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This document specifies RIF-PRD, a Rule Interchange Format (RIF) dialect to enable the interchange of production rules.
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 5 documents:
The document has been reorganized to expose the abstract syntax, which is intended to support features that are shared with many concrete production rule languages. Each abstract construct is associated with normative semantics and a normative XML concrete syntax.
Also, the definition of the operational semantics of rules and rulesets has been completed by adding a specification of a conflict resolution strategy. This strategy is proposed to be the default for rulesets interchanged using RIF-PRD. The WG is particularly interested in feedback regarding the operational semantics of rules and rulesets.
The Rule Interchange Format (RIF) Working Group seeks public feedback on these Working Drafts. Please send your comments to public-rif-comments@w3.org (public archive). If possible, please offer specific changes to the text that would address your concern. You may also wish to check the Wiki Version of this document for internal-review comments and changes being drafted which may address your concerns.
Publication as a Working Draft 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.
Contents
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This document specifies the production rule dialect of the W3C rule interchange format (RIF-PRD), a standard XML serialization format for many production rule languages.
Production rules are rule statements defined in terms of both individual facts or objects, and groups of facts or classes of objects. They 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 the basic logic dialect of the W3C rule interchange format, RIF-BLD). The then part contains actions, which is different to the conclusion part of logic rules which contains only a logical statement. Actions can add, delete, or modify facts in the knowledge base, and have other side-effects.
Example 1.1. «A customer becomes a "Gold" customer as soon as his cumulative purchases during the current year top $5000»; «Customers that become "Gold" customers must be notified immediately, and a golden customer card will be printed and sent to them within one week»; «For shopping carts worth more than $1000, "Gold" customers receive an additional discount of 10% of the total amount», are all examples of production rules. ☐
As a production rule interchange format, RIF-PRD specifies an abstract syntax that shares most features with many concrete production rule languages, and it associates each abstract construct with normative semantics and a normative XML concrete syntax.
Production rules are statements of programming logic that specify the execution of one or more actions in the case that their conditions are satisfied. Production rules therefore have an operational semantic (formalizing state changes, e.g., on the basis of a state transition system formalism). The OMG Production Rule Representation specification [PRR] summarizes it 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 stransitions result from executing the action part of instantiated rules. When several rules are deemed able to be executed during the rule execution process, a conflict resolution strategy is used to determine the order of rules to execute Sub-section Instance Selection specifies how an intended conflict resolution strategy can be attached to a rule set interchanged with RIF-PRD, and defines a default conflict resolution strategy.
However, as a RIF dialect, RIF-PRD has also been designed to allow interoperability between rule languages over the World Wide Web. In RIF, this is achieved by sharing the same syntax for constructs that have the same semantics across multiple dialects. As a consequence, RIF-PRD shares most of the syntax for rule conditions with RIF-BLD [RIF-BLD], and the semantics associated to the syntactic constructs used for representing the condition part of rules in RIF-PRD is specified, in Section Semantics of condition formulas, in terms of a model theory, as it is in the specification of RIF-BLD as well. In addition to exploiting similarities between the two dialects, it allows them to share the same RIF definitions for data types and built-ins [RIF-DTB].
In the section Operational semantics of actions, the semantics associated with the constructs used to represent the action part of rules in RIF-PRD is specified in terms of a transition relation between successive states of the data source, as defined by the condition formulas that they entail, thus making the link between the model-theoretic semantics of conditions and the operational semantics of rules and rulesets.
The abstract syntax is specified in mathematical english, and the abstract syntactic constructs defined in the sections Abstract Syntax of Conditions, Abstract Syntax of Actions and Abstract Syntax of Rules and Rulesets, are mapped one to one onto the concrete XML syntax in Section XML syntax. A lightweight notation is also defined along with the abstract syntax, to allow for a human-friendlier specification of the semantics. A more complete presentation syntax is specified using an EBNF in Section Presentation Syntax. However, only the XML syntax and the associated semantics are normative. A normative XML schema will also be provided in future versions of the document.
Example 1.2. In RIF-PRD presentation syntax, the first rule in example 1.1. might be represented as follows:
Prefix(ex1 http://example.com/2008/prd#) (* ex1:rule_1 *) Forall ?customer ?purchasesYTD ( If And( ?customer#ex1:Customer ?customer[ex1:purchasesYTD->?purchasesYTD] External(pred:numeric-greater-than(?purchasesYTD 5000))) Then ex1:Gold(?customer) )
The condition languages of RIF-PRD and RIF-BLD have much in common, including much of their semantics. Although their abstract syntax and rule semantics are different, due to the operational nature of the actions in production rules, there is a subset for which they are equivalent: essentially, rules with no negation and no uninterpreted functions in the condition, and with only assertions in the action part. For that subset, the XML syntax is the same, so many XML documents are valid in both dialects and have the same meaning. The correspondence between RIF-PRD and RIF-BLD is detailed in Appendix Compatibility with RIF-BLD.
This document is mostly intended for the designers and developers of RIF-PRD implementations, that is, applications that serialize production rules as RIF-PRD XML (producer applications) and/or that deserialize RIF-PRD XML documents into production rules (consumer applications).
This section specifies the language of the rule conditions that can be serialized using RIF-PRD, by specifying:
Note to the reader: this section depends on Section Constants, Symbol Spaces, and Datatypes of RIF data types and builtins [RIF-DTB].
For a production rule language to be able to interchange rules using RIF-PRD, its alphabet for expressing the condition parts of a rule must, at the abstract syntax level, consist of:
For the sake of readibility and simplicity, this specification introduces a notation for these constructs. That 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.
Notice that the production rule systems for which RIF-PRD aims to provide a common XML serialization use only externally specified functions, e.g. builtins. RIF-BLD specifies, in addition, a construct to denote uninterpreted function symbols, which RIF-PRD does not require: this is one of two differences between the alphabets used in the condition languages of RIF-PRD and RIF-BLD.
The second point of difference is that RIF-PRD does support a form of negation. RIF-BLD does not support negation because logic rule languages use many different kinds of negations, none of them prevalent enough to justify inclusion in the basic logic dialect of RIF (see also the RIF framework for logic dialects).
The most basic construct that can be serialized using RIF-PRD is the term. RIF-PRD provides for the representation and interchange of several kinds of terms: constants, variables, positional terms and terms with named arguments
Definition (Term).
The atomic truth-valued constructs that can be serialized using RIF-PRD are called atomic formulas.
Definition (Atomic formula). An atomic formula can have several different forms and is defined as follows:
Note that not only predicates, but also frame atomic formulas can be externally defined. Therefore, external information sources can be modeled in an object-oriented way via frames.
Editor's Note: Objects are commonly used in PR systems. In this draft, we reuse frame, membership, and subclass formulas (from RIF-BLD) to model objects. We are aware of current limits, such as difficulty expressing datatype and cardinality constraints. Future drafts will address that problem. We are interested in feedback on the merits and limitations of this approach.
Observe that the argument names of frames, p1, ..., pn, are terms and so, as a special case, can be variables. In contrast, atoms with named arguments can use only the symbols from ArgNames to represent their argument names, which can neither be constants from Const nor variables from Var.
Note that atomic formulas are sometimes also called terms, e.g. in the realm of logic languages: the specification of RIF-BLD, in particular, follows that usage. The abstract syntactic elements that are called terms in this specification, are called basic terms in the specification of RIF-BLD.
Composite truth-valued constructs that can be serialized using RIF-PRD are called formulas.
Note that terms (constants, variables and functions) are not formulas.
More general formulas are constructed out of the 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.
The function Var(e) that maps a term, atomic formula or formula e 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.
The specification of RIF-PRD does not assign a standard meaning to all the formulas that can be serialized using its concrete XML syntax: formulas that can be meaningfully serialized are called well-formed. Not all formulas are well-formed with respect to 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 several subsets as follows:
Each predicate and function symbol that take at least one argument has precisely one arity. For positional predicate and function symbols, an arity is a non-negative integer that tells how many arguments the symbol can take. For symbols that take named arguments, an arity is a set {s1 ... sk} of argument names (si ∈ ArgNames) that are allowed for that symbol. Nullary symbols (which take zero arguments) are said to have the arity 0.
An important point is that neither the above partitioning of constant symbols nor the arity are specified explicitly. Instead, the arity of a symbol and its type is determined by the context in which the symbol is used.
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 intended semantics of the condition formulas in a RIF-PRD document.
For compatibility with other RIF specifications (in particular, RIF data types and builtins), and to make the interoperability with RIF logic dialects (in particular RIF Core [RIF-Core] and RIF-BLD), the intended semantics for RIF-PRD condition formulas is specified in terms of a model theory.
Definition (Semantic structure). A semantic structure, I, is a tuple of the form <TV, DTS, D, Dind, Dfunc, IC, IV, IF, Iframe, INF, Isub, Iisa, I=, Iexternal, Itruth>. Here D is a non-empty set of elements called the Herbrand domain of 'I, i.e., 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 of RIF data types and builtins [RIF-DTB] for the semantics of datatypes). The set of all ground (positional|named|frame|external) formulas which can be formed by using the function symbols with the ground terms in the Herbrand domain is the Herbrand base, HB. A semantic structure I is a Herbrand interpretation, IH, if the corresponding subset of HB is the set of all ground formulas which are true with respect to I. ☐
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.
This mapping interprets positional terms and gives meaning to positional predicate function.
This mapping interprets function symbols with named arguments and gives meaning to named argument functions. This is analogous to the interpretation of positional terms with two differences:
This mapping interprets frame terms and gives meaning to frame functions. 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. 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: o[a->b a->b]. 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 and ?B, ?D with 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 or function, Iexternal(σ) is specified in [RIF-DTB] 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 RIF data types and builtins [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 RIF data types and builtins [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. In PRD a semantic structure is represented as a Herbrand interpretation.
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 now define what it means for a set of ground formulas to satisfy a condition formula. The satisfaction of condition formulas by a set of ground formulas provides formal underpinning to the operational semantics of rulesets interchanged using RIF-PRD.
Definition
(State). A state S is a Herbrand Interpretation
IH. ☐
Definition (Condition Satisfaction). A condition formula, φ is satisfied under variable assignment σ in a state S, written as S |= φ[σ], iff TValS(φ[σ]) = t. ☐
At the syntactic level, the interpretation of the variables by a valuation function IV is realized by a substitution. The matching substitution of constants to variables, as defined below, provides the formal link between the model-theoretic semantics of condition formulas and the operational semantics of rule sets in RIF-PRD.
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=0..n where Dom(σ) = {xi}i=0..n and σ(xi) = ti, i = 0..,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)) = ∅ ☐
Notice that since RIF-PRD covers only externally defined interpreted functions, a ground term can always be replaced by a constant. In the remainder of this document, it will always be assumed that a ground substitution assigns only constants to the variables in its domain.
Definition (Matching Substitution). Let ψ be a condition formula, and φ be a set of ground formulas that satisfies ψ. We say that ψ matches φ with substitution σ : Var -> Terms if and only if there is a syntactic interpretation I such that for all ?xi in Var(σ), I(?xi) = I(σ(?xi)). ☐
This section specifies the action part of the rules that can be serialized using RIF-PRD (the conclusion of a production rule is often called the action part, or, simply, the action; the then part, with reference to the if-then form of a rule statement; or the right-hand side, or RHS. In the latter case, the condition is usually called the left-hand side of the rule, or LHS). Specifically, this section specifies:
In production rule systems, the action part of the rules is used, in particular, to add, delete or modify facts in the data source with respect to which the condition of rules are evaluated and the rules instantiated. As a rule interchange format, RIF-PRD does not make any assumption regarding the nature of the data source 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 represents the facts that the actions are intended to affect. In the same way, the semantics of the actions is specified in terms of how the effects of their execution are intended to affect the evaluation of rule condition.
Editor's Note: This version of the draft specifies only a very limited set of basic atomic actions. Future draft will extend that set, in particular to support actions whose effect is not, or not only, to modify the fact base.
For a production rule language to be able to interchange rules using RIF-PRD, its alphabet for expressing the action part of a rule must, at the abstract syntax level, consist of syntactic constructs to denote:
Editor's Note: These actions may seem foreign to a reader who is familiar with typical production rule language actions, such as assert an object, modify/update a field of an object, and retract/remove an object. As noted in Section Atomic formulas, in this draft, objects are modeled using frame, membership, and subclass formulas that are re-used from RIF-BLD and RIF-Core. Therefore, the object-oriented actions are defined to act upon frame, membership, and subclass relations. Mappings from a typical Java-like object model to RIF-PRD maps "instanceof" to membership, "extends" and "implements" to subclass, and object properties/fields to frame slots. To assert an object requires asserting both its class membership and its frame slots. To modify a slot, e.g. change color from red to blue, requires retracting the old frame slot and asserting the new frame slot. Indeed, frame slots are multi-valued and, therefore, merely asserting a frame slot does not overwrite a prior value, it adds to the set of values. Frame slots do not inherently constrain either the datatype or the cardinality of their values. Future drafts will address the issue of object representation in RIF-PRD. We are open to suggestions.
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:
Editor's Note: Whether and under what restrictions, if any, membership and subclass atomic formulas are allowable targets for atomic assert actions is still under discussion in the working group. We welcome feedback on that issue.
Definition (Ground atomic action). An atomic action with target t is a ground atomic action if and only if Var(t) = ∅. ☐
The action block is the top level construct to represent the conclusions of the production rules that can be serialized using RIF-PRD. 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.
Editor's Note: This version of RIF-PRD supports only a limited mechanism to initialize local action variables. Action variables may be bound to newly created frame objects or to slot values of frames. Future versions may support different or more elaborate mechanisms.
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 ... al) denotes an
action block. ☐
The specification fo RIF-PRD does not assign a standard meaning to all the action blocks that can be standardized using its concrete XML syntax. Action blocks that can be meaningfully serialized are called well-formed. The notion of well-formedness, already defined for condition formulas, is extended to atomic actions, action variable declarations and action blocks.
The main restrictions are that one and only one action variable bindings can assign a value to each action variable binding, and that the assertion of a membership atomic formula is meaningful only if for a new frame object.
Definition (Well-formed atomic action). An atomic action 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 is 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 intended semantics of the atomic actions in a RIF-PRD document.
The effect intended 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 intended 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.
Since the satisfaction of condition formulas is defined with respect to the Herbrand interpretation of ground formulas (Section Satisfaction of a condition), we will assume in the following that the states of the fact base are represented by such sets, for the purpose of specifying the intended operational semantics of atomic actions, or rules and of rule sets serialized using RIF-PRD.
Definition (RIF-PRD transition relation). The intended semantics of RIF-PRD atomic actions is completely 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.
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.
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.
This section specifies the rules and rulesets that can be serialized using RIF-PRD, by specifying:
For a production rule language to be able to interchange rules using RIF-PRD, in addition to the RIF-PRD condition and action languages, its alphabet must, at the abstract syntax level, contain syntactic constructs:
Definition (Rule). A rule can be either:
RIF-BLD compatibility. A rule If condition, Then action can be equivalently written action :- condition, that is, using RIF-BLD notation. Indeed, the normative XML syntax is the same for a conditional assertion in RIF-BLD and for a conditional action in RIF-PRD. The use of RIF-BLD notation is especially useful if the condition formula, condition, contains no negation, and if the action block, action, contains only Assert atomic actions. The use of the same notation emphasizes that such a rule has the same semantics in RIF-PRD and RIF-BLD.
Editor's Note: At this stage, the above assertion regarding the equivalence of a specific fragment of RIF-PRD and RIF-BLD is mostly the statement of an objective of the working group. That issue will be addressed more completely in a future version of this document.
To emphasize that equivalence even further, an action block can be written as simply And(φ1 ... φn), if it contains only atomic assert actions: Do(Assert(φ1) ... Assert(φn)), n ≥ 1. If the action block consists of a single atomic assert action: Do(Assert(φ)), then it can be written as simply φ.
Notice that the notation for a rule with bound variables uses the keyword Forall for the same reasons, that is, to emphasize the overlap with RIF-BLD. Indeed, Forall does not indicate the universal quantification of the declared variables, in RIF-PRD, but merely that the execution of the rule must be considered for all their bindings as constrained by the binding patterns. However, when no negation is used in the conditions and only assertions in the actions, the XML serialization of a RIF-PRD rule with bound variables is exactly the same as the XML serialization of a RIF-BLD universally quantified rule, and their semantics coincide.
As was already mentioned in Section 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, need be interchanged along with the rules : in RIF-PRD, the group is the construct that 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 to the interchanged rules.
Definition (Group). If strategy is an IRI that denotes 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 is a group:
The function Var(f), that has been defined for condition formulas and extended to actions, is further extended to rules, as follows:
Definition (Well-formed rule). A rule, r, is a well-formed rule if and only if it contains no free variable, that is, Var(r) = ∅, and either:
Definition (Well-formed group). A well-formed group is either a group that contains only well-formed rules and well-formed groups, or a group that contains no rule or group (an empty group). ☐
The set of the well-formed groups contains all the production rulesets that can be meaningfully interchanged using RIF-PRD.
As already mentioned in Section Overview, the description of a production rule system as a transition system can be used to specify the intended semantics that is associated with production rules and rulesets 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 3.1. Judicael, a chicken and potato farmer, uses a rule based system to decide on the daily grain allowance for each of her chicken. Currently, Judicael's rule base contains one single rule, the chicken and mashed potatoes rule:
(* ex:ChickenAndMashedPotatoes *) Forall ?chicken ?potato ?weight (And(?chicken#ex:Chicken (Exists ?age And(?chicken[ex:age->?age] External(pred:numeric-greater-than(?age, 8))))) And(?potato#ex:Potato ex:owns(?chicken ?potato) (Exists ?weight And(?potato[ex:weight->?weight] External(pred:numeric-greater-than(?weight External(func:numeric-divide(?age 2))))))) If And(External(pred:string-not-equals(External(ex:today()), "Tuesday")) Not(External(ex:foxAlarm()))) Then Do( (?allowance ?chicken[ex:allowance->?allowance]) Execute(ex:mash(?potato)) Retract(?potato) Retract(ex:owns(?chicken ?potato)) Retract(?chicken[ex:allowance->?allowance]) Assert(?chicken[ex:allowance->External(func:numeric-multiply(?allowance 1.1))]))
Judicael has four chickens, Jim, Jack, Joe and Julia, that own three potatoes (BigPotato, SmallPotato, UglyPotato) among them:
That is the initial set of facts w0.
When the rule is applied to w0:
Suppose that Judicael's implementation of today() returns Monday and that the foxAlarm() is false when the Chicken and mashed potatoes rule is applied: the condition is satisfied, and the actions in the conclusion are executed with BigPotato substituted for ?potato, Jim substituted for ?chicken, and 10 substituted for ?allowance. This results in the following changes in the set of facts:
The resulting set of facts w1 is thus:
When the Chicken and mashed potatoes rule in applied to w1, the first pattern still selects {Jim/?chicken, Jack/?chicken, Julia/?chicken} as possible values for variable ?chicken, but the second pattern does not select any possible substitution for the couple (?chicken, ?potato) anymore: the rule cannot be satisfied, and the system, having detected a final state, stops.
The result of the execution of the system is w1. ☐
More precisely, a production rule system is defined as a labeled terminal transition system (e.g. PLO04), for the purpose of specifying the intended 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 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 the 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
In the following, we will write previous(s) = NIL to denote that a system state s is the initial state.
Here, a rule instance is defined as the result of the substitution of constants for all the rule variables in a rule.
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 Var(r) ⊆ Dom(σ), where Var(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 ∈ Var(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 Var(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 ground formula 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, 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, s, 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 is called the conflict set determined by RS in s. ☐
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 they are 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 rules instances are picked from the conflict set for execution by the conflict resolution strategy.
Given a ruleset RS ⊆ R, the associated conflict resolution strategy LS, and an initial state of the fact base, w ∈ W, the input function to a RIF-PRD production rule system is defined as:Therefore, the exact behavior of a RIF-PRD production rule system 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.
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 responsability of the producers and consumers of such document to agree on the intended conflict resolution strategies that are denoted by such non-standard keywords.
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):
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, the list denoted by picked(s) contains a single rule instance, for any given system state, s.
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 an 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:
Finally, 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 explicitely associated, or zero.
Given a conflict set, 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, that is, it removes the refracted instances from the current conflict set; 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, arbitrarily.
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 in the following sequence of steps:
Editor's Note: This section is still under discussion (see ISSUE-65). This version specifies a single, default halting test: future version of this draft may specify additional halting tests, and/or a different default. The Working Group seeks feedback on which halting tests and which combinations of tests should be supported by RIF-PRD and/or required from RIF-PRD implementations; and which halting test should be the default, if any.
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 a common concrete XML syntax to serialize any production rule set written in a language that share the abstract syntax speicifed in section 4.1, provided that its intended semantics agrees with the semantics that is described in section 4.2.
In the following, after the notational conventions are introduced, we specify the RIF-PRD XML constructs that carry a normative semantics with respect to the intended interpretation of the interchanged rules. They are specified with respect to the abstract syntax, and their specification is structured according to the specification of the abstract syntax in sections 2.1, 3.1 and 4.1.
The root element of any RIF XML document, Document and other XML constructs that do not carry a normative semantics with respect to the intended interpretation of the interchanged rules are specified in the last sub-section.
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; or positional terms or terms with named arguments, both 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 | 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 litteral, which can be any Unicode character string.
<Const type=xsd:anyURI [xml:lang=xsd:language]? > Any Unicode string </Const>
\{\{EdNote|text=The case of non-standard data types, that is, of constants that do not belong or cannot be cast in one of RIF builtin types for interchange purposes, is still under discussion in the WG. The WG seeks feedback on whether they should be allowed and why.\}\}
Example 2.1. In each of the examples below, a constant is first described, followed by its serialization in RIF-PRD XML syntax.
a. A constant with builtin type xsd:integer and value 123:
<Const type="xsd:integer">123</Const>
b. A constant which symbol today is defined in Joe the Hen Public's namespace http://example.com/2008/joe#. The type of the constant is rif:iri:
<Const type="rif:iri"> http://example.com/2008/joe#today </Const>
c. A constant with symbol BigPotato that is local to the set of rules where it appears (e.g. a RuleSet specific to Paula's farm). The type of the constant is rif:local:
<Const type="rif:local">BigPotato</Const>
d. A constant with non-builtin type xsd:int and value 123:
<Const type="xsd:int">123</Const>
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>
Example 2.2. The example below shows the XML serialization of a reference to a variable named: ?chicken.
<Var> chicken <Var>
As a TERM, the External element is used to serialize a positional term or a term with named arguments. In RIF-PRD, a positional or a named-argument term represents always a call to an externally specified function, e.g. a builtin, a user-defined function, a query to an external data source...
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 or zero of more slot elements:
<External> <content> <Expr> <op> Const </op> [ <args rif:ordered="yes"> TERM* </args>? | <slot rif:ordered="yes"> <Name> Any Unicode string </Name> TERM <slot>* ] </Expr> </content> </External>
Editor's Note: The slotted, or named arguments form of the External TERM construct is still under discussion (see also ISSUE-68). The working group seeks feedback on whether or not it should be included in PRD.
Example 2.3.
a. The first example below shows one way to serialize, in RIF-PRD, the sum of integer 1 and a variable ?x, where the addition conforms to the specification of the builtin fn:numeric-add.
The prefix fn is associated with the namespace http://www.w3.org/2007/rif-builtin-function#.
<External> <content> <Expr> <op> <Const type="rif:iri"> fn:numeric-add </Const> </op> <args rif:ordered="yes"> <Const type="xsd:integer"> 1 </Const> <Var> x </Var> </args> </Expr> </content> </External>
b. Another example, that shows the RIF XML serialization of a call to the application-specific nullary function today(), which symbol is defined in the example's namespace http://example.com/2008/joe#:
<External> <content> <Expr> <op> <Const type="rif:iri"> http://example.com/2008/joe#today </Const> </op> </Expr> </content> </External>
The ATOMIC class is used to serialize atomic formulas: positional and named-arguments 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 or an atomic formula with named arguments.
The Atom element contains one op element, followed by zero or one args element or zero or more slot arguments:
<Atom> <op> Const </op> [ <args rif:ordered="yes"> TERM* </args>? | <slot rif:ordered="yes"> <Name> Any Unicode string </Name> TERM <slot>* ] </Atom>
Editor's Note: The slotted, or named arguments form of the Atom construct is still under discussion (see also ISSUE-68). The working group seeks feedback on whether or not it should be included in PRD.
Example 2.4. The example below shows the RIF XML serialization of the positional atom owns(?c ?p), where the predicate symbol owns is defined in the example namespace http://example.com/2008/joe#.
<Atom> <op> <Const type="rif:iri"> http://example.com/2008/joe#owns </Const> </op> <args rif:ordered="yes"> <Var> c </Var> <Var> p </Var> </args> </Atom>
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. 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 unordered sub-elements:
<Member> <instance> TERM </instance> <class> TERM </class> </Member>
Example 2.5. The example below shows the RIF XML serialization of a boolean expression that tests whether the individual denoted by the variable ?c is a member of the class Chicken that is defined in the example namespace http://example.com/2008/joe#.
<Member> <instance> <Var> c </Var> </instance> <class> <Const type="rif:iri"> http://example.com/2008/joe#Chicken </Const> </class> </Member>
In RIF, the Subclass element is used to serialize subclass atomic formulas.
The Subclass element contains two unordered 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 rif:ordered="yes"> TERM TERM </slot>* </Frame>
Example 2.6. The example below shows the RIF XML syntax that serializes an expression that states that the object denoted by the variable ?c has the value denoted by the variable ?a for the property Chicken/age that is defined in the example namespace http://example.com/2008/joe#.
<Frame> <object> <Var> c </Var> </object> <slot rif:ordered="yes"> <Const type="rif:iri"> ttp://example.com/2008/joe#Chicken/age </Const> <Var> a </Var> </slot> </Frame>
Editor's Note: The example uses an XPath style for the key. How externally specified data models and their elements should be referenced is still under discussion (see ISSUE-37).
In RIF-PRD, the External element is also used to serialize an externally defined atomic formula.
When it is a 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:
<External> <content> Atom </content> </External>
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. It can be one of the builtin predicates specified for RIF dialects, as listed in section List of RIF Builtin Predicates and Functions of the RIF data types and builtins document, or it can be application specific. In the latter case, it is up to the producers and consumers of RIF-PRD rulesets that reference non-builtin predicates to agree on their semantics.
Example 2.7. The example below shows the RIF XML serialization of an externally defined atomic formula that tests whether the value denoted by the variable named ?a (e.g. the age of a chicken) is greater than the integer value 8, where the test is intended to behave like the builtin predicate op:numeric-greater-than as specified in XQuery 1.0 and XPath 2.0 Functions and Operators.
In the example, the prefix op: is associated with the namespace http://www.w3.org/2007/rif-builtin-predicate#.
<External> <content> <Atom> <op> <Const type="rif:iri"> op:numeric-greater-than </Const> </op> <args rif:ordered="yes"> <Var> ?a </Var> <Const type="xsd:decimal"> 8 </Const> </args> </Atom> </content> </External>
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 | NmNot | 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.
<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.
<Or> <formula> FORMULA </formula>* </Or>
A negation is serialized using the NmNot element.
The NnNot element contains exactly one formula sub-element. The formula element contains an element of the FORMULA group, that serializes the negated statement.
<NmNot> <formula> FORMULA </formula> </NmNot>
Editor's Note: The name of that construct may change, including the tag of the XML element.
An existentially quantified formula is serialized using the Exists element.
The Exists element contains:
<Exists> <declare> Var </declare>+ <formula> FORMULA </formula> </Exists>
Example 2.8. The example below shows the RIF XML serialization of a boolean expression that tests whether the chicken denoted by variable ?c is older than 8 months, by testing the existence of a value, denoted by variable ?a, that is both the age of ?c, as serialized as a Frame element, as in example 2.6, and greater than 8, as serialized as an External ATOMIC, as in example 2.7.
<Exists> <declare> <Var> a </Var> </declare> <formula> <And> <Frame> <object> <Var> c </Var> </object> <slot rif:ordered="yes"> <Const type="rif:iri"> http://example.com/2008/joe#Chicken/age </Const> <Var> a </Var> </slot> </Frame> <External> <content> <Atom> <op> <Const type="rif:iri"> op:numeric-greater-than </Const> </op> <args rif:ordered="yes"> <Var> a </Var> <Const type="xsd:decimal"> 8 </Const> </args> </Atom> </content> </External> </And> </formula> </Exists>
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 and retract.
[ Assert | Retract ]
An atomic assertion action is serialized using the Assert element.
An atom (positional or with named arguments), a frame, a membership atomic formula and a subclass atomic formula can be asserted.
The Assert element has one target sub-element that contains an Atom, a Frame, a Member or a Subclass element that represents the facts to be added on performing the action.
<Assert> <target> [ Atom | Frame | Member | Subclass ] </target> </Assert>
The Retract construct is used to serialize retract atomic actions, that result in removing a fact from the fact base. Only atoms (positional or with named arguments), frames and frame objects can be retracted.
The Retract element has one target sub-element that contains an Atom, a Frame, or a TERM construct that represents the facts or the object to be removed on performing the action.
<Retract> <target> [ Atom | Frame | TERM ] </target> </Retract>
Example 2.10. The example below shows the RIF XML representation of an action that updates the chicken-potato ownership table by removing the predicate that states that the chicken denoted by variable ?c owns the potato denoted by variable ?p. The predicate is represented as in example 2.4.
<Retract> <target> <Atom> <op> <Const type="rif:iri"> http://example.com/2008/joe#owns </Const> </op> <args rif:ordered="yes"> <Var> c </Var> <Var> p </Var> </args> </Atom> </target> </Retract>
The INITIALIZATION class of elements is used to serialized the constructs that specify the initial value assigned an action variable, in an action variable declaration: it can be a new frame identifier or the slot value of a frame.
As an abstract class, INITIALIZATION is not associated with specific XML markup in RIF-PRD instance documents.
[ New | Frame ]
The New element is used to serialize the construct used to create a new frame identifer.
The New element has an instance sub-element that contains a Var, which serializes the action variable intended to be assigned the new frame identifier.
<New> <instance> Var </instance>? </New>
The Frame element is used, with restrictions, to the serialize the construct used to assign an action variable the slot value of a frame.
In that position, a Frame must contain, in addition to its object sub-element, one and only one slot sub-element, that contains a sub-element of the TERM class, serializing the slot name, and a Var sub-element, that serializes the action variable intended to be assigned the slot value.
<Frame> <object> TERM </object> <slot rif:ordered="yes"> TERM Var </slot> </Frame>
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 can be serialized like the conclusions of logic rules using RIF-Core or RIF-BLD, that is, as a single asserted ATOMIC or as a conjunction of the asserted ATOMICs.
As an abstract class, ACTION_BLOCK is not associated with specific XML markup in RIF-PRD instance documents.
[ Do | And | ATOMIC ]
An action block is serialized using the Do element.
A Do element contains:
<Do> <actionVar rif:ordered="yes"> Var INITIALIZATION </actionVar>* <actions rif:ordered="yes"> ATOMIC_ACTION+ </actions> </Do>
Example 2.9. The example below shows the RIF XML representation of an action block that asserts a new 100 decigram potato.
<Do> <actionVar> <Var>p</Var> <New> <instance><Var>p</Var></instance> </New> </actionVar> <actions rif:ordered="yes"> <Assert> <target> <Member> <instance><Var>p</Var></instance> <class> <Const type="rif:iri">http://example.com/2008/joe#Potato</Const> </class> </Member> </target> </Assert> <Assert> <target> <Frame> <object><Var>p</Var></object> <slot rif:ordered="yes"> <Const type="rif:iri">http://example.com/2008/joe#weight</Const> <Const type="xsd:decimal">100</Const> </slot> </Frame> </target> </Assert> </actions> </Do>
An action block that contains only assert atomic actions can be serialized using the And element, for compatibility with RIF-Core and RIF-BLD.
However, the atomic formulas allowed as conjuncts are restricted to atoms (positional or with named arguments), frames, and membership or subclass atomic formulas.
In that position, an And element must contain at least one sub-element.
<And> <formula> [ Atom | Frame | Member | Subclass ] </formula>+ </And>
For compatibility with RIF-Core and RIF-BLD, an action block that contains only a single assert atomic action can be serialzed as the ATOMIC that serializes the target of the assert action.
However, the only atomic formulas allowed in tat position are the ones that are allowed as targets to an atomic assert action: atoms (positional or with named arguments), frames, and membership or subclass atomic formulas.
[ Atom | Frame | Member | Subclass ]
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 optional 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>
Editor's Note: Nested Foralls make explicit the scope of the declared variables, and, thus, impose an order on the evaluation of the pattern and if FORMULAs in a rule. That ordering and the use of patterns to constrain the binding of variables may be of practical significance for some production rule systems, but they are irrelevant with respect to the intended semantics of the rules being interchanged (although they would be relevant if RIF-PRD was to be extended to support some kind of "else" or "case" construct). In addition, RIF-BLD does not allow nested Forall and does not support the association of contraining patterns to declared variables. The working group seeks feedback regarding whether nested Forall and constrainting pattern should be supported in RIF-PRD, to the cost of reducing the interoperability with RIF-BLD.
Example 2.10. The example below shows how the CMP rule extract: "if a chicken owns a potato and ..." could be serialized using a binding pattern FORMULA:
<Forall> <declare><Var>chicken</Var></declare> <formula> <Forall> <declare><Var>potato</Var></declare> <pattern> <External> <content> <Atom> <Const type="rif:iri"> http://example.com/2008/joe#owns </Const> <Args rif:ordered="yes"> <Var>chicken</Var> <Var>potato</Var> </Args> </Atom> </content> </External> </pattern> <formula> ... </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 Document is the root element in a RIF-PRD instance document.
The Document contains zero or one payload sub-element, that must contain a Group element.
<Document> <payload> Group </payload>? </Document>
Metadata 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 | ACTION | RULE | Group | Document ]
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:local or rif:iri.
Metadata can be included in any instance of a concrete class element using the meta sub-element.
The RIF-PRD Frame construct is used to serialize metadata: the content of the Frame's object sub-element identifies the object to which the metadata is associated:, and the Frame's slots represent the metadata properly said as property-value pairs.
If the all the metadata is related to the same object, the meta element can contain a single Frame sub-element. If metadata 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.
<CLASSELT> <id> Const </id>? <meta> [ Frame | <And> <formula> Frame </formula>* </And> ] </meta>? other CLASSELT content </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 metadata specifies what the metadata is about, not where it is included in the instance RIF document.
It is suggested to use Dublin Core, RDFS, and OWL properties for metadata, 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 2.11. TBC
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.
Editor's Note: An uptodate version of the RIF-PRD presentation synatx will be included in a future version of this document.
TBD
Editor's Note: RIF-PRD and RIF-BLD [RIF-BLD]] share essentially the same presentation syntax and XML syntax. Future versions of this, or another, RIF document will include a complete, construct by construct, comparison table of RIF-PRD and RIF-BLD presentation and XML syntaxes.
The intended semantics of any RIF XML document which is both a syntactically valid RIF-PRD document and a syntactically valid RIF-BLD document is the same whether it is considered a RIF-PRD or a RIF-BLD document. For any input set of facts, the set of rules contained in the document must produce the same output set of facts whether it is consumed as a RIF-PRD or a RIF-BLD document.
Proof. TBC