RIF Basic Logic Dialect

This documentspecification develops RIF-BLD (the Basic Logic Dialect of the Rule Interchange Format). From a theoretical perspective, RIF-BLD corresponds to the language of definite Horn rules (see Horn Logic )with equality and witha standard first-order semantics.semantics [CL73]. Syntactically, RIF-BLD has a number of extensions to support features such as objects and frames as in F-logic [KLW95], internationalized resource identifiers (or IRIs, defined by [RFC-3987]) as identifiers for concepts, and XML Schema data types.datatypes [XML-SCHEMA2]. In addition, the documentRIF RDF and OWL Compatibility [RIF-RDF+OWL] defines the syntax and semantics of integrated RIF-BLD/RDF and RIF-BLD/OWL languages. These features make RIF-BLD a Web-aware language. However, it should be kept in mind that RIF is designed to enable interoperability among rule languages in general, and its uses are not limited to the Web.

RIF-BLD is defined in two different ways -- both normative:

• As a direct specification, independently of the RIF Framework for Logic Dialects [RIF-FLD], for the benefit of those who desire a direct path to RIF-BLD, e.g., as prospective implementers, and are not interested in extensibility issues. This version of the RIF-BLD specification is given first.
• As a specialization of the RIF Framework for Logic-based Dialects (RIF-FLD) ,[RIF-FLD], which is part of the RIF extensibility framework. Building on RIF-FLD, this version of the RIF-BLD specification is verycomparatively short and is presented at the end of this document,in Section RIF-BLD as a Specialization of the RIF Framework . Itat the end of this document. This is intended for the reader who is already familiar with RIF-FLD and, therefore,and does not need to go through the much longer direct specification of RIF-BLD. This version of the specificationsection is also useful for dialect designers, as it is a concrete example of how a non-trivial RIF dialect can be derived from the RIF framework for logic dialects.

Independently of the RIF framework for logic dialects, for the benefit of those who desire a quicker path to RIF-BLD, e.g. as prospective implementers, and are not interested in the extensibility issues. This version of the RIF-BLD specification is given first. Logic-based RIF dialects that extend RIF-BLD in accordance withLogic-based RIF dialects that specialize or extend RIF-BLD in accordance with the RIF Framework for Logic Dialects [RIF-FLD] will be specifieddeveloped in other documentsspecifications by thisthe RIF working group.

Editor's Note: This documentTo give a preview, here is the latest draft of thea simple complete RIF-BLD specification.example deriving a number of extensions is plannedternary relation from its inverse.

Example 1 (An introductory RIF-BLD example).

A rule can be written in English to support importderive buy relationships (rather than store any of RIF documents,them) from sell relationships (e.g., stored as facts, as exemplified by the notion of RIF compliance, andsecond line):

The fact Mary buys LeRif from John can be logically derived by a modus ponens argument. Assuming Web IRIs for the predicates buy and sell, as well as for the individuals John, Mary, and LeRif, the above English text can be represented in RIF-BLD Presentation Syntax as follows.

Document(
  Prefix(cpt http://example.com/concepts#)
  Prefix(ppl http://example.com/people#)
  Prefix(bks http://example.com/books#)

  Group
  (
    Forall ?Buyer ?Item ?Seller (
        cpt:buy(?Buyer ?Item ?Seller) :- cpt:sell(?Seller ?Item ?Buyer)
    )
 
    cpt:sell(ppl:John bks:LeRif ppl:Mary)
  )
)

For the interchange of such rule (and fact) documents, an equivalent RIF-BLD XML Syntax is given in this specification. To formalize their meaning, a RIF-BLD Semantics is forthcoming.specified.

This normative section specifies the syntax of RIF-BLD directly, without relying on [RIF-FLD .]. We define both athe presentation syntax (below) and an XML syntax.syntax in Section XML Serialization Syntax for RIF-BLD. The presentation syntax is normative, but not intended to be a concrete syntax for RIF-BLD. It is defined in mathematical English and is meant to be used in the definitions and examples. This syntax deliberately leaves out details such as the delimiters of the various syntactic components, escape symbols, parenthesizing, precedence of operators, and the like. Since RIF is an interchange format, it uses XML as its concrete syntax. Editor's Note: A future versionsyntax and RIF-BLD conformance is described in terms of this document might introduce syntactic shortcutssemantics-preserving transformations.

Note to simplify writingthe examplesreader: this section depends on Section Constants, Symbol Spaces, and test cases.Datatypes of [RIF-DTB].

Constants are written as "literal"^^symspace, where literal is a sequence of Unicode characters and symspace is an identifier for a symbol space. Symbol spaces are defined in Section Constants and Symbol Spaces of the RIF-FLD document . Editor's Note: The definition of symbol spaces will eventually be also given in the document Data Types and Builtins , so the above reference will be to that document instead of RIF-FLD.[RIF-DTB].

The symbols =, #, and ## are used in formulas that define equality, class membership, and subclass relationships. The symbol -> is used in terms that have named arguments and in frame formulas. The symbol External indicates that an atomic formula or a function term is defined externally (e.g., a builtin).built-in) and the symbols Prefix and Base are used in abridged representations of IRIs.

The symbol Document is used to definespecify RIF-BLD documents, Import is an import directive, and the symbol Group is used to organize RIF-BLD formulas into collections optionally annotated with metadata.collections.   ☐

The language of RIF-BLD is the set of formulas constructed using the above alphabet according to the rules given below.

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 are base terms then t(t₁ ... t_n) is a positional term.
3. Terms with named arguments. A term with named arguments is of the form t(s₁->v₁ ... s_n->v_n), where t ∈ Const and v₁, ..., v_n are base terms and s₁, ..., s_n are pairwise distinct symbols from the set ArgNames.

   The constant t here represents a predicate or 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 both positional and with named arguments.

4. Equality terms. t = s is an equality term, if t and s are base terms then t = s is an equality term .terms.
5. Class membership terms (or just membership terms). t#s is a membership term if t and s are base terms.
6. Subclass terms. t##s is a subclass term if t and s are base terms.
7. Frame terms. t[p₁->v₁ ... p_n->v_n] is a frame term (or simply a frame) if t, p₁, ..., p_n, v₁, ..., v_n, n ≥ 0, are base terms.

   Membership, subclass, and frame terms are used to describe objects and class hierarchies.

8. Externally defined terms. If t is an internal non-variablea positional, named-argument, or a frame term then External(t) is an externally defined term.

9. Such terms are used for representing builtinbuilt-in functions and predicates as well as "procedurally attached" terms or predicates, which might exist in various rule-based systems, but are not specified by RIF.

     ☐ 2.3 Well-formedness ofNote that frame terms are allowed to be externally defined. Therefore, externally defined objects can be accessed using the setmore natural frame-based interface. For instance, External("http://example.com/acme"^^rif:iri["http://example.com/mycompany/president"^^rif:iri(?Year) -> ?Pres]) could be an interface provided to access an externally defined method "http://example.com/mycompany/president"^^rif:iri of all symbols, Const ,an external object "http://example.com/acme"^^rif:iri.   ☐

   Feature At Risk #1: External frames

   Note: This feature is partitioned into positional predicate symbols predicate symbols with named arguments positional function symbols function symbols"at risk" and may be removed from this specification based on feedback. Please send feedback to public-rif-comments@w3.org.

Observe that the argument names of frame terms, p₁, ..., p_n, are base terms and, as a special case, can be variables. In contrast, terms with named arguments individuals.can use only the symbols infrom ArgNames to represent their argument names. They cannot be constants from Const that belongor variables from Var. (The reason for this restriction has to do with the supported RIF data types are individuals. Each predicate and function symbol has precisely one arity . For positional symbols, an aritycomplexity of unification, which is a non-negative integer that tells how many arguments the symbol can take. For symbols that takeused by several inference mechanisms of first-order logic.)

• Rule implication: φ :- ψ is determined by its context. Ifa symbol from Const occurs in more than one context informula, called rule implication, if:
  • φ is an atomic formula or a setconjunction of atomic formulas,
  • the setψ is not well-formed in RIF-BLD. Fora termcondition formula, and
  • none of the form External(t) to be well-formed, t must be an instance of an external schema , i.e., a schema of an externally specified term, as definedatomic formulas in Section Schemas forφ is an externally defined Terms of RIF-FLD. Also, ifterm (i.e., a term of the form External(p(...)) occurs as an atomic formula then p is considered a predicate symbol. Editor's Note:External(...)).

  Feature At Risk #2: Equality in the definition of external schemas will eventually also appearrule conclusion (φ in the document Data Typesabove)

  Note: This feature is "at risk" and Builtins , so the above reference willmay be removed from this specification based on feedback. Please send feedback to that document instead of RIF-FLD.public-rif-comments@w3.org.

• Universal rule: If φ is a well-formed termrule implication and ?V₁, ..., ?V_n are variables then Forall ?V₁ ... ?V_n(φ) is onea formula, called a universal rule. It is required that occursall the free variables in φ occur among variables ?V₁ ... ?V_n in the quantification part. A well-formed setvariable ?v is free in φ if it does not occur in a subformula of fomulas. 2.4 Formulas Any term (positional or with named arguments)φ of the form p(...)Q ?v (ψ), where pQ is a predicate symbol, isquantifier (Forall or Exists). Universal rules will also an atomic formulabe referred to as RIF-BLD rules.
• Equality, membership, subclass, and frame terms are also atomic formulas. A statement of the form External(φ) , whereUniversal fact: If φ is an atomic formula,formula then Forall ?V₁ ... ?V_n(φ) is also an atomica formula, called an externally defined atomic formula. Simple terms (constants and variables) are not formulas. Not all atomic formulas are well-formed.a well-formed atomic formula is an atomic formulauniversal fact, provided that is also a well-formed term (see Section Well-formedness of Terms ). More general formulas are constructed out ofall the atomic formulas withfree variables in φ occur among the help of logical connectives. Definition (Well-formed formula) . A well-formed formula is a statement that has one of the following forms: Atomic : If φ is a well-formed atomic formula then it is also a well-formed formula. Conjunctionvariables ?V₁ ... ?V_n.

  Universal facts are often considered to be rules without premises (or having true as their premises).

• Group: If φ₁, ..., φ_n , n ≥ 0 ,are well-formedRIF-BLD rules, universal facts, variable-free rule implications, variable-free atomic formulas, or group formulas then so is And(φGroup(φ₁ ... φ_n) , called a conjunctive formula. As a special case, And()is allowed and is treated as a tautology, i.e.,a group formula.

  Group formulas are used to represent sets of rules and facts. Note that is always true. Disjunction : If φ 1 , ...,some of the φ _{n , n ≥ 0 , are well-formedi}'s can be group formulas then so is Or(φthemselves, which means that groups can be nested.

• Document: An expression of the form Document(directive₁ ... φdirective_n ) , called a disjunctive formula. When n=0 , we get Or() as a special case; itΓ) is treated asa contradiction, i.e.,RIF-BLD document formula (or simply a document formula that is always false. Existentials :), if
  • φΓ is a well-formedgroup formula and ?Vthat makes the actual logical content of the document.
  • directive₁, ..., ?V n are variables then Exists ?V 1 ... ?Vdirective_n (φ) is an existential formula. Formulas constructed using the above definitionsare called RIF-BLD conditionsdirectives. The following defines the notion ofA RIF-BLD rule. Rule implication : If φ isdirective can be an import directive, a well-formed atomic formula and ψ isprefix directive, or a RIF-BLD condition then φ :- ψ isbase directive.
  • • A well-formed formula, called rule implicationbase directive has the form Base(iri), provided that φwhere iri is not an externally defined term (i.e.,a term ofunicode string in the form External(...) ). Quantified rule : If φ is a rule implication and ?V 1 , ..., ?V nof an IRI.

      Like prefix directives, base directives do not affect the semantics. They are variables then Forall ?V 1 ... ?V n (φ) isused as syntactic shortcuts for expanding relative IRIs into full IRIs, as described in Section Constants and Symbol Spaces of [RIF-DTB].

    • A well-formed formula, called quantified rule . Itprefix directive has the form Prefix(p v), where p is requiredan alphanumeric string that all the free (i.e., non-quantified) variables in φ occur inserves as the prefix Forall ?V 1 ... ?V n . Quantified rules will also be referred to as RIF-BLD rules . Group : If φname and v is a frame term and ρ 1 , ..., ρ n are RIF-BLD rules or group formulas (they can be mixed) then Group φ (ρ 1 ... ρ n ) and Group (ρ 1 ... ρ n ) are group formulas . Group formulasmacro-expansion for p -- a string that forms an IRI.

      Prefix directives do not affect the semantics of RIF documents. Instead, they are used as shorthands to represent setsallow more concise representation of rules annotated with metadata.IRI constants. This metadatamechanism is specified using an optional frame term φexplained in [RIF-DTB], Section Constants and Symbol Spaces.

    • Note that some of the ρ i 's can be group formulas themselves, which means that groupsAn import directive can be nested. This allowshave one to attach metadata to various subsets of rules, which may be inside larger rule sets, which in turn can be annotated. Document : An expressionof the form Document(φ Import 1 ... Import n Γ) is a document formula , if φ is a frame term, which is intended to represent the metadata associated with the document. Γ is a group formula that makes the actual logical content of the document. Import 1 , ..., Import n are import directives , which have the formthese two forms: Import(t) or Import(t p) , where. Here t is an IRI constant and p is a term. The constant t indicates the addresslocation of another rule setdocument to be imported and p is called the profile of import.

      Section Direct Specification of RIF-BLD Semantics of this document defines the semantics for the directive Import(t) only. The semantics of the directive Import(t p) is given in the document RIF RDF and OWL Compatibility .[RIF-RDF+OWL]. It is used for importing non-RIF-BLD logical entities, such as RDF data and OWL ontologies. The profile specifies what kind of entity is being imported and under what semantics (for instance, the various RDF entailment regimes).

    There can be at most one Base directive in the sequence of directives in a document formula. It must be the first directive in the sequence, if present, followed by a sequence of Prefix directives (again, if present), followed by a sequence of Import directives.

  • All parts of thea document formula, the metadata,formula -- the directives,directives and the group formula -- are optional and can be omitted.

  ☐ It canIn this definition, the component formulas φ, φ_i, ψ_i, and Γ are said to be seen fromsubformulas of the definitionsrespective formulas (condition, rule, group, etc.) that are built with the help of these components.   ☐

The above definitions endow RIF-BLD haswith a wide variety of syntactic forms for terms and formulas. This provides theformulas, which creates infrastructure for exchanging syntactically diverse rule languages that support rich collections of syntactic forms.languages. Systems that do not support some of the syntax directly can still support it through syntactic transformations. For instance, disjunctions in the rule body can be eliminated through a standard transformation, such as replacing p :- Or(q r) with a pair of rules p :- q,   p :- r. Terms with named arguments can be reduced to positional terms by ordering the arguments by their names and incorporating them into the predicate name. For instance, p(bb->1 aa->2) can be represented as p_aa_bb(2,1).

ofRIF-BLD So far, the syntaxallows every term and formula (including terms and formulas that occur inside other terms and formulas) to be optionally preceded by an annotation of RIF-BLD has been specified in mathematical English. Tool developers, however, may prefer EBNF notation, which providesthe form (* id φ *), where id is a more succinct overviewrif:iri constant and φ is a frame formula or a conjunction of frame formulas. Both items inside the syntax. Several points should be kept in mind regarding this notation.annotation are optional. The syntax of first-order logic is not context-free, so EBNF does not captureid part represents the syntaxidentifier of RIF-BLD precisely. For instance, it cannot capturethe section on well-formedness conditions , i.e.,term/formula to which the requirement that each symbol in RIF-BLD can occur in at most one context. As a result,annotation is attached and φ is the EBNF grammar defines a strict supersetmetadata part of RIF-BLD (not all rules that are derivable using the EBNF grammar are well-formed rules in RIF-BLD).the EBNF syntax is not a concrete syntax: itannotation. RIF-BLD does not address the details of how constants and variables are represented, and itimpose any restrictions on φ apart from what is not sufficiently precise about the delimitersstated above. In particular, it may include variables, function symbols, rif:local constants, and escape symbols. Instead, white space is informally usedso on.

Document formulas with and without annotations will be referred to as RIF-BLD documents.

A delimiter, and white spaceconvention is impliedused to avoid a syntactic ambiguity in productions that use Kleene star.the above definition. For instance, TERM* is toin (* id φ *) t[w -> v] the metadata annotation could be understood as TERM TERM ... TERM , where each ' ' abstracts from oneattributed to the term t or more blanks, tabs, newlines, etc. Thisto the entire frame t[w -> v]. The convention in RIF-BLD is done intentionally,that the above annotation is considered to be syntactically attached to the entire frame. Yet, since RIF's presentation syntaxφ is used asa tool for specifyingconjunction, some conjuncts can be used to provide metadata targeted to the semantics and for illustrationobject part, t, of the main RIF concepts through examples.frame. Generally, the convention associates each annotation to the largest term or formula it precedes.

It is not intended as a concrete syntax for a rule language. RIF defines a concrete syntax onlysuggested to use Dublin Core, RDFS, and OWL properties for exchanging rules,metadata, along the lines of Section 7.1 of [OWL-Reference]-- specifically owl:versionInfo, rdfs:label, rdfs:comment, rdfs:seeAlso, rdfs:isDefinedBy, dc:creator, dc:description, dc:date, and foaf:maker.

• If s occurs as an atomic term, i.e. an Atom , External Atom , Equal , Member , Subclass , or Frame . A TERMsubformula of the form s(...) with arity α (the arity can becorrespond to a constant, variable, Expr ,positional occurrence of s or External Expr . The RIF-BLD presentation syntax does not committo any particular vocabulary and permits arbitrary Unicode stringsan occurrence with named arguments) then s occurs in constant symbols, argument names, and variables. Constant symbols havethe form: "UNICODESTRING"^^SYMSPACE , where SYMSPACE is a Unicode string that represents an identifier or an aliascontext of thea predicate symbol spacewith arity α.
• If s occurs as a term (not subformula) of the constant, and UNICODESTRING is a Unicode string fromform s(...) with arity α then s occurs in the lexical spacecontext of that symbol space. Names are denoted by Unicode character sequences. Variables are denoted bya UNICODESTRING prefixedfunction symbol with a ?-sign. Equality, membership, and subclass terms are self-explanatory.arity α.
• If s occurs as an Atom and Expr (expression) can either be positional oratomic subformula External(s(...)) with named arguments. A frame term is a term composedarity α then s occurs in the context of an object Id andexternal predicate symbol with arity α.
• If s occurs as a collectionterm (not subformula) External(s(...)) with arity α then s occurs in the context of attribute-value pairs.an external ( ATOMICfunction symbol with arity α.   ☐

Definition (Imported document). Let Δ be a document formula and Import(t) be one of its import directives, where t is a call toan externally defined predicate, equality, membership, subclassing, or frame. Likewise, External ( Expr )IRI constant that identifies another document formula, Δ'. We say that Δ' is directly imported into Δ.

A calldocument formula Δ' is said to an externally defined function. Example 1 (RIF-BLD conditions). This example shows conditionsbe imported into Δ if it is either directly imported into Δ or it is imported (directly or not) into some other formula that are composed of atoms, expressions, frames, and existentials.is directly imported into Δ.     ☐

Definition (Well-formed formula). A formula φ is well-formed iff:

• every constant symbol (whether rif:local or not) mentioned in frame formulas variablesφ occurs in exactly one context.
• if φ is a document formula and Δ'₁, ..., Δ'_k are shownall of its imported documents, then every non-rif:local constant symbol mentioned in φ or any of the positionsimported Δ'_is must occur in exactly one context (in all of object Ids, object properties, and property values. For brevity, we usethe compact URI notation [ CURIE ], prefix:suffix , which should be understood asΔ'_is).
• Whenever a macro that expands intoformula contains a concatenationterm or a subformula of the prefix definition and suffix . Thus, if bks is a prefix that expands into http://example.com/books# then bks:LeRif shouldform External(t), t must be understood merely asan abbreviationinstance of the coherent set of external schemas (Section Schemas for http://example.com/books#LeRif .Externally Defined Terms of [RIF-DTB]) associated with the compact URI notationlanguage of RIF-BLD.   ☐
• If t is not partan instance of the RIF-BLD syntax. Compact URI prefixes: bks expands into http://example.com/books# auth expands into http://example.com/authors# cpt expands into http://example.com/concepts# Positional terms: "cpt:book"^^rif:iri("auth:rifwg"^^rif:iri "bks:LeRif"^^rif:iri) Exists ?X ("cpt:book"^^rif:iri(?X "bks:LeRif"^^rif:iri)) Termscoherent set of external schemas associated with named arguments: "cpt:book"^^rif:iri(cpt:author->"auth:rifwg"^^rif:iri cpt:title->"bks:LeRif"^^rif:iri) Exists ?X ("cpt:book"^^rif:iri(cpt:author->?X cpt:title->"bks:LeRif"^^rif:iri)) Frames: "bks:wd1"^^rif:iri["cpt:author"^^rif:iri->"auth:rifwg"^^rif:iri "cpt:title"^^rif:iri->"bks:LeRif"^^rif:iri] Exists ?X ("bks:wd2"^^rif:iri["cpt:author"^^rif:iri->?X "cpt:title"^^rif:iri->"bks:LeRif"^^rif:iri]) Exists ?X (And ("bks:wd2"^^rif:iri#"cpt:book"^^rif:iri "bks:wd2"^^rif:iri["cpt:author"^^rif:iri->?X "cpt:title"^^rif:iri->"bks:LeRif"^^rif:iri])) Exists ?I ?X (?I["cpt:author"^^rif:iri->?X "cpt:title"^^rif:iri->"bks:LeRif"^^rif:iri]) Exists ?I ?X (And (?I#"cpt:book"^^rif:iri ?I["cpt:author"^^rif:iri->?X "cpt:title"^^rif:iri->"bks:LeRif"^^rif:iri])) Exists ?S ("bks:wd2"^^rif:iri["cpt:author"^^rif:iri->"auth:rifwg"^^rif:iri ?S->"bks:LeRif"^^rif:iri]) Exists ?X ?S ("bks:wd2"^^rif:iri["cpt:author"^^rif:iri->?X ?S->"bks:LeRif"^^rif:iri]) Exists ?I ?X ?S (And (?I#"cpt:book"^^rif:iri ?I[author->?X ?S->"bks:LeRif"^^rif:iri])) 2.5.2 EBNF forthe RIF-BLD Rulelanguage then t can occur only as External(t), i.e., as an external term or atomic formula.

Definition (Language of RIF-BLD). The presentation syntax forlanguage of RIF-BLD rules extendsconsists of the syntax in Sectionset of all well-formed formulas and is determined by:

• the alphabet of the language and
• a set of coherent external schemas, which determine the available built-ins and other externally defined predicates and functions.   ☐

• The Working Group. Inputsyntax of first-order logic is welcome. See Issue-51 Document ::= 'Document' '(' IRIMETA? DIRECTIVE* Group? ')' DIRECTIVE ::= Import Import ::= 'Import' '(' IRI PROFILE? ')' Group ::= 'Group' IRIMETA? '(' (RULE | Group)* ')' IRIMETA ::= Frame RULE ::= 'Forall' Var+ '(' CLAUSE ')' | CLAUSE CLAUSE ::= Implies | ATOMIC Implies ::= ATOMIC ':-' FORMULA IRI ::= UNICODESTRING PROFILE ::= UNICODESTRINGnot context-free, so EBNF cannot capture the syntax of RIF-BLD precisely. For convenient reference, we reproduceinstance, it cannot capture the condition language partsection on well-formedness conditions, i.e., the requirement that each symbol in RIF-BLD can occur in at most one context. As a result, the EBNF grammar defines a strict superset of RIF-BLD (not all rules that are derivable using the EBNF below. FORMULA ::= 'And' '(' FORMULA* ')' | 'Or' '(' FORMULA* ')' | 'Exists' Var+ '(' FORMULA ')' | ATOMIC | 'External' '(' ATOMIC ')' ATOMIC ::= Atom | Equal | Member | Subclass | Frame Atom ::= UNITERM UNITERM ::= Const '(' (TERM*grammar are well-formed rules in RIF-BLD).
• The EBNF grammar does not address the details of how constants and variables are represented, and it is not sufficiently precise about the delimiters and escape symbols. Instead, white space is informally used as the delimiter, and white space is implied in productions that use Kleene star. For instance, TERM* is to be understood as TERM TERM ... TERM, where each ' ' abstracts from one or more blanks, tabs, newlines, etc. This is so because RIF's presentation syntax is a tool for specifying the semantics and for illustration of the main RIF concepts through examples. It is not intended as a concrete syntax for a rule language. RIF defines a concrete syntax only for exchanging rules, and that syntax is XML-based, obtained as a refinement and serialization of the presentation syntax.
• For all the above reasons, the EBNF grammar is not normative. (The non-normative status of the EBNF grammer should not be confused with the normative status of the RIF-BLD presentation syntax.)

  FORMULA        ::= IRIMETA? 'And' '(' FORMULA* ')' |
                     IRIMETA? 'Or' '(' FORMULA* ')' |
                     IRIMETA? 'Exists' Var+ '(' FORMULA ')' |
                     ATOMIC |
                     IRIMETA? 'External' '(' Atom | Frame ')'
  ATOMIC         ::= IRIMETA? (Atom | Equal | Member | Subclass | Frame)
  Atom           ::= UNITERM
  UNITERM        ::= Const '(' (TERM* | (Name '->' TERM)*) ')'
  Equal          ::= TERM '=' TERM
  Member         ::= TERM '#' TERM
  Subclass       ::= TERM '##' TERM
  Frame          ::= TERM '[' (TERM '->' TERM)* ']'
  TERM           ::=  ConstIRIMETA? (Const | Var | Expr | 'External' '(' Expr  ')'')')
  Expr           ::= UNITERM
  Const          ::= '"' UNICODESTRING '"^^' SYMSPACE | CONSTSHORT
  IRICONST       ::= '"' IRI '"^^' 'rif:iri'
  Name           ::= UNICODESTRING
  Var            ::= '?' UNICODESTRING
  SYMSPACE       ::=  UNICODESTRING A RIF-BLD Document consists of an optional Directive and an optional Group annotated with optional metadata,ANGLEBRACKIRI | CURIE
 
  IRIMETA         . A Directive can contain any number of Import s. A::= '(*' IRICONST? (Frame | 'And' '(' Frame* ')')? '*)'

As explained in Section RIF-BLD Group is a nested collection ofAnnotations in the Presentation Syntax, RIF-BLD rules annotatedformulas and terms can be prefixed with optional metadata,annotations, IRIMETA ., for identification and metadata. IRIMETA areis represented using (*...*)-brackets that contain an optional IRI constant, IRICONST, as identifier followed by an optional Frame s. A Group can contain any numberor conjunction of RULEFrames along with any numberas metadata. The IRI of nested Group s. Rules are generated by CLAUSE , which can be inan IRICONST has the scopeform of a Forall quantifier. If a CLAUSE inan internationalized resource identifier as defined by [RFC-3987].

The RULEproduction has a free (non-quantified) variable, it must occur inrule for the Var+ sequence. Frame , Var , ATOMIC , andnon-terminal FORMULA were defined as part ofrepresents RIF condition formulas (defined earlier). The syntaxconnectives And and Or define conjunctions and disjunctions of conditions, respectively. Exists introduces existentially quantified variables. Here Var+ stands for positive conditionsthe list of variables that are free in Section EBNF for RIF-BLD Condition LanguageFORMULA. In the CLAUSE productionRIF-BLD conditions permit only existential variables. A RIF-BLD FORMULA can also be an ATOMIC is treated as a rule withterm, i.e. an empty condition part -- in which case it is usually called a factAtom, External Atom, Equal, Member, Subclass, or Frame. Note that, byA definition in Section FormulasTERM can be a constant, variable, Expr, formulasor External Expr.

The RIF-BLD presentation syntax does not commit to any particular vocabulary and permits arbitrary Unicode strings in constant symbols, argument names, and variables. Constant symbols can have this form: "UNICODESTRING"^^SYMSPACE, where SYMSPACE is a ANGLEBRACKIRI or CURIE that query externallyrepresents an identifier of the symbol space of the constant, and UNICODESTRING is a Unicode string from the lexical space of that symbol space. ANGLEBRACKIRI and CURIE are defined atoms (i.e., formulasin Section Shortcuts for Constants in RIF's Presentation Syntax of [RIF-DTB]. Constant symbols can also have several shortcut forms, which are represented by the form External(Atom(...)) )non-terminal CONSTSHORT. These shortcuts are not allowedalso defined in the conclusion partsame section of [RIF-DTB]. One of them is the CURIE shortcut, which is extensively used in the examples in this document. Names are Unicode character sequences. Variables are composed of UNICODESTRING symbols prefixed with a ?-sign.

Equality, membership, and subclass terms are self-explanatory. An Atom and Expr (expression) can either be positional or with named arguments. A frame term is a term composed of an object Id and a rulecollection of attribute-value pairs. An External( ATOMIC does not expandAtom) is a call to an externally defined predicate; External ).(Frame) is a call to an externally defined frame. Likewise, External(Expr) is a call to an externally defined function.

Example 2 (RIF-BLD rules).conditions).

This example shows a business rule borrowed from the document RIF Use Cases and Requirements : If an item is perishableconditions that are composed of atoms, expressions, frames, and it is delivered to John more than 10 days after the scheduled delivery date thenexistentials. In frame formulas variables are shown in the item will be rejected by him. As before,positions of object Ids, object properties, and property values. For better readabilitybrevity, we use the compact URI notation. Compact URI prefixes: ppl expands into http://example.com/people# cpt expands into http://example.com/concepts# op expands into the yet-to-be-determined IRICURIE shortcut notation prefix:suffix for RIF builtin predicates a. Universal form: Forall ?item ?deliverydate ?scheduledate ?diffduration ?diffdays ( "cpt:reject"^^rif:iri("ppl:John"^^rif:iri ?item) :- And("cpt:perishable"^^rif:iri(?item) "cpt:delivered"^^rif:iri(?item ?deliverydate "ppl:John"^^rif:iri) "cpt:scheduled"^^rif:iri(?item ?scheduledate) External("fn:subtract-dateTimes-yielding-dayTimeDuration"^^rif:iri(?deliverydate ?scheduledate ?diffduration)) External("fn:get-days-from-dayTimeDuration"^^rif:iri(?diffduration ?diffdays)) External("op:numeric-greater-than"^^rif:iri(?diffdays "10"^^xsd:integer))) ) b. Universal-existential form: Forall ?item ( "cpt:reject"^^rif:iri("ppl:John"^^rif:iri ?item ) :- Exists ?deliverydate ?scheduledate ?diffduration ?diffdays ( And("cpt:perishable"^^rif:iri(?item) "cpt:delivered"^^rif:iri(?item ?deliverydate "ppl:John"^^rif:iri) "cpt:scheduled"^^rif:iri(?item ?scheduledate) External("fn:subtract-dateTimes-yielding-dayTimeDuration"^^rif:iri(?deliverydate ?scheduledate ?diffduration)) External("fn:get-days-from-dayTimeDuration"^^rif:iri(?diffduration ?diffdays)) External("op:numeric-greater-than"^^rif:iri(?diffdays "10"^^xsd:integer))) ) ) Example 3 (A RIF-BLD group annotated with metadata). This example shows a group formula that consists of two RIF-BLD rules. The first of these rules is copied from Example 2a. The groupconstant symbols, which is annotated with Dublin Core metadata representedunderstood as a frame. Compact URI prefixes: ppl expands into http://example.com/people# cpt expands into http://example.com/concepts# dc expands into http://purl.org/dc/terms/ w3macro that expands into http://www.w3.org/ Group " http://sample.org "^^rif:iri["dc:publisher"^^rif:iri->"w3:W3C"^^rif:iri "dc:date"^^rif:iri->"2008-04-04"^^xsd:date] ( Forall ?item ?deliverydate ?scheduledate ?diffduration ?diffdays ( "cpt:reject"^^rif:iri("ppl:John"^^rif:iri ?item) :- And("cpt:perishable"^^rif:iri(?item) "cpt:delivered"^^rif:iri(?item ?deliverydate "ppl:John"^^rif:iri) "cpt:scheduled"^^rif:iri(?item ?scheduledate) External("fn:subtract-dateTimes-yielding-dayTimeDuration"^^rif:iri(?deliverydate ?scheduledate ?diffduration)) External("fn:get-days-from-dayTimeDuration"^^rif:iri(?diffduration ?diffdays)) External("op:numeric-greater-than"^^rif:iri(?diffdays "10"^^xsd:integer))) ) Forall ?item ( "cpt:reject"^^rif:iri("ppl:Fred"^^rif:iri ?item) :- "cpt:unsolicited"^^rif:iri(?item) ) ) 3 Direct Specification of RIF-BLD Semantics This normative section specifies the semanticsan IRI obtained by concatenation of RIF-BLD directly, without relying on RIF-FLD . 3.1 Truth Valuesthe set TV of truth values in RIF-BLD consists of just two values, tprefix definition and fsuffix. 3.2 Semantic Structures The key concept in a model-theoretic semantics of a logic languageThus, if bks is the notion ofa semantic structure . The definition, below,prefix that expands into http://example.com/books# then bks:LeRif is a little bit more general than necessary. This is done in order to better see the connection with the semantics of the RIF framework . Definition (Semantic structure)an abbreviation for "http://example.com/books#LeRif"^^rif:iri. A semantic structure , I , is a tuple of the form < TV , DTS , D , D ind , D func , I C , I V , I F , I frame , I SF , I sub , I isa , I = , I external , I truth >. Here D is a non-empty set of elements called the domain of I ,This and D ind , D funcother shortcuts are nonempty subsets of D . D ind is used to interpret the elements of Const , which denote individuals and D func is used to interpretdefined in [RIF-DTB]. Assume that the elements of Const , which denote function symbols. As before, Const denotesfollowing prefix directives appear in the set of all constant symbols and Varpreamble to the set of all variable symbols. TV denotesdocument:

Prefix(bks  http://example.com/books#)
Prefix(auth http://example.com/authors#)
Prefix(cpt  http://example.com/concepts#)

Positional terms:
  
  cpt:book(auth:rifwg bks:LeRif)
  Exists ?X (cpt:book(?X bks:LeRif))

Terms with named arguments:

  cpt:book(cpt:author->auth:rifwg  cpt:title->bks:LeRif)
  Exists ?X (cpt:book(cpt:author->?X cpt:title->bks:LeRif))

Frames:

  bks:wd1[cpt:author->auth:rifwg cpt:title->bks:LeRif]
  Exists ?X (bks:wd2[cpt:author->?X  cpt:title->bks:LeRif])
  Exists ?X (And (bks:wd2#cpt:book  bks:wd2[cpt:author->?X  cpt:title->bks:LeRif]))
  Exists ?I ?X (?I[cpt:author->?X  cpt:title->bks:LeRif])
  Exists ?I ?X (And (?I#cpt:book ?I[cpt:author->?X  cpt:title->bks:LeRif]))
  Exists ?S (bks:wd2[cpt:author->auth:rifwg ?S->bks:LeRif])
  Exists ?X ?S (bks:wd2[cpt:author->?X ?S->bks:LeRif])
  Exists ?I ?X ?S (And (?I#cpt:book  ?I[author->?X ?S->bks:LeRif]))

The semantic structure uses and DTS ispresentation syntax for RIF-BLD rules extends the set of primitive data types usedsyntax in I (please refer toSection Primitive Data Types of RIF-FLDEBNF for RIF-BLD Condition Language with the semantics of data types). Editor's Note: In the future versions of this document, the above reference will point to thefollowing productions.

 Document   Data Types and Builtins instead::= IRIMETA? 'Document' '(' Base? Prefix* Import* Group? ')'
 Base      ::= 'Base' '(' IRI ')'
 Prefix    ::= 'Prefix' '(' Name IRI ')'
 Import    ::= IRIMETA? 'Import' '(' IRICONST PROFILE? ')'
 Group     ::= IRIMETA? 'Group' '(' (RULE | Group)* ')'
 RULE      ::= (IRIMETA? 'Forall' Var+ '(' CLAUSE ')') | CLAUSE
 CLAUSE    ::= Implies | ATOMIC
 Implies   ::= IRIMETA? (ATOMIC | 'And' '(' ATOMIC* ')') ':-' FORMULA
 PROFILE   ::= TERM

For convenience, we reproduce the condition language part of RIF-FLD.the other componentsEBNF below.

  FORMULA        ::= IRIMETA? 'And' '(' FORMULA* ')' |
                     IRIMETA? 'Or' '(' FORMULA* ')' |
                     IRIMETA? 'Exists' Var+ '(' FORMULA ')' |
                     ATOMIC |
                     IRIMETA? 'External' '(' Atom | Frame ')'
  ATOMIC         ::= IRIMETA? (Atom | Equal | Member | Subclass | Frame)
  Atom           ::= UNITERM
  UNITERM        ::= Const '(' (TERM* | (Name '->' TERM)*) ')'
  Equal          ::= TERM '=' TERM
  Member         ::= TERM '#' TERM
  Subclass       ::= TERM '##' TERM
  Frame          ::= TERM '[' (TERM '->' TERM)* ']'
  TERM           ::= IRIMETA? (Const | Var | Expr | 'External' '(' Expr ')')
  Expr           ::= UNITERM
  Const          ::= '"' UNICODESTRING '"^^' SYMSPACE | CONSTSHORT
  IRICONST       ::= '"' IRI '"^^' 'rif:iri'
  Name           ::= UNICODESTRING
  Var            ::= '?' UNICODESTRING
  SYMSPACE       ::= ANGLEBRACKIRI | CURIE
 
  IRIMETA        ::= '(*' IRICONST? (Frame | 'And' '(' Frame* ')')? '*)'

Recall that an IRI has the form of I are total mappings definedan internationalized resource identifier as follows: I C maps Const to D . This mapping interprets constant symbols. In addition: Ifdefined by [RFC-3987].

A constant, c  ∈  Const , denotesRIF-BLD Document consists of an individual then it is required that I C ( c ) ∈  D ind . If c  ∈  Constoptional Base, denotes a function symbol (positional or with named arguments) then it is required that I C ( c ) ∈  D func . I V maps Var to D indfollowed by any number of Prefixes, followed by any number of Imports, followed by an optional Group. This mapping interprets variable symbols. I F maps DBase and Prefix just serve as shortcut mechanisms for (long) IRIs. An Import indicates the location of a document to functions D* ind → D (here D* indbe imported and an optional profile. A RIF-BLD Group is a setnested collection of all sequencesany number of RULE elements along with any finite length overnumber of nested Groups.

Rules are generated using CLAUSE elements. The domain D ind ) This mapping interprets positional terms.RULE production has two alternatives:

• In addition: If d ∈ D func then I F ( d ) must be a function D* ind → D ind . This means that whenthe first, a function symbolCLAUSE is applied to argumentsin the scope of the Forall quantifier. In that case, all variables mentioned in CLAUSE are individual objects then the result is also an individual object. I SF maps Drequired to also appear among the set of total functionsvariables in the Var+ sequence.
• In the second alternative, CLAUSE appears on its own. In that case, CLAUSE cannot have variables.

Frame, Var, ATOMIC, and FORMULA were defined as part of the form SetOfFiniteSets ( ArgNames × D ind ) → Dsyntax for positive conditions in Section EBNF for RIF-BLD Condition Language. This mapping interprets function symbols with named arguments.In addition: If d ∈ D func then I SF ( d ) must be a function SetOfFiniteSets ( ArgNames × D ind ) → D ind . This is analogous tothe interpretation of positional terms with two differences: Each pair < s,v > ∈ ArgNames × D ind representsCLAUSE production, an argument/value pair instead of justATOMIC is what is usually called a value in the case offact. An Implies rule can have an ATOMIC or a positional term. The argumentsconjunction of ATOMIC elements as conclusion; it has a term with named arguments constitute a finite set of argument/value pairs rather thanFORMULA as premise. Note that, by a finite ordered sequencedefinition in Section Formulas, formulas that query externally defined atoms (i.e., formulas of simple elements. So,the order ofform External(Atom(...))) are not allowed in the argumentsconclusion part of a rule (ATOMIC does not matter. I frame maps D indexpand to total functions of the form SetOfFiniteBags ( D ind × D ind ) → D .External).

Example 3 (RIF-BLD rules).

This mapping interprets frame terms. An argument, d ∈ D ind , to I frame representexample shows a business rule borrowed from the document RIF Use Cases and Requirements:

As before, for better readability we use the attribute/value pairscompact URI notation defined in a frame is immaterial[[RIF-DTB], Section Constants and pairs may repeat: o[a->b a->b]Symbol Spaces. 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 ?CAgain, prefix directives are instantiated withassumed in the symbol a and ?B , ?D with b . I sub gives meaningpreamble to the subclass relationship. It is a mappingdocument. Then, two versions of the form D ind × D ind → D .main part of the operator ## is required to be transitive, i.e., c1 ## c2 and c2 ## c3 must imply c1 ## c3 .document are given.

Prefix(ppl  http://example.com/people#)
Prefix(cpt  http://example.com/concepts#)
Prefix(func http://www.w3.org/2007/rif-builtin-function#)
Prefix(pred http://www.w3.org/2007/rif-builtin-predicate#)

a. Universal form:

   Forall ?item ?deliverydate ?scheduledate ?diffduration ?diffdays (
        cpt:reject(ppl:John ?item) :-
            And(cpt:perishable(?item)
                cpt:delivered(?item ?deliverydate ppl:John)
                cpt:scheduled(?item ?scheduledate)
                ?diffduration = External(func:subtract-dateTimes(?deliverydate ?scheduledate))
                ?diffdays = External(func:days-from-duration(?diffduration))
                External(pred:numeric-greater-than(?diffdays 10)))
   )

b. Universal-existential form:

   Forall ?item (
        cpt:reject(ppl:John ?item ) :-
            Exists ?deliverydate ?scheduledate ?diffduration ?diffdays (
                 And(cpt:perishable(?item)
                     cpt:delivered(?item ?deliverydate ppl:John)
                     cpt:scheduled(?item ?scheduledate)
                     ?diffduration = External(func:subtract-dateTimes(?deliverydate ?scheduledate))
                     ?diffdays = External(func:days-from-duration(?diffduration))
                     External(pred:numeric-greater-than(?diffdays 10)))
            )
   )

Example 4 (A RIF-BLD document containing an annotated group).

This is ensured byexample shows a restriction in Section Interpretation of Formulas . I isa gives meaning to class membership. It iscomplete document containing a mapping of the form D ind × D ind → D . The relationships # and ## are required to have the usual propertygroup formula that all members of a subclass are also membersconsists of two RIF-BLD rules. The superclass, i.e., o # cl and cl ## scl must imply o # scl . This is ensured by a restriction in Section Interpretationfirst of Formulas . I =these rules is a mappingcopied from Example 3a. The group is annotated with an IRI identifier and frame-represented Dublin Core metadata.

Document(
  Prefix(ppl  http://example.com/people#)
  Prefix(cpt  http://example.com/concepts#)
  Prefix(dc   http://purl.org/dc/terms/)
  Prefix(func http://www.w3.org/2007/rif-builtin-function#)
  Prefix(pred http://www.w3.org/2007/rif-builtin-predicate#)
  Prefix(xs   http://www.w3.org/2001/XMLSchema#)
  
  (* "http://sample.org"^^rif:iri pd[dc:publisher -> http://www.w3.org/
                                     dc:date -> "2008-04-04"^^xs:date] *)
  Group
  (
    Forall ?item ?deliverydate ?scheduledate ?diffduration ?diffdays (
        cpt:reject(ppl:John ?item) :-
            And(cpt:perishable(?item)
                cpt:delivered(?item ?deliverydate ppl:John)
                cpt:scheduled(?item ?scheduledate)
                ?diffduration = External(func:subtract-dateTimes(?deliverydate ?scheduledate))
                ?diffdays = External(func:days-from-duration(?diffduration))
                External(pred:numeric-greater-than(?diffdays 10)))
    )
 
    Forall ?item (
        cpt:reject(ppl:Fred ?item) :- cpt:unsolicited(?item)
    )
  )
)