RIF Production Rule Dialect

1 Overview

This document specifies the production rule dialect of the W3C rule interchange format (RIF-PRD), a commonstandard XML serialisationserialization format for many production rule languages.

Production rules are rules withrule statements defined in terms of both individual facts or objects, and groups of facts or classes of objects. They have an "if" partif part, or condition, and a "then" part. The "if"then part, also called a "condition",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 ).RIF-BLD). The "then"then part of production rules may containcontains actions, unlikewhich is different to the conclusion part of logic rules that may containwhich contains only a logical statement. Actions can add, delete, or modify the facts, not onlyfacts in the knowledge base;base, and they canhave 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 is shared byshares most features with many concrete production rule languages for the most widely used features,languages, and it associates each abstract construct with normative semantics (section 2, Abstract syntax and Semantics )and a normative XML concrete syntax (section 3, XML syntax ).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:

1. Match: the rules are instantiated based on the definition of the rule conditions and the current state of the data source;
2. Conflict resolution: a decision algorithm, often called the conflict resolution strategy, is applied to select the rule instances to be executed, per strategy;executed;
3. Act: changethe state of the data source,source is changed, by executing the selected rule instances’ actions. If a terminal state has not been reached, the control loops back to the first step (Match).

2 Abstact syntax and Semantics 2.1Conditions

This section specifies the language of the rule conditions that can be serialized using RIF-PRD, by specifying:

• the abstract syntax that all production rule languages interchanging rules using RIF-PRD must have in common for expressing conditions;
• the concrete XML syntax used to serialize production rule conditions in RIF-PRD;and the intended semantics of the condition formulas in a RIF-PRD document.

2.1.12.1 Abstract syntax

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:

• a countably infinite set of constant symbols Const;
• a countably infinite set of variable symbols Var (disjoint from Const ;);
• a countably infinite set of argument names, ArgNames (disjoint from Const and Var);
• syntactic constructs to denote:
  • Function calls;
  • Relations, including equality, class membership and subclass relationship; Arbitrary relationships;relations;
  • conjunction, disjunction and negation;
  • existential conditions.

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 andsyntax, so it leaves out many details that are not needed for its purpose:details: the only concrete syntax for RIF-PRD is the XML syntax.

2.1.1.12.1.1 Terms

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).

1. Constants and variables. If t ∈ Const or t ∈ Var then t is a simple term.
2. Positional terms. If t ∈ Const and t₁, ..., t_n, n≥0, are terms then t(t₁ ... t_n) is a positional term.
   Here, the constant t represents a function and t₁, ..., t_n represent argument values.
3. Terms with named arguments. A term with named arguments is of the form t(s₁->v₁ ... s_n->v_n), where n≥0, t ∈ Const and v₁, ..., v_n are terms and s₁, ..., s_n are pairwise distinct symbols from the set ArgNames.
   The constant t here represents a function; s₁, ..., s_n represent argument names; and v₁, ..., v_n represent argument values. The argument names, s₁, ..., s_n, are required to be pairwise distinct. Terms with named arguments are like positional terms except that the arguments are named and their order is immaterial. Note that a term of the form f() is, trivially, both a positional term and a term with named arguments. 2.1.1.2 Atomics  ☐

2.1.2 Atomic formulas

The atomic truth-valued constructs that can be serialized using RIF-PRD are called atomicsatomic formulas.

Definition (Atomic)(Atomic formula). An atomic formula can have several different forms and is defined as follows:

1. Positional atomicsatomic formulas. If t ∈ Const and t₁, ..., t_n, n≥0, are terms then t(t₁ ... t_n) is a positional atomic formula (or simply a positional atom).
2. AtomicsAtomic formulas with named arguments. An atomic formula with named arguments (or simply a atom with named arguments) is of the form t(s₁->v₁ ... s_n->v_n), where n≥0, t ∈ Const and v₁, ..., v_n are terms and s₁, ..., s_n are pairwise distinct symbols from the set ArgNames.
   The constant t here represents a predicate; s₁, ..., s_n represent argument names; and v₁, ..., v_n represent argument values. The argument names, s₁, ..., s_n, are required to be pairwise distinct. Atoms with named arguments are like positional Atoms except that the arguments are named and their order is immaterial. Note that an atom of the form t() is, trivially, both a positional atom and an atom with named arguments.
3. Equality atomicsatomic formulas. t = s is an equality atomic ,formula (or, simply, an equality), if t and s are terms.
4. Class membership atomicsatomic formulas (or just membership atomics). t#s is a membership atomic formula if t and s are terms. the term t is the object and the term s is the class.
5. Subclass atomicsatomic formulas. t##s is a subclass atomic formula if t and s are terms.
6. Frame atomicsatomic formulas. t[p₁->v₁ ... p_n->v_n] is a frame atomic formula (or simply a frame) if t, p₁, ..., p_n, v₁, ..., v_n, n ≥ 0, are terms. The term t is the object of the frame; the p_i are the property or attribute names; and the v_i are the property or attribute values. In this document, an attribute/value pair is sometimes called a slot.
   Membership, subclass, and frame atomicsatomic formulas are used to describe objects, classifications and class hierarchies.
7. Externally defined atomics.atomic formulas. If t is a positional, named-argument, or a frame atomic formula then External(t) is an externally defined atomic formula. Such atomicsatomic formulas are used for representing built-in predicates as well as "procedurally attached" predicates, which might exist in various rule-based systems or applications, but are not specified by RIF-PRD.predicates.   ☐

Note that not only predicates, but also frame atomicsatomic formulas can be externally defined. Therefore, external information sources can be modeled in an object-oriented way via frames.

For instance, External("http://example.com/acme"^^rif:iri["http://example.com/mycompany/president"^^rif:iri(?Year) -> ?Pres]) could be a representationEditor'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 an externally defined method "http://example.com/mycompany/president"^^rif:iricurrent limits, such as difficulty expressing datatype and cardinality constraints. Future drafts will address that problem. We are interested in an external object "http://example.com/acme"^^rif:iri .   ☐feedback on the merits and limitations of this approach.

Observe that the argument names of frames, p₁, ..., p_n, 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. They cannotnames, which can neither be constants from Const ornor variables from Var.

2.1.1.32.1.3 Formulas

Composite truth-valued constructs that can be serialized using RIF-PRD are called formulas.

Any atomic is also an atomic formula .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:

1. Atomic formula: If φ is an atomic formula then it is also a condition formula.
2. Conjunction: If φ₁, ..., φ_n, n ≥ 0, are condition formulas then so is And(φ₁ ... φ_n), called a conjunctive formula. As a special case, And() is allowed and is treated as a tautology, i.e., a formula that is always true.
3. Disjunction: If φ₁, ..., φ_n, n ≥ 0, are condition formulas then so is Or(φ₁ ... φ_n), called a disjunctive formula. As a special case, Or() is permitted and is treated as a contradiction, i.e., a formula that is always false.
4. Negation: If φ is a condition formula, then so is Not(φ), called a negative formula.
5. Existentials: If φ is a condition formula and ?V₁, ..., ?V_n, n>0, are variables then Exists ?V₁ ... ?V_n(φ) is an existential formula.   ☐

In the definition of a formula, the component formulas φ and φ_i 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:

• if e ∈ Const, then Var(e) = {};
• if e ∈ Var, then Var(e) = {e};
• if p and arg_i, i = 0..n,0...n, are terms, then, Var(p(arg_i) = Var(p) ∪ _{i=0..ni=0...n} Var(arg_i);
• if p and arg_i, i = 0..n,0...n, are terms, then, Var(External(p(arg_i)) = Var(p) ∪ _{i=0..ni=0...n} Var(arg_i);
• if t₁ and t₂ are terms, then Var(t₁ [=|#|##] t₂) Var(t₁) ∪ Var(t₂);
• if o', k_i, i = 1..n,1...n, and v_i, i = 1..n,1...n, are terms, then Var(o[k₁->v₁ ... k_n->v_n]) Var(o) ∪ _{i=1..ni=1...n} Var(k_i) ∪ _{i=1..ni=1...n} Var(v_i);
• if f_i, i = 0..n,0...n, are condition formulas, then Var([AND|OR|NOT](f_i)) ∪ _{i=0..ni=0...n} Var(f_i);
• if f is a condition formula and x_i ∈ Var for i = 1..n,1...n, then, Var(Exists x₁ ..... x_n (f)) = Var(f) - {x_i }| i = 1...n}.

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.

2.1.1.42.1.4 Well-formed formulas

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:

• A subset of individuals.
  The symbols in Const that belong to the primitive datatypes are required to be individuals.
• A number of subsets for predicate symbols such that there is one subset per symbol arity (defined below) for externally defined predicates and one for non-external predicates.
  Note that this implies that symbols used for external predicate names cannot be used for other predicates. Also, the definition of arity, below, implies that the arities for positional predicate symbols and for predicate symbols with named arguments are distinct even if the numbers of arguments are the same. Therefore, symbols that are used for positional predicates cannot be used for predicates with named arguments, and vice versa.
• A number of subsets of function symbols (remember that only procedurally attached(only externally defined function can be serialized using RIF-PRD). As with predicate symbols, there are separate subsets for symbols with different arities; function symbols with named arguments are in their own subsets. The only exception is the case of nullary symbols, which take zero arguments as in f(), since they are considered to be both positional and named-argument symbols.

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 ... s_k} of argument names (s_i ∈ 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:

2.2 Semantics of condition formulas

This section specifies the intended semantics of the condition formulas in a RIF-PRD document.

2.1.2.12.2.1 Semantic structures

2.1.2.22.2.2 Interpretation of condition formulas

This section defines how a semantic structure, I, determines the truth value TVal_I(φ) of a condition formula, φ. In PRD a semantic structure is represented as a Herbrand interpretation.

We define a mapping, TVal_I, from the set of all condition formulas to TV. Note that the definition implies that TVal_I(φ) is defined only if the set DTS of the datatypes of I includes all the datatypes mentioned in φ and I_external 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 TVal_I:

2.2.3 Satisfaction of a condition

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 (Models).(State). A semantic structure Istate S is a model ofHerbrand Interpretation I_H.   ☐

Definition (Condition Satisfaction). A condition formula, φ is satisfied under variable assignment σ in a state S, written as I  |= φ ,S |= φ[σ], iff TVal _IS(φ )[σ]) = t. Definition (Logical entailment). Let φ and ψ be formulas. We say that φ entails ψ , written as φ |= ψ , if and only if for every semantic structure, I , for which both TVal I ( φ ) and TVal I ( ψ ) are defined, I  |= φ implies  ☐

2.2.4 Matching substitution

At the syntactic level, the interpretation of the variables by a valuation function I  _{|= ψ .V} is realized by extension, in this document,a setsubstitution. The matching substitution of formulas, Φ = { φ 1 , ..., φ n }, n ≥ 1, is saidconstants to entail a formula ψ , written as Φ |= ψ , if and only if for every semantic structure, I , for which TVal I ( φ 0 ), ..., TVal I ( φ n ), and TVal I ( ψ ) are defined, I  |= φ 0 and ... and I  |= φ n implies I  |= ψ . Definition (Condition Satisfaction). Let Φ = { φ 1 , ..., φ m }, m ≥ 1, be a set of ground formulas and ψ be a condition formula. We say that Φ satisfies ψ if and only if, for every semantic structure I that is a model of all the ground formulas φ i in Φ : I  |= φ i , i= 1..m, there is at least one semantic structure I * such that: I *  |= ψ , and I * is exactly like I , except that a mapping I * V is used instead of I V , such that   I * V is defined to coincide with I V on all variables except, possibly, on the variables ?v 0 ... ?v n , n ≥ 0, that are free in ψ , that is, such that: Var( ψ ) = { ?v 0 ... ?v n }. In other words, a set of ground formulas Φ = { φ 1 , ..., φ m } m ≥ 1 satisfies a condition formula ψ iff Φ |= Exists ?v 0 ... ?v n (ψ) , where { ?v 0 , ..., ?v n } n ≥ 0 = Var( ψ ). 2.1.2.4 Matching substitution At the syntactic level, the interpretation of the variables by a valuation function I V is realized by a substitution . The matching substitution of constants to variables,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.

3 Actions

This section specifies the definitionaction part of a matching substitution, conditions 1 and 2 are the same as inthe definition of Condition Satisfaction , and they guaranteerules that the Φ -consistency of a substitution for the free variables in ψcan be serialized using RIF-PRD (the conclusion of a production rule is definedoften called the action part, or, simply, the action; the then part, with respectreference to the same semantic structures that make Φ satisfy ψ . Condition 3 guarantees that Φ |= ψ[σ] , where ψ[σ] denotes the ground condition formula obtained by substituting σ( ?x ) for every occurenceif-then form of ?x in ψ , for every variable ?x in Var ( ψ ). In other words, a formula ψ matchesa ground formula And(φ 1 , ..., φ n ) , n > 0rule statement; or the right-hand side, with respect to a ground substitution σ,or RHS. In the usual sense of pattern matching algorithms, e.g. [REFERENCE], if and only if σlatter case, the condition is a matching substitution forusually called the free variablesleft-hand side of ψ with respect tothe set of ground formulas Φ = { φ 1 , ..., φ n }. 2.2 Actionsrule, or LHS). Specifically, this section specifies the actions that can be serialized using RIF-PRD, by specifying:specifies:

• the abstract syntax that all production rule languages interchanging rules using RIF-PRD must have in common for expressing actions;
• the concrete XML syntax used to serialize the action part of production rule in RIF-PRD;and the intended semantics of the individual action formulas in a RIF-PRD document.

(See also: Proposed modified abstract syntax and semantics for option 3 ) 2.2.1 Abstract Syntax For aIn production rule language to be able to interchange rules using RIF-PRD, its alphabet for expressingsystems, the action part of a rule must, atthe abstract syntax level, consist of syntactic constructsrules is used, in particular, to denote:add, delete or modify facts in the assertion of a positional atom, an atomdata source with named arguments, or a frame, membership, or subclass atomic;respect to which the retractioncondition of rules are evaluated and the rules instantiated. As a positional atom, an atomrule 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.

3.1 Abstract syntax

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:

• the assertion of a positional atom, an atom with named arguments, or a frame, membership, or subclass atomic formula;
• the retraction of a positional atom, an atom with named arguments, or a frame;
• the addition of a new frame object;
• the removal of a frame object and the retraction of the corresponding frame and class atomics;atomic formulas;
• a sequence of these actions, including local variables and a mechanism to bind a local variable to a frame slot value or a new frame object.

3.1.1 Atomic actions

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:

1. Assert: If φ is a positional atom, an atom with named arguments, a frame, a membership atomic,atomic formula, or a subclass atomic formula in the RIF-PRD condition language, then Assert(φ) is an atomic action. φ is called the target of the action.
2. Retract: If φ is a positional atom, an atom with named arguments, or a frame in the RIF-PRD condition language, then Retract(φ) is an atomic action. φ is called the target of the action.
3. Retract object: If t is a term in the RIF-PRD condition language, then Retract(t) is an atomic action. t is called the target of the action. 2.2.1.2  ☐

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) = ∅.   ☐

3.1.2 Action blocks

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 bindingsdeclarations.

The action variable bindings providedeclaration 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. Definition (ActionFuture versions may support different or more elaborate mechanisms.

Definition (Action variable binding).declaration). An action variable binding can have two forms and is defined as follows: New : if ?odeclaration is a variable defined inpair, (v p) made of an enclosingaction block (described below), then New(?o) isvariable, v, and an action variable binding.binding (or, simply, binding), p, where p has one of two forms:

1. frame slot valueobject declaration: if fthe action variable, v, is to be assigned the identifier of a new frame, then the action variable binding is a frame object declaration: New(v). In that case, the notation for the RIF-PRD condition language, then f is anaction variable binding. 2.2.1.3declaration is: (?o New(?o));
2. frame slot value: if the action blocks A sequencevariable, v, is to be assigned the value of zero or more variables followed bya sequenceslot of zero or morea ground frame, then the action variable bindings followed bybinding is a sequenceframe: p = o[s->v], where o is a term that represents the identifier of one or more atomic actionsthe ground frame and s is called an action blocka term that represents the name of the slot. The associaed notation is: (?value o[s->?value]).   ☐

Definition (Action block). If v(v₁ ,p₁), ..., v(v_n 1 ,p_n 1 ≥ 0, are variables (sometimes called action variables) and b 1 , ..., b n 2, n 2≥ 0,0, are action variable bindingsdeclarations, and if a₁, ..., a _{n 3m}, n 3m ≥ 1,1, are atomic actions, if n 1 = 0then
Do(aDo((v₁ ... a n 3 ) is an action block . else Do vp₁ ... v), ..., (v_n 1 (b 1 ... bp_n 2 ;) a₁ ... a _{n 3l}) isdenotes an action block. Definition (Well-formed action block). An action block is  ☐

3.1.3 Well-formed if and only if: every action variable occurs in exactly oneaction variable binding contained inblocks

3.2 Operational semantics of atomic actions

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 changemodify 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 implemented.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 ⊆ P(W)W × L × P(W)W, where W denotes the set of all the ground condition formulas in the RIF-PRD condition languages; where P(W) denotes the power setstates of W ;the fact base, and where L denotes the set of all the ground atomic actions in the RIF-PRD action language.

Rule4 says that the effect of a block of actions is the effect of executing each action one after the other. 2.3Production rules and rulesets

This section specifies the rules and rulesets that can be serialized using RIF-PRD, by specifying:

• the abstract syntax that all production rule languages interchanging rules using RIF-PRD must have in common for rules and rule sets;
• the concrete XML syntax used to serialize production rules and rulesets in RIF-PRD;and the intended semantics of the rules and ruleset in a RIF-PRD document.

In addition, this section specifies additional concrete XML syntax for wrapping a ruleset in a RIF-PRD document and for adding meta-data to elements in a RIF-PRD document. 2.3.14.1 Abstract syntax

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:

• to associate a condition and an action block into a rule;
• to declare the variables that are free in a rule, to specify their bindings, and to associate them with that rule into a rule with less free variables;
• to group rules and to associate specific operational semantics to groups of rules.

For the sake of readability and simplicity, this specification introduces a notation for these constructs. That notation is not intended to be a concrete syntax and it leaves out many details that are not needed for its purpose: the only concrete syntax for RIF-PRD is the XML syntax. 2.3.1.14.1.1 Rules

Definition (Rule). A rule can be either:

• an unconditional action block;
• a conditional action block: if condition is a formula in the RIF-PRD condition language, and if action is a well-formed action,action block, then If condition, Then action is a conditional action;
• a rule with bound variables: if ?v₁ ... ?v_n, n > 0, are variables; p₁ ... p_m, m ≥ 0, are condition formulas (called binding patterns), and rule is a rule, then Forall ?v₁...?v_n (p₁...p_m) (rule) is a rule.   ☐

RIF-BLD compatibility. A rule If condition, Then action can be equivalently notedwritten action :- condition, that is, using RIF-BLD logic programmingnotation. 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 is an atomic conclusion or a conclusionblock, to emphasizeaction, 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 ... φ_n), if it contains only atomic assert actions: Do(Assert(φ₁) ... Assert(φ_n)), 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, althoughForall 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,patterns. However, when no negation is used in the semanticsconditions and only assertions in the actions, the XML serialization of a RIF-PRD rule with bound variables andis exactly the semanticssame as the XML serialization of a RIF-BLD universally quantified rule coincide whenever they have the same RIF XML syntax. 2.3.1.2rule, and their semantics coincide.

4.1.2 Groups

4.1.3 Well-formed rules and groups

2.3.24.2 Operational semantics of rules and rule sets

For the purpose of specifying4.2.1 Motivation and example