a new state of the fact base, represented as follows:
w1 = {_john#ex1:Customer _john[ex1:status->"Gold"] _s1#ex1:ShoppingCart _john[ex1:shoppingCart->_s1] _s1[ex1:value->2000]}
In the next cycle, there is no substitution for the rule variable ?customer that matches the pattern to the state of the fact base, and the only matching rule instance is: ex1:DiscountRule/{(_john/?customer)}, which is selected for execution. The action variables ?s and ?v are bound, based on the state of the fact base, to _s1 and 200, respectively, and the ground atomic action, Modify(_s1[ex1:value->1900]), is executed, resulting in a new state of the fact base:
w2 = {_john#ex1:Customer _john[ex1:status->"Gold"] _s1#ex1:ShoppingCart _john[ex1:shoppingCart->_s1] _s1[ex1:value->1900]}
In w2, the only matching rule instance is, again: ex1:DiscountRule/{(_john/?customer)}. However, that same instance has already been selected and the corresponding action has been executed. Nothing has changed in the state of the fact base that would justify that the rule instance be selected gain. The principle of refraction applies, and the rule instance is removed from consideration.
This leaves the conflict set empty, and the system, having detected a final state, stops.
The result of the execution of the system is w2. ☐
Formally, a production rule system is defined as a labeled terminal transition system (e.g. PLO04), for the purpose of specifying the semantics of a RIF-PRD rule or group of rules.
Definition (labeled terminal transition system): A labeled terminal transition system is a structure {C, L, →, T}, where
For many purposes, a representation of the states of the fact base is an appropriate representation of the states of a production rule system seen as a transition system. However, the most widely used conflict resolution strategies require information about the history of the system, in particular with respect to the rule instances that have been selected for execution in previous states. Therefore, each state of the transition system used to represent a production rule system must keep a memory of the previous states and the rule instances that where selected and triggered the transition in those states.
To avoid confusion between the states of the fact base and the states of the transition system, the latter will be called production rule system states.
Definition (Production rule system state). A production rule system state (or, simply, a system state), s, is characterized by
Here, a rule instance is defined as the result of the substitution of constants for all the rule variables in a rule.
In the following, we will write previous(s) = NIL to denote that a system state s is the initial state.
Let R denote the set of all the rules in the rule language under consideration.
Definition (Rule instance). Given a rule, r ∈ R, and a ground substitution, σ, such that CVar(r) ⊆ Dom(σ), where CVar(r) denotes the set of the rule variables in r, the result, ri = σ(r), of the substitution of the constant σ(?x) for each variable ?x ∈ CVar(r) is a rule instance (or, simply, an instance) of r. ☐
Given a rule instance ri, let rule(ri) identify the rule from which ri is derived by substitution of constants for the rule variables, and let substitution(ri) denote the substitution by which ri is derived from rule(ri).
In the following, two rule instances ri1 and ri2 of a same rule r will be considered different if and only if substitution(ri1) and substitution(ri2) substitute a different constant for at least one of the rule variables in CVar(r).
In the definition of a production rule system state, a rule instance, ri, is said to match a state of a fact base, w, if its defining substitution, substitution(ri), matches the RIF-PRD condition formula that represents the condition of the instantiated rule, rule(ri), to the set of ground atomic formulas that represents the state of facts w.
Let W denote the set of all the possible states of a fact base.
Definition (Matching rule instance). Given a rule instance, ri, and a state of the fact base, w ∈ W, ri is said to match w if and only if one of the following is true:
Definition (Conflict set). Given a rule set, RS ⊆ R, and a system state, s, the conflict set determined by RS in s is the set, conflictSet(RS, s) of all the different instances of the rules in RS that match the state of the fact base, facts(s) ∈ W. ☐
The rule instances that are in the conflict set are, sometimes, said to be fireable.
In each non-final state, s, of a production rule system, a subset, picked(s), of the rule instances in the conflict set is selected and ordered; their action parts are instantiated, and the resulting sequence of ground atomic actions is executed. This is sometimes called: firing the selected instances.
Definition (Action instance). Given a system state, s, given a rule instance, ri, of a rule in a rule set, RS, and given the action block in the action part of the rule rule(ri): Do((v1 p1)...(vn pn) a1...am), n ≥ 0, m ≥ 1, where the (v1 p1), 0 ≤ i ≤ n, represent the action variable declarations and the aj, 1 ≤ j ≤ m, represent the sequence of atomic actions in the action block; if ri is a matching instance in the conflict set determined by RS in system state s: ri ∈ conflictSet(RS, s), the substitution σ = substitution(ri) is extended to the action variables v1...vn, n ≥ 0, in the following way:
The sequence of ground atomic actions that is the result of substituting a constant for each variable in the atomic actions of the action block of the rule instance, ri, according to the extended substitution, is the action instance associated to ri. ☐
Let actions(ri) denote the action instance that is associated to a rule instance ri. By extension, given an ordered set of rule instances, ori, actions(ori) denotes the sequence of ground atomic actions that is the concatenation, preserving the order in ori, of the action instances associated to the rule instances in ori.
All the elements that are required to define a production rule system as a labeled terminal transition system have now been defined.
Definition (RIF-PRD Production Rule System). A RIF-PRD production rule system is defined as a labeled terminal transition system PRS = {S, A, →PRS, T}, where :
Intuitively, the first condition in the definition of the transition relation →PRS states that a production rule system can transition from one system state to another only if the state of facts in the latter system state can be reached from the state of facts in the former by performing a sequence of ground atomic actions supported by RIF-PRD, according to the semantics of the atomic actions.
The second condition states that the allowed paths out of any given system state are determined only by how rule instances are picked for execution, from the conflict set, by the conflict resolution strategy.
Given a rule set RS ⊆ R, the associated conflict resolution strategy, LS, and halting test, H, and an initial state of the fact base, w ∈ W, the input function to a RIF-PRD production rule system is defined as:The execution of a rule set, RS, in a state, w, of a fact base, may result in zero, one or more final state of the fact base, w' = facts(s'), depending on the conflict resolution strategy and the set of final system states.
Therefore, the behavior of a RIF-PRD production rule system also depends on:
The process of selecting one or more rule instances from the conflict set for firing is often called: conflict resolution.
In RIF-PRD the conflict resolution algorithm (or conflict resolution strategy) that is intended for a set of rules is denoted by a keyword or a set of keywords that is attached to the rule set. In this version of the RIF-PRD specification, a single conflict resolution strategy is specified normatively: it is denoted by the keyword rif:forwardChaining (a constant of type rif:IRI), for it accounts for a common conflict resolution strategy used in most forward-chaining production rule systems. That conflict resolution strategy selects a single rule instance for execution.
Future versions of the RIF-PRD specification may specify normatively the intended conflict resolution strategies to be attached to additional keywords. In addition, RIF-PRD documents may include non-standard keywords: it is the responsibility of the producers and consumers of such document to agree on the intended conflict resolution strategies that are denoted by such non-standard keywords. Future or non-standard conflict resolution strategies may select an ordered set of rule instances for execution, instead of a single one: the functions picked and actions, in the previous section, have been defined to take this case into account.
Conflict resolution strategy: rif:forwardChaining
Most existing production rule systems implement conflict resolution algorithms that are a combination of the following elements (under these or other, idiosyncratic names; and possibly combined with additional, idiosyncratic rules):
Many existing production rule systems implement also some kind of fire the most specific rule first strategy, in combination with the above. However, whereas they agree on the definition of refraction and the priority or recency ordering, existing production rule systems vary widely on the precise definition of the specificity ordering. As a consequence, rule instance specificity was not included in the basic conflict resolution strategy that RIF-PRD specifies normatively.
The RIF-PRD keyword rif:forwardChaining denotes the common conflict resolution strategy that can be summarized as follows: given a conflict set
As specified earlier, picked(s) denotes the ordered list of the rule instances that were picked in a system state, s. Under the conflict resolution strategy denoted by rif:forwardChaining, for any given system state, s, the list denoted by picked(s) contains a single rule instance.
Given a system state, s, a rule set, RS, and a rule instance, ri ∈ conflictSet(RS, s), let recency(ri, s) denote the number of system states before s, in which ri has been continuously a matching instance: if s is the current system state, recency(ri, s) provides a measure of the recency of the rule instance ri. recency(ri, s) is specified recursively as follows:
In the same way, given a rule instance, ri, and a system state, s, let lastPicked(ri, s) denote the number of system states before s, since ri has been last fired. lastPicked(ri, s) is specified recursively as follows:
Given a rule instance, ri, let priority(ri) denote the priority that is associated to rule(ri), or zero, if no priority is associated to rule(ri). If rule(ri) is inside nested Groups, priority(ri) denotes the priority that is associated with the innermost Group to which a priority is explicitly associated, or zero.
Example 4.3. Consider the following RIF-PRD document:
Document ( Prefix( ex2 <http://example.com/2009/prd3#> ) (* ex2:ExampleRuleSet *) Group ( (* ex2:Rule_1 *) Forall ... (* ex2:HighPriorityRules *) Group 10 ( (* ex2:Rule_2 *) Forall ... (* ex2:Rule_3 *) Group 9 (Forall ... ) ) (* ex2:NoPriorityRules *) Group ( (* ex2:Rule_4 *) Forall ... (* ex2:Rule_5 *) Forall ... ) )
No conflict resolution strategy is identified explicitly, so the default strategy rif:forwardChaining is used.
Because the ex2:ExampleRuleSet group does not specify a priority, the default priority 0 is used. Rule 1, not being in any other group, inherits its priority, 0, from the top-level group.
Rule 2 inherits its priority, 10, from the enclosing group, identified as ex2:HighPriorityRules. Rule 3 specifies its own, lower, priority: 9.
Since neither Rule 4 nor Rule 5 specify a priority, they inherit their priority from the enclosing group ex2:NoPriorityRules, which does not specify one either, and, thus, they inherit 0 from the top-level group, ex2:ExampleRuleSet. ☐
Given a set of rule instances, cs, the conflict resolution strategy rif:forwardChaining can now be described with the help of four rules, where ri and ri' are rule instances:
The refraction rule removes the instances that have been in the conflict set in all the system states at least since they were last fired; the priority rule removes the instances such that there is at least one instance with a higher priority; the recency rule removes the instances such that there is at least one instance that is more recent; and the tie-break rule keeps one rule from the set.
To select the singleton rule instance, picked(s), to be fired in a system state, s, given a rule set, RS, the conflict resolution strategy denoted by the keyword rif:forwardChaining consists of the following sequence of steps:
Example 4.4. Consider, from example 4.2, the conflict set that the rule set ex1:CheckoutRuleset determines in the system state, s2, that corresponds to the state w2 = facts(s2) of the fact base, and use it to initialize the set of rule instance considered for firing, picked(s2):
conflictSet(ex1:CheckoutRuleset, s2) = { ex1:DiscountRule/{(_john/?customer)} } = picked(s2)
The single rule instance in the conflict set, ri = ex1:DiscountRule/{(_john/?customer)}, did already belong to the conflict sets in the two previous states, conflictSet(ex1:CheckoutRuleset, s1) and conflictSet(ex1:CheckoutRuleset, s0); so that its recency in s2 is: recency(ri, s2) = 3.
On the other hand, that rule instance was fired in system state s1: picked(s1) = (ex1:DiscountRule/{(_john/?customer)}); so that, in s2, it has been last fired one cycle before: lastPicked(ri, s2) = 1.
Therefore, lastPicked(ri, s2) < recency(ri, s2), and ri is removed from picked(s2) by refraction, leaving picked(s2) empty. ☐
By default, a system state is final, given a rule set, RS, and a conflict resolution strategy, LS, if there is no rule instance available for firing after application of the conflict resolution strategy.
For the conflict resolution strategy identified by the RIF-PRD keyword rif:forwardChaining, a system state, s, is final given a rule set, RS if and only if the remaining conflict set is empty after application of the refraction rule to all the rule instances in conflictSet(RS, s). In particular, all the system states, s, such that conflictSet(RS, s) = ∅ are final.
This section specifies the structure of a RIF-PRD document and its semantics when it includes import directives.
In addition to the language of conditions, actions, and rules, RIF-PRD provides a construct to denote the import of a RIF or non-RIF document. Import enables the modular interchange of RIF documents, and the interchange of combinations of multiple RIF and non-RIF documents.
Definition (Import directive). An import directive consists of:
RIF-PRD gives meaning to one-argument import directives only. Such directives can be used to import other RIF-PRD and RIF-Core documents. Two-argument import directives are provided to enable import of other types of documents, and their semantics is covered by other specifications. For example, the syntax and semantics of the import of RDF and OWL documents, and their combination with a RIF document, is specified in [RIF-RDF-OWL].
Definition (RIF-PRD document). A RIF-PRD document consists of zero or more import directives, and zero or one group. ☐
Definition (Imported document). A document is said to be directly imported by a RIF document, D, if and only if it is identified by the locator IRI in an import directive in D. A document is said to be imported by a RIF document, D, if it is directly imported by D, or if it is imported, directly or not, by a RIF document that is directly imported by D. ☐
Definition (Document safeness). (from [RIF-Core]) A document is safe if and only if it
Definition (Conflict resolution strategy associated with a document). A conflict resolution strategy is associated with a RIF-PRD document, D, if and only if
Definition (Well-formed RIF-PRD document). A RIF-PRD document, D, is well-formed if and only if it satisfies all the following conditions:
The last condition in the above definition makes the intent behind the rif:local constants clear: occurrences of such constants in different documents can be interpreted differently even if they have the same name. Therefore, each document can choose the names for the rif:local constants freely and without regard to the names of such constants used in the imported documents.
The semantics of a well-formed RIF-PRD document that contains no import directive is the semantics of the rule set that is represented by the top-level group in the document, evaluated with the conflict resolution strategy that is associated to the document, and the default halting test, as specified above, in section Halting test.
The semantics of a well-formed RIF-PRD document, D, that imports the well-formed RIF-PRD documents D1, ..., Dn, n ≥ 1, is the semantics of the rule set that is the union of the rule sets represented by the top-level groups in D and the imported documents, with the rif:local constants renamed to ensure that the same symbol does not occur in two different component rule sets, and evaluated with the conflict resolution strategy that is associated to the document, and the default halting test.
In addition to externally specified functions and predicates, and in particular, in addition to the functions and predicates built-ins defined in [RIF-DTB], RIF-PRD supports externally specified actions, and defines action built-ins.
The syntax and semantics of action built-ins are specified like for the other buit-ins, as described in the section Syntax and Semantics of Built-ins in [RIF-DTB]. However, their formal semantics is trivial: action built-ins behave like predicates that are always true, since action built-ins, in RIF-PRD, MUST NOT affect the semantics of the rules.
Although they must not affect the semantics of the rules, action built-ins may have other side effects.
RIF action built-ins are defined in the namespace: http://www.w3.org/2007/rif-builtin-action#. In this document, we will use the prefix: act: to denote the RIF action built-ins namespace.
(?arg; act:print(?arg))
The value space of the single argument is xs:string.
When s belongs to its domain, Itruth ο IExternal( ?arg; act:print(?arg) )(s) = t.
If an argument value is outside of its domain, the truth value of the function is left unspecified.
The value of the argument MUST be printed to an output stream, to be determined by the user implementation.
RIF-PRD conformance is described partially in terms of semantics-preserving transformations.
The intuitive idea is that, for any initial state of facts, the conformant consumer of a conformant RIF-PRD document must reach at least one of the final state of facts intended by the conformant producer of the document, and that it must never reach any final state of facts that was not intended by the producer. That is:
Let Τ be a set of datatypes and symbol spaces that includes the datatypes specified in [RIF-DTB] and the symbol spaces rif:iri and rif:local. Suppose also that Ε is a set of external predicates and functions that includes the built-ins listed in [RIF-DTB] and in the section Built-in actions. We say that a rule r is a RIF-PRDΤ,Ε rule if and only if
Suppose, further, that C is a set of conflict resolution strategies that includes the one specified in section Conflict resolution, and that H is a set of halting tests that includes the one specified in section Halting test: we say that a rule set , R, is a RIF-PRDΤ,Ε,C,H rule set if and only if
Given a RIF-PRDΤ,Ε,C,H rule set, R, an initial state of the fact base, w, a conflict resolution strategy c ∈ C and a halting test h ∈ H, let FR,w,c,h denote the set of all the sets, f, of RIF-PRD ground atomic formulas that represent final states of the fact base, w' , according to the operational semantics of a RIF-PRD production rule system, that is: f ∈ FR,w,c,h if and only if there is a state, s' , of the system, such that Eval(R, c, h, w) →*PRS s' and w' = facts(s') and f is a representation of w' .
In addition, given a rule language, L, a rule set expressed in L, RL, a conflict resolution strategy, c, a halting test, h, and an initial state of the fact base, w, let FL,RL, c, h, w denote the set of all the formulas in L that represent a final state of the fact base that an L processor can possibly reach.
Definition (Semantics preserving mapping).
Definition (RIF-PRD conformance).
In addition, conformant RIF-PRD producers and consumers SHOULD preserve annotations.
Feature At Risk #3: Strictness Requirement
Note: This feature is "at risk" and may be altered or removed from this specification based on feedback. If you have concerns about this or information which may be useful in our eventual decision, please tell us at public-rif-comments@w3.org. See the full list of features "at risk" in RIF.
The two preceding clauses are features AT RISK. In particular, the "strictness" requirement is under discussion.
[RIF-Core] is specified as a specialization of RIF-PRD: all valid [RIF-Core] documents are valid RIF-PRD documents and must be accepted by any conformant RIF-PRD consumer.
Conversely, it is desirable that any valid RIF-PRD document that uses only abstract syntax that is defined in [RIF-Core] be a valid [RIF-Core] document as well. For some abstract constructs that are defined in both RIF-Core and RIF-PRD, RIF-PRD defines alternative XML syntax that is not valid RIF-Core XML syntax. For example, an action block that contains no action variable declaration and only assert atomic actions can be expressed in RIF-PRD using the XML elements Do or And. Only the latter option is valid RIF-Core XML syntax.
To maximize interoperability with RIF-Core and its non-RIF-PRD extensions, a conformant RIF-PRD consumer SHOULD produce valid [RIF-Core] documents whenever possible. Specifically, a conformant RIF-PRD producer SHOULD use only valid [RIF-Core] XML syntax to serialize a rule set that satisfies all of the following:
When processing a rule set that satisfies all the above conditions, a RIF-PRD producer is guaranteed to produce a valid [RIF-Core] XML document by applying the following rules recursively:
Example 7.1. Consider the following rule, R, derived from the Gold rule, in the running example, to have only assertions in the action part:
R: Forall ?customer such that (And( ?customer # ex1:Customer ?customer[status->"Silver"] ) ) (Forall ?shoppingCart such that (?customer[shoppingCart->?shoppingCart]) (If Exists ?value (And( ?shoppingCart[value->?value] pred:numeric-greater-than-or-equal(?value 2000)) Then Do( Assert(ex1:Foo(?customer)) Assert(ex1:Bar(?shoppingCart)) ) ) )
The serialization of R in the following RIF-Core conformant XML form does not impacts its semantics (see example 8.12 for another valid RIF-PRD XML serialization, that is not RIF-Core conformant):
<Forall> <declare><Var>?customer</Var></declare> <declare><Var>?shoppingCart</Var></declare> <formula> <Implies> <if> <And> <formula> <!-- first pattern --> <And> <formula><Member> ... </Member></formula> <formula><Frame> ... </Frame></formula> </And> </formula> <formula> <!-- second pattern --> <Member> ... </Member> </formula> <formula> <!-- original existential condition --> ... </formula> </And> </if> <then> <And> <formula> <!-- serialization of ex1:Foo(?customer) --> ... </formula> <formula> <!-- serialization of ex1:Bar(?shoppingCart) --> ... </formula> </then> </Implies> </formula> </Forall>
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This section specifies the concrete XML syntax of RIF-PRD. The concrete syntax is derived from the abstract syntax defined in sections 2.1, 3.1 and 4.1 using simple mappings. The semantics of the concrete syntax is the same as the semantics of the abstract syntax.
Throughout this document, the xsd: prefix stands for the XML Schema namespace URI http://www.w3.org/2001/XMLSchema#, the rdf: prefix stands for http://www.w3.org/1999/02/22-rdf-syntax-ns#, and rif: stands for the URI of the RIF namespace, http://www.w3.org/2007/rif#.
Syntax such as xsd:string should be understood as a compact URI (CURIE) -- a macro that expands to a concatenation of the character sequence denoted by the prefix xsd and the string string. The compact URI notation is used for brevity only, and xsd:string should be understood, in this document, as an abbreviation for http://www.w3.org/2001/XMLSchema#string.
The XML syntax of RIF-PRD is specified for each component as a pseudo-schema, as part of the description of the component. The pseudo-schemas use BNF-style conventions for attributes and elements: "?" denotes optionality (i.e. zero or one occurrences), "*" denotes zero or more occurrences, "+" one or more occurrences, "[" and "]" are used to form groups, and "|" represents choice. Attributes are conventionally assigned a value which corresponds to their type, as defined in the normative schema. Elements are conventionally assigned a value which is the name of the syntactic class of their content, as defined in the normative schema.
<!-- sample pseudo-schema --> <defined_element required_attribute_of_type_string="xs:string" optional_attribute_of_type_int="xs:int"? > <required_element /> <optional_element />? <one_or_more_of_these_elements />+ [ <choice_1 /> | <choice_2 /> ]* </defined_element>
Three kinds of syntactic components are used to specify RIF-PRD:
This section specifies the XML constructs that are used in RIF-PRD to serialize condition formulas.
The TERM class of constructs is used to serialize terms, be they simple terms, that is, constants and variables; lists; or positional terms, the latter being, per the definition of a well-formed formula, representations of externally defined functions.
As an abstract class, TERM is not associated with specific XML markup in RIF-PRD instance documents.
[ Const | Var | List | External ]
In RIF, the Const element is used to serialize a constant.
The Const element has a required type attribute and an optional xml:lang attribute:
The content of the Const element is the constant's literal, which can be any Unicode character string.
<Const type=rif:iri [xml:lang=xsd:language]? > Any Unicode string </Const>
Example 8.1.
a. A constant with built-in type xsd:integer and value 2,000:
<Const type="xsd:integer">2000</Const>
b. The Customer class, in the running example, is identified by a constant of type rif:iri, in the namespace http://example.com/2009/prd2#:
<Const type="rif:iri"> http://example.com/2009/prd2#Customer </Const>
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In RIF, the Var element is used to serialize a variable.
The content of the Var element is the variable's name, serialized as an Unicode character string.
<Var> any Unicode string </Var>
In RIF, the List element is used to serialize a list.
The List element contains either zero or more TERMs (without variables) that serialise the elements of the list. The order of the sub-elements is significant and MUST be preserved.
<List> GROUNDTERM* </List>
Example 8.2.
<List> <Const type="xsd:string> New </Const> <Const type="xsd:string> Bronze </Const> <Const type="xsd:string> Silver </Const> <Const type="xsd:string> Gold </Const> </List>
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As a TERM, the External element is used to serialize a positional term. In RIF-PRD, a positional term represents always a call to an externally defined function, e.g. a built-in, a user-defined function, a query to an external data source, etc.
The External element contains one content element, which in turn contains one Expr element that contains one op element, followed zero or one args element:
<External> <content> <Expr> <op> Const </op> <args ordered="yes"> TERM+ </args>? </Expr> </content> </External>
Example 8.3. The example shows one way to serialize, in RIF-PRD, the product of a variable named ?value and the xsd:decimal value 0.9, where the operation conforms to the specification of the built-in func:numeric-multiply, as specified in [RIF-DTB].
RIF built-in functions are associated with the namespace http://www.w3.org/2007/rif-builtin-function#.
<External> <content> <Expr> <op> <Const type="rif:iri"> http://www.w3.org/2007/rif-builtin-function#numeric-multiply </Const> </op> <args ordered="yes"> <Var> ?value </Var> <Const type="xsd:decimal"> 0.9 </Const> </args> </Expr> </content> </External>
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The ATOMIC class is used to serialize atomic formulas: positional atoms, equality, membership and subclass atomic formulas, frame atomic formulas and externally defined atomic formulas.
As an abstract class, ATOMIC is not associated with specific XML markup in RIF-PRD instance documents.
[ Atom | Equal | Member | Subclass | Frame | External ]
In RIF, the Atom element is used to serialize a positional atomic formula.
The Atom element contains one op element, followed by zero or one args element:
<Atom> <op> Const </op> <args ordered="yes"> TERM+ </args>? </Atom>
Example 8.4. The example shows the RIF XML serialization of the positional atom ex1:gold(?customer), where the predicate symbol gold is defined in the example namespace http://example.com/2009/prd2#.
<Atom> <op> <Const type="rif:iri"> http://example.com/2009/prd2#gold </Const> </op> <args ordered="yes"> <Var> ?customer </Var> </args> </Atom>
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In RIF, the Equal element is used to serialize equality atomic formulas.
The Equal element must contain one left sub-element and one right sub-element. The content of the left and right elements must be a construct from the TERM abstract class, that serialize the terms of the equality. The order of the sub-elements is not significant.
<Equal> <left> TERM </left> <right> TERM </right> </Equal>
In RIF, the Member element is used to serialize membership atomic formulas.
The Member element contains two required sub-elements:
<Member> <instance> TERM </instance> <class> TERM </class> </Member>
Example 8.5. The example shows the RIF XML serialization of class membership atom that tests whether a variable named ?customer belongs to a class identified by the name Customer in the namespace http://example.com/2009/prd2#
<Member> <instance> <Var> ?customer </Var> </instance> <class> <Const type="rif:iri"> http://example.com/2009/prd2#Customer </Const> </class> </Member>
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In RIF, the Subclass element is used to serialize subclass atomic formulas.
The Subclass element contains two required sub-elements:
<Subclass> <sub> TERM </sub> <super> TERM </super> </Subclass>
In RIF, the Frame element is used to serialize frame atomic formulas.
Accordingly, a Frame element must contain:
<Frame> <object> TERM </object> <slot ordered="yes"> TERM TERM </slot>* </Frame>
Example 8.6. The example shows the RIF XML serialization of an expression that states that the object denoted by the variable ?customer has the value denoted by the string "Gold" for the property identified by the symbol status that is defined in the example namespace http://example.com/2009/prd2#
<Frame> <object> <Var> ?customer </Var> </object> <slot ordered="yes"> <Const type="rif:iri"> http://example.com/2009/prd2#status </Const> <Const type="xsd:string> Gold </Const> </slot> </Frame>
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In RIF-PRD, the External element is also used to serialize an externally defined atomic formula, in addition to serializing externally defined functions.
When it is an ATOMIC (as opposed to a TERM; that is, in particular, when it appears in a place where an ATOMIC is expected, and not a TERM), the External element contains one content element that contains one Atom element. The Atom element serializes the externally defined atom properly said:
The op Const in the Atom element must be a symbol of type rif:iri that must uniquely identify the externally defined predicate to be applied to the args TERMs.
<External> <content> Atom </content> </External>
Example 8.7. The example below shows the RIF XML serialization of an externally defined atomic formula that tests whether the value denoted by the variable named ?value is greater than or equal to the integer value 2000, where the test is intended to behave like the built-in predicate pred:numeric-greater-than-or-equal as specified in [RIF-DTB]:
RIF built-in predicates are associated with the namespace http://www.w3.org/2007/rif-builtin-predicate#.
<External> <content> <Atom> <op> <Const type="rif:iri"> http://www.w3.org/2007/rif-builtin-predicate#numeric-greater-than-or-equal </Const> </op> <args ordered="yes"> <Var> ?value </Var> <Const type="xsd:integer"> 2000 </Const> </args> </Atom> </content> </External>
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The FORMULA class is used to serialize condition formulas, that is, atomic formulas, conjunctions, disjunctions, negations and existentials.
As an abstract class, FORMULA is not associated with specific XML markup in RIF-PRD instance documents.
[ ATOMIC | And | Or | INeg | Exists ]
An atomic formula is serialized using a single ATOMIC statement. See specification of ATOMIC, above.
A conjunction is serialized using the And element.
The And element contains zero or more formula sub-elements, each containing an element of the FORMULA group, that serializes one of the conjuncts.
<And> <formula> FORMULA </formula>* </And>
A disjunction is serialized using the Or element.
The Or element contains zero or more formula sub-elements, each containing an element of the FORMULA group, that serializes one of the disjuncts.
<Or> <formula> FORMULA </formula>* </Or>
The kind of negation that is used in RIF-PRD is serialized using the INeg element.
The Negate element contains exactly one formula sub-element. The formula element contains an element of the FORMULA group, that serializes the negated statement.
<INeg> <formula> FORMULA </formula> </INeg>
An existentially quantified formula is serialized using the Exists element.
The Exists element contains:
<Exists> <declare> Var </declare>+ <formula> FORMULA </formula> </Exists>
Example 8.8. The example shows the RIF XML serialization of a condition on the existence of a value greater than or equal to 2.000, in the Gold rule of the running example, as represented in example 4.2.
<Exists> <declare> <Var> ?value </Var> </declare> <formula> <And> <Frame> <object> <Var> ?shoppingCart </Var> </object> <slot ordered="yes"> <Const type="rif:iri"> http://example.com/2009/prd2#value </Const> <Var> ?value </Var> </slot> </Frame> <External> <content> <Atom> <op> <Const type="rif:iri"> http://www.w3.org/2007/rif-builtin-predicate#numeric-greater-than-or-equal </Const> </op> <args ordered="yes"> <Var> ?value </Var> <Const type="xsd:integer"> 2000 </Const> </args> </Atom> </content> </External> </And> </formula> </Exists>
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This section specifies the XML syntax that is used to serialize the action part of a rule supported by RIF-PRD.
The ATOMIC_ACTION class of elements is used to serialize the atomic actions: assert, retract, modify and execute.
As an abstract class, ATOMIC_ACTION is not associated with specific XML markup in RIF-PRD instance documents.
[ Assert | Retract | Modify | Execute ]
An atomic assertion action is serialized using the Assert element.
The Assert element has one target sub-element that contains an Atom, a Frame or a Member element that represents the target of the action.
<Assert> <target> [ Atom | Frame | Member ] </target> </Assert>
The Retract construct is used to serialize retract atomic actions.
The Retract element has one target sub-element that contains an Atom, a Frame, or a TERM construct that represents the target of the action.
<Retract> <target> [ Atom | Frame | TERM ] </target> </Retract>
An atomic modification is serialized using the Modify element.
The Modify element has one target sub-element that contains one Frame that represents the target of the action.
<Modify> <target> Frame </target> </Modify>
Example 8.9. The example shows the RIF XML representation of the action that updates the status of a customer, in the Gold rule, in the running example, as represented in example 4.2: Modify(?customer[status->"Gold"])
<Modify> <target> <Frame> <object> <Var> ?customer </Var> </object> <slot ordered="yes"> <Const type="rif:iri"> http://example.com/2009/prd2#status </Const> <Const type="xsd:string"> Gold </Const> </slot> </Frame> </target> </Modify>
☐
The execution of an externally defined action is serialized using the Execute element.
The Execute element has one target sub-element that contains an Atom, that represents the externally defined action to be executed.
The op Const in the Atom element must be a symbol of type rif:iri that must uniquely identify the externally defined action to be applied to the args TERMs.
<Execute> <target> Atom </target> </Execute>
Example 8.10. The example shows the RIF XML serialization of the message printing action, in the Unknonw status rule, in the running example, using the act:print action built-in.
The namespace for RIF-PRD action built-ins is http://www.w3.org/2007/rif-builtin-action#.
<Execute> <target> <Atom> <op> <Constant type="rif:iri"> http://www.w3.org/2007/rif-builtin-action#print </Const> </op> <args ordered="yes"> <External> <content> <Expr> <op> <Constant type="rif:iri"> http://www.w3.org/2007/rif-builtin-function#concat </Const> </op> <args ordered="yes"> <Const type="xsd:string> New customer: </Const> ?customer </args> </Expr> </content> </External> </args> </Atom> </target> </Execute>
☐
The ACTION_BLOCK class of constructs is used to represent the conclusion, or action part, of a production rule serialized using RIF-PRD.
If action variables are declared in the action part of a rule, or if some atomic actions are not assertions, the conclusion must be serialized as a full action block, using the Do element. However, simple action blocks that contain only one or more assert actions SHOULD be serialized like the conclusions of logic rules using RIF-Core or RIF-BLD, that is, as a single asserted Atom or Frame, or as a conjunction of the asserted facts, using the And element.
In the latter case, to conform with the definition of an action block well-formedness, the formulas that serialize the individual conjuncts MUST be atomic Atoms and/or Frames.
As an abstract class, ACTION_BLOCK is not associated with specific XML markup in RIF-PRD instance documents.
[ Do | And | Atom | Frame ]
The New element is used to serialize the construct used to create a new frame identifer, in an action variable declaration.
The New element is always empty.
<New />
An action block is serialized using the Do element.
A Do element contains:
<Do> <actionVar ordered="yes"> Var [ New | Frame ] </actionVar>* <actions ordered="yes"> ATOMIC_ACTION+ </actions> </Do>
Example 8.11. The example shows the RIF XML serialization of an action block that asserts that a customer gets a new $5 voucher.
<Do> <actionVar ordered="yes"> <Var>?voucher</Var> <New /> </actionVar> <actions ordered="yes"> <Assert> <target> <Member> <instance><Var>?voucher</Var></instance> <class> <Const type="rif:iri">http://example.com/2009/prd2#Voucher</Const> </class> </Member> </target> </Assert> <Assert> <target> <Frame> <object><Var>?voucher</Var></object> <slot ordered="yes"> <Const type="rif:iri">http://example.com/2009/prd2#value</Const> <Const type="xsd:integer">5</Const> </slot> </Frame> </target> </Assert> <Assert> <target> <Frame> <object><Var>?customer</Var></object> <slot ordered="yes"> <Const type="rif:iri">http://example.com/2009/prd2#voucher</Const> <Var>?voucher</Var> </slot> </Frame> </target> </Assert> </actions> </Do>
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This section specifies the XML constructs that are used, in RIR-PRD, to serialize rules and groups.
In RIF-PRD, the RULE class of constructs is used to serialize rules, that is, unconditional as well as conditional actions, or rules with bound variables.
As an abstract class, RULE is not associated with specific XML markup in RIF-PRD instance documents.
[ Implies | Forall | ACTION_BLOCK ]
An unconditional action block is serialized, in RIF-PRD XML, using the ACTION_BLOCK class of construct.
Conditional actions are serialized, in RIF-PRD, using the XML element Implies.
The Implies element contains an if sub-element and a then sub-element:
<Implies> <if> FORMULA </if> <then> ACTION_BLOCK </then> </Implies>
The Forall construct is used, in RIF-PRD, to represent rules with bound variables.
The Forall element contains:
<Forall> <declare> Var </declare>+ <pattern> FORMULA </pattern>* <formula> RULE </formula> </Forall>
Example 8.12. The example shows the rule variables declaration part of the Gold rule, from the running example, as represented in example 4.2.
<Forall> <declare><Var>?customer</Var></declare> <pattern> <And> <formula><Member> ... </Member></formula> <formula><Frame> ... </Frame></formula> </And> </pattern> <formula> <Forall> <declare><Var>?shoppingCart</Var></declare> <pattern><Member> ... </Member></pattern> <formula> <Implies> ... </Implies> </formula> </Forall> </formula> </Forall>
☐
The Group construct is used to serialize a group.
The Group element has zero or one behavior sub-element and zero or more sentence sub-elements:
<Group> <behavior> <ConflictResolution> xsd:anyURI </ConflictResolution>? <Priority> -10,000 ≤ xsd:int ≤ 10,000 </Priority>? </behavior>? <sentence> [ RULE | Group ] </sentence>* </Group>
The Import directive is used to serialize the reference to an RDF graph or an OWL ontology to be combined with a RIF document. The Import directive is inherited from [RIF-Core]. Its abstract syntax and its semantics are specified in [RIF-RDF-OWL].
The Import directive contains:
<Import> <location> xsd:anyURI </location> <profile> xsd:anyURI </profile>? </Import>
The Document is the root element of any RIF-PRD instance document.
The Document contains zero or more directive sub-elements, each containing an Import directive, and zero or one payload sub-element, that must contain a Group element.
<Document> <directive> Import </Import>* <payload> Group </payload>? </Document>
The semantics of a document that imports RDF and/or OWL documents is specified in [RIF-RDF-OWL] and [RIF-BLD]. The semantics of a document that does not import other documents is the semantics of the rule set that is serialised by the Group in the document's payload sub-element, if any.
Annotations can be associated with any concrete class element in RIF-PRD: those are the elements with a CamelCase tagname starting with an upper-case character:
CLASSELT = [ TERM | ATOMIC | FORMULA | ATOMIC_ACTION | ACTION_BLOCK | New | RULE | Group | Document | Import ]
An identifier can be associated to any instance element of the abstract CLASSELT class of constructs, as an optional id sub-element that MUST contain a Const of type rif:iri.
Annotations can be included in any instance of a concrete class element using the meta sub-element.
The Frame construct is used to serialize annotations: the content of the Frame's object sub-element identifies the object to which the annotation is associated:, and the Frame's slots represent the annotation properly said as property-value pairs.
If all the annotations are related to the same object, the meta element can contain a single Frame sub-element. If annotations related to several different objects need be serialized, the meta role element can contain an And element with zero or more formula sub-elements, each containing one Frame element, that serializes the annotations relative to one identified object.
<any concrete element in CLASSELT> <id> Const </id>? <meta> [ Frame | <And> <formula> Frame </formula>* </And> ] </meta>? other CLASSELT content </any concrete element in CLASSELT>
Notice that the content of the meta sub-element of an instance of a RIF-PRD class element is not necessarily associated to that same instance element: only the content of the object sub-element of the Frame that represents the annotations specifies what the annotations are about, not where it is included in the instance RIF document.
It is suggested to use Dublin Core, RDFS, and OWL properties for annotations, along the lines of http://www.w3.org/TR/owl-ref/#Annotations -- specifically owl:versionInfo, rdfs:label, rdfs:comment, rdfs:seeAlso, rdfs:isDefinedBy, dc:creator, dc:description, dc:date, and foaf:maker.
Example 8.13. The example shows the structure of the document that contains the runnig example rule set, as represented in example 4.2, including annotations such as rule set and rule names.
<Document> <payload> <Group> <id><Const type="rif:iri">http://example.com/2009/prd2#CheckoutRuleSet</Const></id> <meta> <Frame> <object><Const type="rif:iri">http://example.com/2009/prd2#CheckoutRuleSet</Const></object> <slot ordered="yes"> <Const type="rif:iri">http://dublincore.org/documents/dcmi-namespace/#creator</Const> <Const type="xsd:string>W3C RIF WG</Const> </slot> <slot> <Const type="rif:iri">http://dublincore.org/documents/dcmi-namespace/#description</Const> <Const type="xsd:string">Running example rule set from the RIF-PRD specification</Const> </slot> </Frame> </meta> <behavior> ... </behavior> <sentence> <Group> <id><Const type="rif:iri">http://example.com/2009/prd2#GoldRule</Const></id> <behavior> ... </behavior> <sentence><Forall> ... </Forall></sentence> </Group> </sentence> <sentence> <Group> <id><Const type="rif:iri">http://example.com/2009/prd2#DiscountRule</Const></id> <sentence><Forall> ... </Forall></sentence> </Group> </sentence> </Group> </payload> </Document>
☐
To make it easier to read, a non-normative, lightweight notation was introduced to complement the mathematical English specification of the abstract syntax and the semantics of RIF-PRD. This section specifies a presentation syntax for RIF-PRD, that extends that notation. The presentation syntax is not normative. However, it may help implementers by providing a more succinct overview of RIF-PRD syntax.
The EBNF for the RIF-PRD presentation syntax is given as follows. For convenience of reading we show the entire EBNF in its four parts (rules, conditions, actions, and annotations).
Rule Language:
Document ::= IRIMETA? 'Document' '(' Base? Prefix* Import* Group? ')' Base ::= 'Base' '(' ANGLEBRACKIRI ')' Prefix ::= 'Prefix' '(' Name ANGLEBRACKIRI ')' Import ::= IRIMETA? 'Import' '(' LOCATOR PROFILE? ')' Group ::= IRIMETA? 'Group' Strategy? Priority? '(' (RULE | Group)* ')' Strategy ::= Const Priority ::= Const RULE ::= (IRIMETA? 'Forall' Var+ ' such that ' FORMULA* '(' RULE ')') | CLAUSE CLAUSE ::= Implies | ACTION_BLOCK Implies ::= IRIMETA? 'If' FORMULA 'Then' ACTION_BLOCK LOCATOR ::= ANGLEBRACKIRI PROFILE ::= ANGLEBRACKIRI
Action Language:
ATOMIC_ACTION ::= IRIMETA? (Assert | Retract | Modify | Execute ) Assert ::= 'Assert' '(' Atom | Frame | Member ')' Retract ::= 'Retract' '(' ( Atom | Frame | Var | Const ) ')' Modify ::= 'Modify' '(' Frame ')' Execute ::= 'Execute' '(' Atom ')' ACTION_BLOCK ::= IRIMETA? ('Do (' (IRIMETA? Var (Frame | 'New()'))* ATOMIC_ACTION+ ')' | 'And (' (Atom | Frame)* ')' | Atom | Frame)
Condition Language:
FORMULA ::= IRIMETA? 'And' '(' FORMULA* ')' | IRIMETA? 'Or' '(' FORMULA* ')' | IRIMETA? 'Exists' Var+ '(' FORMULA ')' | ATOMIC | IRIMETA? NEGATEDFORMULA | IRIMETA? Equal | IRIMETA? Member | IRIMETA? Subclass | IRIMETA? 'External' '(' Atom ')' ATOMIC ::= IRIMETA? (Atom | Frame) Atom ::= UNITERM UNITERM ::= Const '(' (TERM* ')' GROUNDUNITERM ::= Const '(' (GROUNDTERM* ')' NEGATEDFORMULA ::= 'Not' '(' FORMULA ')' | 'INeg' '(' FORMULA ')' Equal ::= TERM '=' TERM Member ::= TERM '#' TERM Subclass ::= TERM '##' TERM Frame ::= TERM '[' (TERM '->' TERM)* ']' TERM ::= IRIMETA? (Const | Var | List | 'External' '(' Expr ')') GROUNDTERM ::= IRIMETA? (Const | List | 'External' '(' 'Expr' '(' GROUNDUNITERM ')' ')') Expr ::= UNITERM List ::= 'List' '(' GROUNDTERM* ')' Const ::= '"' UNICODESTRING '"^^' SYMSPACE | CONSTSHORT Name ::= UNICODESTRING Var ::= '?' UNICODESTRING SYMSPACE ::= ANGLEBRACKIRI | CURIE
Annotations:
IRIMETA ::= '(*' IRICONST? (Frame | 'And' '(' Frame* ')')? '*)'
A NEGATEDFORMULA can be written using either Not or INeg. INeg is short for inflationary negation and is preferred over 'Not' to avoid ambiguity about the semantics of the negation.
The RIF-PRD presentation syntax does not commit to any particular vocabulary and permits arbitrary Unicode strings in constant symbols, argument names, and variables. Constant symbols can have this form: "UNICODESTRING"^^SYMSPACE, where SYMSPACE is an ANGLEBRACKIRI or CURIE that represents the identifier of the symbol space of the constant, and UNICODESTRING is a Unicode string from the lexical space of that symbol space. ANGLEBRACKIRI and CURIE are defined in the section Shortcuts for Constants in RIF's Presentation Syntax in [RIF-DTB]. Constant symbols can also have several shortcut forms, which are represented by the non-terminal CONSTSHORT. These shortcuts are also defined in the same section of [RIF-DTB]. One of them is the CURIE shortcut, which is extensively used in the examples in this document. Names are Unicode character sequences. Variables are composed of UNICODESTRING symbols prefixed with a ?-sign.
Example 9.1. Here is the transcription, in the RIF-PRD presentation syntax, of the complete RIF-PRD document corresponding to the running example:
Document( Prefix( ex1 <http://example.com/2009/prd2> ) (* ex1:CheckoutRuleset *) Group rif:forwardChaining ( (* ex1:GoldRule *) Group 10 ( Forall ?customer such that (And( ?customer # ex1:Customer ?customer[status->"Silver"] )) (Forall ?shoppingCart such that (?customer[shoppingCart->?shoppingCart]) (If Exists ?value (And( ?shoppingCart[value->?value] pred:numeric-greater-than-or-equal(?value 2000)) Then Do( Modify( ?customer[status->"Gold"] ) ) ) ) ) ) (* ex1:DiscountRule *) Group ( Forall ?customer such that (And( ?customer # ex1:Customer ) ) (If Or( ?customer[status->"Silver"] ?customer[status->"Gold"] ) Then Do( (?s ?customer[shoppingCart->?s]) (?v ?s[value->?v]) Modify( ?s[value->func:numeric-multiply(?v 0.95)] ) ) ) ) (* ex1:NewCustomerAndWidgetRule *) Group Forall ?customer such that (And( ?customer # ex1:Customer ?customer[status->"New"] ) ) (If Exists ?shoppingCart ?item ( And ( ?customer[shoppingCart->?shoppingCart] ?shoppingCart[containsItem->?item] ?item # ex1:Widget ) ) ) Then Do( (?s ?customer[shoppingCart->?s]) (?val ?s[value->?val]) (?voucher ?customer[voucher->?voucher]) Retract( ?customer[voucher->?voucher] ) Retract( ?voucher ) Modify( ?s[value->func:numeric-multiply(?val 0.90)] ) ) ) ) (* ex1:UnknownStatusRule *) Group ( Forall ?customer such that ( ?customer # ex1:Customer ) (If Not(Exists ?status (And( ?customer[status->?status] External(pred:list-contains(List("New", "Bronze", "Silver", "Gold"), ?status)) ))) Then Do( Execute( act:print(func:concat("New customer: " ?customer)) ) Assert( ?customer[status->"New"] ) ) ) ) ) )
☐
This document is the product of the Rules Interchange Format (RIF) Working Group (see below) whose members deserve recognition for their time and commitment. The editors extend special thanks to Harold Boley and Changhai Ke for their thorough reviews and insightful discussions; the working group chairs, Chris Welty and Christian de Sainte Marie, for their invaluable technical help and inspirational leadership; and W3C staff contact Sandro Hawke, a constant source of ideas, help, and feedback.
The regular attendees at meetings of the Rule Interchange Format (RIF) Working Group at the time of the publication were:
Adrian Paschke (Freie Universitaet Berlin),
Axel Polleres (DERI),
Changhai Ke (ILOG),
Chris Welty (IBM),
Christian de Sainte Marie (ILOG),
Dave Reynolds (HP),
Gary Hallmark (ORACLE),
Harold Boley (NRC),
Hassan Aït-Kaci (ILOG),
Jos de Bruijn (FUB),
Leora Morgenstern (IBM),
Michael Kifer (Stony Brook),
Mike Dean (BBN),
Sandro Hawke (W3C/MIT), and
Stella Mitchell (IBM).
This appendix provides an alternative specification of the Semantics of condition formulas, and it is also normative.
This alternative specification is provided for the convenience of the reader, for compatibility with other RIF specifications, such as [RIF-DTB] and [RIF-RDF-OWL], and to make explicit the interoperability with RIF logic dialects, in particular [RIF-Core] and [RIF-BLD].
The key concept in a model-theoretic semantics of a logic language is the notion of a semantic structure [Enderton01, Mendelson97].
Definition (Semantic structure). A semantic structure, I, is a tuple of the form <TV, DTS, D, Dind, Dfunc, IC, IV, Ilist, Itail, IP, Iframe, Isub, Iisa, I=, Iexternal, Itruth>. Here D is a non-empty set of elements called the Herbrand domain of I, that is, the set of all ground terms which can be formed by using the elements of Const. Dind, Dfunc are nonempty subsets of D. Dind is used to interpret the elements of Const that are individuals and Dfunc is used to interpret the elements of Const that are function symbols. Const denotes the set of all constant symbols and Var the set of all variable symbols. TV denotes the set of truth values that the semantic structure uses and DTS is a set of identifiers for primitive datatypes (please refer to Section Datatypes in the RIF data types and builtins specification [RIF-DTB] for the semantics of datatypes).
As far as the assignment of a standard meaning to formulas in the RIF-PRD condition language is concerned, the set TV of truth values consists of just two values, t and f.
The other components of I are total mappings defined as follows:
This mapping interprets constant symbols. In addition:
This mapping interprets variable symbols.
In addition, these mappings are required to satisfy the following conditions:
Note that the last condition above restricts Itail only when its last argument is in Ilist(Dind), the image of Ilist. If the last argument of Itail is not in Ilist(Dind), then the list is malformed and there are no restrictions on the value of Itail except that it must be in Dind.
This mapping interprets positional terms atoms.
This mapping interprets frame terms. An argument, d ? Dind, to Iframe represents an object and the finite bag {<a1,v1>, ..., <ak,vk>} represents a bag of attribute-value pairs for d. We will see shortly how Iframe is used to determine the truth valuation of frame terms.
Bags (multi-sets) are used here because the order of the attribute/value pairs in a frame is immaterial and pairs may repeat. Such repetitions arise naturally when variables are instantiated with constants. For instance, o[?A->?B ?C->?D] becomes o[a->b a->b] if variables ?A and ?C are instantiated with the symbol a while ?B and ?D are instantiated with b. (We shall see later that o[a->b a->b] is equivalent to o[a->b].)
The operator ## is required to be transitive, i.e., c1 ## c2 and c2 ## c3 must imply c1 ## c3. TThis is ensured by a restriction in Section Interpretation of condition formulas;
The relationships # and ## are required to have the usual property that all members of a subclass are also members of the superclass, i.e., o # cl and cl ## scl must imply o # scl. This is ensured by a restriction in Section Interpretation of condition formulas;
It gives meaning to the equality operator.
It is used to define truth valuation for formulas.
For every external schema, σ, associated with the language, Iexternal(σ) is assumed to be specified externally in some document (hence the name external schema). In particular, if σ is a schema of a RIF built-in predicate, function or action, Iexternal(σ) is specified so that:
For convenience, we also define the following mapping I from terms to D:
The effect of datatypes. The set DTS must include the datatypes described in Section Primitive Datatypes of the RIF data types and builtins specification [RIF-DTB].
The datatype identifiers in DTS impose the following restrictions. Given dt ∈ DTS, let LSdt denote the lexical space of dt, VSdt denote its value space, and Ldt: LSdt → VSdt the lexical-to-value-space mapping (for the definitions of these concepts, see Section Primitive Datatypes of the RIF data types and builtins specification [RIF-DTB]. Then the following must hold:
That is, IC must map the constants of a datatype dt in accordance with Ldt.
RIF-PRD does not impose restrictions on IC for constants in symbol spaces that are not datatypes included in DTS. ☐
This section defines how a semantic structure, I, determines the truth value TValI(φ) of a condition formula, φ.
We define a mapping, TValI, from the set of all condition formulas to TV. Note that the definition implies that TValI(φ) is defined only if the set DTS of the datatypes of I includes all the datatypes mentioned in φ and Iexternal is defined on all externally defined functions and predicates in φ.
Definition (Truth valuation). Truth valuation for well-formed condition formulas in RIF-PRD is determined using the following function, denoted TValI:
We define, now, what it means for a state of the fact base to satisfy a condition formula. The satisfaction of condition formulas in a state of the fact base provides formal underpinning to the operational semantics of rule sets interchanged using RIF-PRD.
Definition (Models). A semantic structure I is a model of a condition formula, φ, written as I |= φ, iff TValI(φ) = t. ☐
Definition (Herbrand interpretation). Given a non-empty set of constants, Const, the Herbrand domain is the set of all the ground terms that can be formed using the elements of Const, and the Herbrand base is the set of all the well-formed ground atomic formulas that can be formed with the elements in the Herbrand domain.
A semantic structure, I, is a Herbrand interpretation, if the set of all the ground formulas which are true with respect to I (that is, of which I is a model), is a subset of the corresponding Herbrand base, BI. ☐
In RIF-PRD, the semantics of condition formulas is defined with respect to semantic structures where the domain, D is the Herbrand domain that is determined by the set of all the constants, Const; that is, with respect to Herbrand interpretations.
Definition (State of the fact base). To every Herbrand interpretation I, we associate a state of the fact base, wI, that is represented by the subset of the Herbrand base that contains all the ground atomic formulas of which I is a model; or, equivalently, by the conjunction of all these ground atomic formulas. ☐
Definition (Condition satisfaction). A RIF-PRD condition formula φ is satisfied in a state of the fact base, wI, if and only if I is a model of φ. ☐
At the syntactic level, the interpretation of the variables by a valuation function IV is realized by a substitution. As a consequence, a ground substitution σ matches a condition formula ψ to a set of ground atomic formulas Φ if and only if σ realizes the valuation function IV of a semantics structure I that is a model of ψ and Φ is a representation of a state of the fact base, wI (as defined above), that is associated to I; that is, if and only if ψ is satisfied in wI (as defined above).
This provides the formal link between the satisfaction of a condition formula, as defined above, and a matching substitution, and, followingly, between the alternative definitions of a state of facts and the satisfaction of a condition, here and in section Semantics of condition formulas.
The RIF-PRD XML Schema is specified as a redefinition and an extension of the RIF-Core XML Schema [RIF-Core].
<?xml version="1.0" encoding="UTF-8"?> <xs:schema targetNamespace="http://www.w3.org/2007/rif#" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xml="http://www.w3.org/XML/1998/namespace" xmlns="http://www.w3.org/2007/rif#" elementFormDefault="qualified"> <xs:import namespace='http://www.w3.org/XML/1998/namespace' schemaLocation='http://www.w3.org/2001/xml.xsd'/> <!-- ================================================== --> <!-- Redefine some elements in the Core Conditions --> <!-- Extension of the choice --> <!-- ================================================== --> <xs:group name="ATOMIC"> <xs:choice> <xs:element ref="Atom"/> <xs:element ref="Frame"/> <xs:element ref="Member"/> <xs:element ref="Equal"/> <xs:element ref="Subclass"/> <!-- Subclass is not in RIF-Core --> <xs:element name="External" type="External-FORMULA.type"/> </xs:choice> </xs:group> <xs:group name="FORMULA"> <xs:choice> <xs:group ref="ATOMIC"/> <xs:element ref="And"/> <xs:element ref="Or"/> <xs:element ref="Exists"/> <xs:element ref="INeg"/> <!-- INeg is nt in RIF-Core --> </xs:choice> </xs:group> <!-- ================================================== --> <!-- Additional elements to the Core Condition schema --> <!-- ================================================== --> <xs:element name="Subclass"> <!-- --> <!-- <Subclass> --> <!-- <sub> TERM </sub> --> <!-- <super> TERM </super> --> <!-- </Subclass> --> <!-- --> <xs:complexType> <xs:sequence> <xs:element name="sub"> <xs:complexType> <xs:group ref="TERM" minOccurs="1" maxOccurs="1"/> </xs:complexType> </xs:element> <xs:element name="super"> <xs:complexType> <xs:group ref="TERM" minOccurs="1" maxOccurs="1"/> </xs:complexType> </xs:element> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="INeg"> <!-- --> <!-- <INeg> --> <!-- <formula> FORMULA </formula> --> <!-- </INeg> --> <!-- --> <xs:complexType> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> <xs:element ref="formula" minOccurs="1" maxOccurs="1"/> </xs:sequence> </xs:complexType> </xs:element> <!-- ============================================ --> <!-- CoreCond.xsd starts here --> <!-- ============================================ --> <xs:complexType name="External-FORMULA.type"> <!-- sensitive to FORMULA (Atom) context--> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> <xs:element name="content" type="content-FORMULA.type"/> </xs:sequence> </xs:complexType> <xs:complexType name="content-FORMULA.type"> <!-- sensitive to FORMULA (Atom) context--> <xs:sequence> <xs:element ref="Atom"/> </xs:sequence> </xs:complexType> <xs:element name="And"> <xs:complexType> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> <xs:element ref="formula" minOccurs="0" maxOccurs="unbounded"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Or"> <xs:complexType> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> <xs:element ref="formula" minOccurs="0" maxOccurs="unbounded"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Exists"> <xs:complexType> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> <xs:element ref="declare" minOccurs="1" maxOccurs="unbounded"/> <xs:element ref="formula"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="formula"> <xs:complexType> <xs:sequence> <xs:group ref="FORMULA"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="declare"> <xs:complexType> <xs:sequence> <xs:element ref="Var"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Atom"> <!-- Atom ::= UNITERM --> <xs:complexType> <xs:sequence> <xs:group ref="UNITERM"/> </xs:sequence> </xs:complexType> </xs:element> <xs:group name="UNITERM"> <!-- UNITERM ::= Const '(' (TERM* ')' --> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> <xs:element ref="op"/> <xs:element name="args" type="args-UNITERM.type" minOccurs="0" maxOccurs="1"/> </xs:sequence> </xs:group> <xs:group name="GROUNDUNITERM"> <!-- sensitive to ground terms GROUNDUNITERM ::= Const '(' (GROUNDTERM* ')' --> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> <xs:element ref="op"/> <xs:element name="args" type="args-GROUNDUNITERM.type" minOccurs="0" maxOccurs="1"/> </xs:sequence> </xs:group> <xs:element name="op"> <xs:complexType> <xs:sequence> <xs:element ref="Const"/> </xs:sequence> </xs:complexType> </xs:element> <xs:complexType name="args-UNITERM.type"> <!-- sensitive to UNITERM (TERM) context--> <xs:sequence> <xs:group ref="TERM" minOccurs="1" maxOccurs="unbounded"/> </xs:sequence> <xs:attribute name="ordered" type="xs:string" fixed="yes"/> </xs:complexType> <xs:complexType name="args-GROUNDUNITERM.type"> <!-- sensitive to GROUNDUNITERM (TERM) context--> <xs:sequence> <xs:group ref="GROUNDTERM" minOccurs="0" maxOccurs="unbounded"/> </xs:sequence> <xs:attribute name="ordered" type="xs:string" fixed="yes"/> </xs:complexType> <xs:element name="Equal"> <!-- Equal ::= TERM '=' ( TERM | IRIMETA? 'External' '(' Expr ')' ) --> <xs:complexType> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> <xs:element ref="left"/> <xs:element ref="right"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="left"> <xs:complexType> <xs:sequence> <xs:group ref="TERM"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="right"> <xs:complexType> <xs:group ref="TERM"/> </xs:complexType> </xs:element> <xs:element name="Member"> <!-- Member ::= TERM '#' TERM --> <xs:complexType> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> <xs:element ref="instance"/> <xs:element ref="class"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="instance"> <xs:complexType> <xs:sequence> <xs:group ref="TERM"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="class"> <xs:complexType> <xs:sequence> <xs:group ref="TERM"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Frame"> <!-- Frame ::= TERM '[' (TERM '->' TERM)* ']' --> <xs:complexType> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> <xs:element ref="object"/> <xs:element name="slot" type="slot-Frame.type" minOccurs="0" maxOccurs="unbounded"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="object"> <xs:complexType> <xs:sequence> <xs:group ref="TERM"/> </xs:sequence> </xs:complexType> </xs:element> <xs:complexType name="slot-Frame.type"> <!-- sensitive to Frame (TERM) context--> <xs:sequence> <xs:group ref="TERM"/> <xs:group ref="TERM"/> </xs:sequence> <xs:attribute name="ordered" type="xs:string" fixed="yes"/> </xs:complexType> <xs:group name="TERM"> <!-- TERM ::= IRIMETA? (Const | Var | External | List ) --> <xs:choice> <xs:element ref="Const"/> <xs:element ref="Var"/> <xs:element name="External" type="External-TERM.type"/> <xs:element ref="List"/> </xs:choice> </xs:group> <xs:group name="GROUNDTERM"> <!-- GROUNDTERM ::= IRIMETA? (Const | List | 'External' '(' 'Expr' '(' GROUNDUNITERM ')' ')') --> <xs:choice> <xs:element ref="Const"/> <xs:element ref="List"/> <xs:element name="External" type="External-GROUNDUNITERM.type"/> </xs:choice> </xs:group> <xs:element name="List"> <!-- List ::= 'List' '(' GROUNDTERM* ')' --> <xs:complexType> <xs:choice minOccurs="0" maxOccurs="unbounded"> <xs:group ref="GROUNDTERM"/> </xs:choice> </xs:complexType> </xs:element> <xs:complexType name="External-TERM.type"> <!-- sensitive to TERM (Expr) context--> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> <xs:element name="content" type="content-TERM.type"/> </xs:sequence> </xs:complexType> <xs:complexType name="External-GROUNDUNITERM.type"> <!-- sensitive to GROUNDTERM (Expr) context--> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> <xs:element name="content" type="content-GROUNDUNITERM.type"/> </xs:sequence> </xs:complexType> <xs:complexType name="content-TERM.type"> <!-- sensitive to TERM (Expr) context--> <xs:sequence> <xs:element ref="Expr"/> </xs:sequence> </xs:complexType> <xs:complexType name="content-GROUNDUNITERM.type"> <!-- sensitive to GROUNDTERM (Expr) context--> <xs:sequence> <xs:element name="Expr" type="content-GROUNDEXPR.type"/> </xs:sequence> </xs:complexType> <xs:complexType name="content-GROUNDEXPR.type"> <!-- sensitive to GROUNDEXPR context--> <xs:sequence> <xs:group ref="GROUNDUNITERM"/> </xs:sequence> </xs:complexType> <xs:element name="Expr"> <!-- Expr ::= Const '(' (TERM | IRIMETA? 'External' '(' Expr ')')* ')' --> <xs:complexType> <xs:sequence> <xs:element ref="op"/> <xs:element name="args" type="args-Expr.type" minOccurs="0" maxOccurs="1"/> </xs:sequence> </xs:complexType> </xs:element> <xs:complexType name="args-Expr.type"> <!-- sensitive to Expr (TERM) context--> <xs:choice minOccurs="1" maxOccurs="unbounded"> <xs:group ref="TERM"/> </xs:choice> <xs:attribute name="ordered" type="xs:string" fixed="yes"/> </xs:complexType> <xs:element name="Const"> <!-- Const ::= '"' UNICODESTRING '"^^' SYMSPACE | CONSTSHORT --> <xs:complexType mixed="true"> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> </xs:sequence> <xs:attribute name="type" type="xs:anyURI" use="required"/> <xs:attribute ref="xml:lang"/> </xs:complexType> </xs:element> <xs:element name="Var"> <!-- Var ::= '?' UNICODESTRING --> <xs:complexType mixed="true"> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> </xs:sequence> </xs:complexType> </xs:element> <xs:group name="IRIMETA"> <!-- IRIMETA ::= '(*' IRICONST? (Frame | 'And' '(' Frame* ')')? '*)' --> <xs:sequence> <xs:element ref="id" minOccurs="0" maxOccurs="1"/> <xs:element ref="meta" minOccurs="0" maxOccurs="1"/> </xs:sequence> </xs:group> <xs:element name="id"> <xs:complexType> <xs:sequence> <xs:element name="Const" type="IRICONST.type"/> <!-- type="&rif;iri" --> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="meta"> <xs:complexType> <xs:choice> <xs:element ref="Frame"/> <xs:element name="And" type="And-meta.type"/> </xs:choice> </xs:complexType> </xs:element> <xs:complexType name="And-meta.type"> <!-- sensitive to meta (Frame) context--> <xs:sequence> <xs:element name="formula" type="formula-meta.type" minOccurs="0" maxOccurs="unbounded"/> </xs:sequence> </xs:complexType> <xs:complexType name="formula-meta.type"> <!-- sensitive to meta (Frame) context--> <xs:sequence> <xs:element ref="Frame"/> </xs:sequence> </xs:complexType> <xs:complexType name="IRICONST.type" mixed="true"> <!-- sensitive to location/id context--> <xs:sequence/> <xs:attribute name="type" type="xs:anyURI" use="required" fixed="http://www.w3.org/2007/rif#iri"/> </xs:complexType> <!-- ============================================ --> <!-- Definition of the actions (not in RIF-Core) --> <!-- ============================================ --> <xs:element name="New"/> <xs:group name="INITIALIZATION"> <xs:choice> <xs:element ref="New"/> <xs:element ref="Frame"/> </xs:choice> </xs:group> <xs:element name="Do"> <!-- --> <!-- <Do> --> <!-- <actionVar ordered="yes"> --> <!-- Var --> <!-- INITIALIZATION --> <!-- </actionVar>* --> <!-- <actions ordered="yes"> --> <!-- ATOMIC_ACTION+ --> <!-- </actions> --> <!-- </Do> --> <!-- --> <xs:complexType> <xs:sequence> <xs:element name="actionVar" minOccurs="0" maxOccurs="unbounded"> <xs:complexType> <xs:sequence> <xs:element ref="Var" minOccurs="1" maxOccurs="1"/> <xs:group ref="INITIALIZATION" minOccurs="1" maxOccurs="1"/> </xs:sequence> <xs:attribute name="ordered" type="xs:string" fixed="yes"/> </xs:complexType> </xs:element> <xs:element name="actions" minOccurs="1" maxOccurs="1"> <xs:complexType> <xs:sequence> <xs:group ref="ATOMIC_ACTION" minOccurs="1" maxOccurs="unbounded"/> </xs:sequence> <xs:attribute name="ordered" type="xs:string" fixed="yes"/> </xs:complexType> </xs:element> </xs:sequence> </xs:complexType> </xs:element> <xs:group name="ATOMIC_ACTION"> <xs:choice> <xs:element ref="Assert"/> <xs:element ref="Retract"/> <xs:element ref="Modify"/> <xs:element ref="Execute"/> </xs:choice> </xs:group> <xs:element name="Assert"> <!-- --> <!-- <Assert> --> <!-- <target> [ Atom --> <!-- | Frame --> <!-- | Member ] --> <!-- </target> --> <!-- </Assert> --> <!-- --> <xs:complexType> <xs:choice> <xs:element name="target" minOccurs="1" maxOccurs="1"> <xs:complexType> <xs:choice> <xs:element ref="Atom"/> <xs:element ref="Frame"/> <xs:element ref="Member"/> </xs:choice> </xs:complexType> </xs:element> </xs:choice> </xs:complexType> </xs:element> <xs:element name="Retract"> <!-- --> <!-- <Assert> --> <!-- <target> [ Atom --> <!-- | Frame --> <!-- | TERM ] --> <!-- </target> --> <!-- </Assert> --> <!-- --> <xs:complexType> <xs:choice> <xs:element name="target" minOccurs="1" maxOccurs="1"> <xs:complexType> <xs:choice> <xs:element ref="Atom"/> <xs:element ref="Frame"/> <xs:group ref="TERM"/> </xs:choice> </xs:complexType> </xs:element> </xs:choice> </xs:complexType> </xs:element> <xs:element name="Modify"> <!-- --> <!-- <Modify> --> <!-- <target> Frame </target> --> <!-- </Modify> --> <!-- --> <xs:complexType> <xs:choice> <xs:element name="target" minOccurs="1" maxOccurs="1"> <xs:complexType> <xs:sequence> <xs:element ref="Frame"/> </xs:sequence> </xs:complexType> </xs:element> </xs:choice> </xs:complexType> </xs:element> <xs:element name="Execute"> <!-- --> <!-- <Execute> --> <!-- <target> Atom </target> --> <!-- </Execute> --> <!-- --> <xs:complexType> <xs:choice> <xs:element name="target" minOccurs="1" maxOccurs="1"> <xs:complexType> <xs:sequence> <xs:element ref="Atom"/> </xs:sequence> </xs:complexType> </xs:element> </xs:choice> </xs:complexType> </xs:element> <!-- ================================================== --> <!-- Redefine Group related Core construct --> <!-- ================================================== --> <xs:complexType name="Group-contents"> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> <xs:element ref="behavior" minOccurs="0" maxOccurs="1"/> <!-- behavior in not in RIF-Core --> <xs:element ref="sentence" minOccurs="0" maxOccurs="unbounded"/> </xs:sequence> </xs:complexType> <!-- ================================================== --> <!-- Group related addition --> <!-- ================================================== --> <xs:element name="behavior"> <!-- --> <!-- <behavior> --> <!-- <ConflictResolution> --> <!-- xsd:anyURI --> <!-- <ConflictResolution>? --> <!-- <Priority> --> <!-- -10,000 ≤ xsd:int ≤ 10,000 --> <!-- </Priority>? --> <!-- </behavior> --> <!-- --> <xs:complexType> <xs:sequence> <xs:element name="ConflictResolution" minOccurs="0" maxOccurs="1" type="xs:anyURI"/> <xs:element name="Priority" minOccurs="0" maxOccurs="1"> <xs:simpleType> <xs:restriction base="xs:int"> <xs:minInclusive value="-10000"/> <xs:maxInclusive value="10000"/> </xs:restriction> </xs:simpleType> </xs:element> </xs:sequence> </xs:complexType> </xs:element> <!-- ================================================== --> <!-- Redefine rule related Core constructs --> <!-- ================================================== --> <xs:group name="RULE"> <!-- RULE ::= (IRIMETA? 'Forall' Var+ '(' CLAUSE ')') | CLAUSE --> <xs:choice> <xs:element name="Forall" type="Forall-premises"/> <xs:group ref="CLAUSE"/> </xs:choice> </xs:group> <xs:complexType name="Forall-premises"> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> <xs:element ref="declare" minOccurs="1" maxOccurs="unbounded"/> <xs:element name="pattern" minOccurs="0" maxOccurs="unbounded"> <xs:complexType> <xs:sequence> <xs:group ref="FORMULA"/> </xs:sequence> </xs:complexType> </xs:element> <!-- different from formula in And, Or and Exists --> <xs:element name="formula"> <xs:complexType> <xs:group ref="RULE"/> </xs:complexType> </xs:element> </xs:sequence> </xs:complexType> <xs:group name="CLAUSE"> <!-- CLAUSE ::= Implies | ACTION_BLOCK --> <xs:choice> <xs:element ref="Implies"/> <xs:group ref="ACTION_BLOCK"/> </xs:choice> </xs:group> <xs:complexType name="then-part"> <xs:group ref="ACTION_BLOCK" minOccurs="1" maxOccurs="1"/> </xs:complexType> <!-- ================================================== --> <!-- Rule related additions --> <!-- ================================================== --> <xs:group name="ACTION_BLOCK"> <!-- ACTION_BLOCK ::= 'Do (' (Var (Frame | 'New'))* ATOMIC_ACTION+ ')' | 'And (' (Atom | Frame)* ')' | Atom | Frame --> <xs:choice> <xs:element ref="Do"/> <xs:element name="And" type="And-then.type"/> <xs:element ref="Atom"/> <xs:element ref="Frame"/> </xs:choice> </xs:group> <!-- ================================================== --> <!-- CoreRule.xsd starts here --> <!-- ================================================== --> <xs:element name="Document"> <!-- Document ::= IRIMETA? 'Document' '(' Base? Prefix* Import* Group? ')' --> <xs:complexType> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> <xs:element ref="directive" minOccurs="0" maxOccurs="unbounded"/> <xs:element ref="payload" minOccurs="0" maxOccurs="1"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="directive"> <!-- Base and Prefix represented directly in XML --> <xs:complexType> <xs:sequence> <xs:element ref="Import"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="payload"> <xs:complexType> <xs:sequence> <xs:element name="Group" type="Group-contents"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Import"> <!-- Import ::= IRIMETA? 'Import' '(' IRICONST PROFILE? ')' --> <xs:complexType> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> <xs:element ref="location"/> <xs:element ref="profile" minOccurs="0" maxOccurs="1"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="location" type="xs:anyURI"/> <xs:element name="profile" type="xs:anyURI"/> <xs:element name="sentence"> <xs:complexType> <xs:choice> <xs:element name="Group" type="Group-contents"/> <xs:group ref="RULE"/> </xs:choice> </xs:complexType> </xs:element> <xs:element name="Implies"> <!-- Implies ::= IRIMETA? ATOMIC ':-' FORMULA --> <xs:complexType> <xs:sequence> <xs:group ref="IRIMETA" minOccurs="0" maxOccurs="1"/> <xs:element ref="if"/> <xs:element name="then" type="then-part"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="if"> <xs:complexType> <xs:sequence> <xs:group ref="FORMULA"/> </xs:sequence> </xs:complexType> </xs:element> <xs:complexType name="And-then.type"> <!-- sensitive to then (And) context--> <xs:sequence> <xs:element name="formula" type="formula-then.type" minOccurs="0" maxOccurs="unbounded"/> </xs:sequence> </xs:complexType> <xs:complexType name="formula-then.type"> <!-- sensitive to then (And) context--> <xs:choice> <xs:element ref="Atom"/> <xs:element ref="Frame"/> </xs:choice> </xs:complexType> </xs:schema>
This appendix summarizes the main changes to this document since the draft of July 3, 2009.