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This document, developed by the Rule Interchange Format (RIF) Working Group, specifies a basic format that allows logic rules to be exchanged between rule-based systems.
A separate document RIF Data Types and Built-Ins describes data types and built-in functions and predicates.
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Contents |
This document 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 with a standard first-order semantics. 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. In addition, the document RIF RDF and OWL Compatibility 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:
This version of the RIF-BLD specification is very short and is presented at the end of this document, in Section RIF-BLD as a Specialization of the RIF Framework. It is intended for the reader who is familiar with RIF-FLD and, therefore, does not need to go through the much longer direct specification of RIF-BLD. This version of the specification 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.
Logic-based RIF dialects that extend RIF-BLD in accordance with the RIF Framework for Logic Dialects will be specified in other documents by this working group.
Editor's Note:
This document is the latest draft of the RIF-BLD specification. A
number of extensions areis planned to support import of RIF documents,
the notion of RIF compliance, and a few others. Tool support for
RIF-BLD is forthcoming.
This normative section specifies the syntax of RIF-BLD directly, without relying on RIF-FLD. We define both a presentation syntax and an XML syntax. The presentation syntax is 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 version of this document might introduce syntactic shortcuts to simplify writing the examples and test cases.
Definition (Alphabet). The alphabet of RIF-BLD consists of
The set of connective symbols, quantifiers, =, etc., is disjoint from Const and Var. The argument names in ArgNames are written as unicode strings that must not start with a question mark, "?". Variables are written as Unicode strings preceded with the symbol "?".
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 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.
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).
The symbol Document is used to define RIF-BLD
documents, Import is an import directive, and the symbol
Group is used to organize RIF-BLD rulesformulas into
collections and annotate themoptionally annotated with metadata. ☐
The language of RIF-BLD is the set of formulas constructed using the above alphabet according to the rules given below.
RIF-BLD supportsdefines several kinds of terms: constants and
variables, positional terms, terms with named
arguments, plus equality, membership,
andsubclass atomic formulas, and, frame formulas., and external terms. The word
"term" will be used to refer to any of these constructs.
To simplify the language in the next definition, we will use the following terminology:
Definition (Term).
The constant t here represents a predicate or a function; s1, ..., sn represent argument names; and v1, ..., vn represent argument values. The argument names, s1, ..., sn, 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.
Membership, subclass, and frame terms are used to describe objects and class hierarchies.
Such terms are used for representing builtin 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. ☐
The set of all symbols, Const, is partitioned into
The symbols in Const that belong to the supported RIF data types are individuals.
Each predicate and function symbol has precisely one arity.
The arity of a symbol (or whether it is a predicate, a function, or an individual) is not specified in RIF-BLD explicitly. Instead, it is inferred as follows. Each constant symbol, p, in a RIF-BLD formula (or a set of formulas) may occur in at most one context:
This means that p is a term by itself, which appears inside some other term (positional, with named arguments, in a frame, etc.).
This means that p occurs in a term t of the form p(...) and t itself occurs inside some other term.
This means that p occurs in a term t of the form p(...) and t does not occur inside some other term.
The arity of the symbol and its type is determined by its context. If a symbol from Const occurs in more than one context in a set of formulas, the set is not well-formed in RIF-BLD.
For a term 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 defined in Section Schemas for Externally Defined Terms of RIF-FLD.
Also, if a term of the form External(p(...)) occurs as an atomic formula then p is considered a predicate symbol.
Editor's Note: The definition of external schemas will eventually also appear in the document Data Types and Builtins, so the above reference will be to that document instead of RIF-FLD.
A well-formed
term is one that occurs in a well-formed set of
fomulas.
Any term (positional or with named arguments) of the form
p(...) (or External(p(...)), where p is a predicate symbol, is also an
atomic formula. Equality, membership, subclass, and
frame terms are also atomic formulas. A formulastatement of the form
External(p(...))External(φ), where φ is an atomic formula, is
also an atomic 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 formula that is also a well-formed term (see Section Well-formedness of Terms). More general formulas are constructed out of the atomic formulas with the help of logical connectives.
Definition (Well-formed formula). A well-formed formula is a statement that has one of the following forms:
Formulas constructed using the above definitions are called RIF-BLD conditions. The following defines the notion of a RIF-BLD rule.
Group formulas are used to represent sets of rules annotated with metadata. This metadata is specified using an optional frame term φ. Note that some of the ρi's can be group formulas themselves, which means that groups can be nested. This allows one to attach metadata to various subsets of rules, which may be inside larger rule sets, which in turn can be annotated.
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. 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).
It can be seen from the definitions that RIF-BLD has a wide variety of syntactic forms for terms and formulas. This provides the infrastructure for exchanging rule languages that support rich collections of syntactic forms. 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).
So far, the syntax of RIF-BLD has been specified in mathematical English. Tool developers, however, may prefer EBNF notation, which provides a more succinct overview of the syntax. Several points should be kept in mind regarding this notation.
The Condition Language represents formulas that can be used in the body of RIF-BLD rules. The EBNF grammar for a superset of the RIF-BLD condition language is as follows.
FORMULA ::= 'And' '(' FORMULA* ')' | 'Or' '(' FORMULA* ')' | 'Exists' Var+ '(' FORMULA ')' | ATOMIC | 'External' '(' ATOMIC ')' ATOMIC ::= 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 ::= Const | Var | Expr | 'External' '(' Expr ')' Expr ::= UNITERM Const ::= '"' UNICODESTRING '"^^' SYMSPACE Name ::= UNICODESTRING Var ::= '?' UNICODESTRING SYMSPACE ::= UNICODESTRING
The production rule for the non-terminal FORMULA
represents RIF condition formulas (defined earlier). The
connectives And and Or define conjunctions and
disjunctions of conditions, respectively. Exists
introduces existentially quantified variables. Here Var+
stands for the list of variables that are free in FORMULA.
RIF-BLD conditions permit only existential variables. A RIF-BLD
FORMULA can also be an ATOMIC term, i.e. an
Atom, External Atom, Equal,
Member, Subclass, or Frame. A
TERM can be a constant, variable, Expr, or
External Expr.
The RIF-BLD presentation syntax does not commit to any
particular vocabulary except for usingand permits arbitrary Unicode strings in
constant symbols, asargument names, and for variables (where UNICODESTRING does not start with a special character such as the ?-sign).variables. Constant symbols
have the form: "UNICODESTRING"^^SYMSPACE, where
SYMSPACE is a Unicode string that represents an identifier
or an alias of the symbol space of the constant, and
UNICODESTRING is a Unicode string from the lexical space
of that symbol space. Names are denoted by Unicode character
sequences. Variables are denoted by a UNICODESTRING
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 collection of
attribute-value pairs. An External(ATOMIC) is a
call to an externally defined predicate, equality, membership,
subclassing, or frame. Likewise, External(Expr)
is a call to an externally defined function.
Example 1 (RIF-BLD conditions).
This example shows conditions that are composed of atoms, expressions, frames, and existentials. In frame formulas variables are shown in the positions of object Ids, object properties, and property values. For brevity, we use the compact URI notation [CURIE], prefix:suffix, which should be understood as a macro that expands into a concatenation of the prefix definition and suffix. Thus, if bks is a prefix that expands into http://example.com/books# then bks:LeRif should be understood merely as an abbreviation for http://example.com/books#LeRif. The compact URI notation is not part 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)) Terms 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]))
The presentation syntax for RIF-BLD rules extends the syntax in Section EBNF for RIF-BLD Condition Language with the following productions.
Editor's Note: The metadata syntax and the approach to rule identification presented in this draft are currently under discussion by the Working Group. Input 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 ':-' FORMULAEditor'sNote:IRI ::= UNICODESTRING PROFILE ::= UNICODESTRING
For convenient reference, we reproduce the metadata syntax and the approach to rule identification presented in this draft are currently under discussion bycondition language
part of the Working Group. Input is welcome. See Issue-51EBNF below.
FORMULA ::= 'And' '(' FORMULA* ')' | 'Or' '(' FORMULA* ')' | 'Exists' Var+ '(' FORMULA ')' | ATOMIC | 'External' '(' ATOMIC ')' ATOMIC ::= 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 ::= Const | Var | Expr | 'External' '(' Expr ')' Expr ::= UNITERM Const ::= '"' UNICODESTRING '"^^' SYMSPACE Name ::= UNICODESTRING Var ::= '?' UNICODESTRING SYMSPACE ::= UNICODESTRING
A RIF-BLD Document consists of an optional
Directive and an optional Group annotated with
optional metadata, IRIMETA. A Directive can
contain any number of Imports. A RIF-BLD Group is
a nested collection of RIF-BLD rules annotated with optional
metadata, IRIMETA ,. IRIMETA are represented as
Frames. A Group can contain any number of
RULEs along with any number of nested Groups.
Rules are generated by CLAUSE, which can be in the scope
of a Forall quantifier. If a CLAUSE in the
RULE production has a free (non-quantified) variable, it
must occur in the Var+ sequence. Frame,
Var, ATOMIC, and FORMULA were defined as
part of the syntax for positive conditions in Section EBNF for RIF-BLD Condition
Language. In the CLAUSE production an ATOMIC
is treated as a rule with an empty condition part -- in which case
it is usually called a fact. Note that, by a definition in
Section Formulas, formulas
that query externally defined atoms (i.e., formulas of the form
External(Atom(...))) are not allowed in the conclusion
part of a rule (ATOMIC does not expand to
External).
Example 2 (RIF-BLD rules).
This example shows a business rule borrowed from the document RIF Use Cases and Requirements:
As before, for better readability 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 IRI 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 group is annotated with Dublin Core metadata represented as a frame.
Compact URI prefixes:bksexpandsintohttp://example.com/books#authppl expands intohttp://example.com/authors#http://example.com/people# cpt expands into http://example.com/concepts# dc expands intohttp://dublincore.org/documents/dces/http://purl.org/dc/terms/ w3 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) ) )
This normative section specifies the semantics of RIF-BLD directly, without relying on RIF-FLD.
The set TV of truth values in RIF-BLD consists of just two values, t and f.
The key concept in a model-theoretic semantics of a logic language is the notion of a semantic structure. The definition, below, 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). A semantic structure, I, is a tuple of the form <TV, DTS, D, Dind, Dfunc, IC, IV, IF, Iframe, ISF, Isub, Iisa, I=, Iexternal, Itruth>. Here D is a non-empty set of elements called the domain of I, and Dind, Dfunc are nonempty subsets of D. Dind is used to interpret the elements of Const, which denote individuals and Dfunc is used to interpret the elements of Const, which denote function symbols. As before, 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 the set of primitive data types used in I (please refer to Section Primitive Data Types of RIF-FLD for the semantics of data types).
Editor's Note: In the future versions of this document, the above reference will point to the document Data Types and Builtins instead of RIF-FLD.
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. In addition:
This mapping interprets function symbols with named arguments. In addition:
This mapping interprets frame terms. An argument, d ∈ Dind, to Iframe represent an object and the finite bag {<a1,v1>, ..., <ak,vk>} represents a bag of attribute-value pairs for d. We will see shortly how Iframe is used to determine the truth valuation of frame terms.
Bags (multi-sets) are used here because the order of the
attribute/value pairs in a frame is immaterial and pairs may
repeat: 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 variablevariables ?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. This is ensured by a restriction in Section Interpretation of 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 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 builtin predicate or function, Iexternal(σ) is specified in the document Data Types and Builtins so that:
For convenience, we also define the following mapping I from terms to D:
Here we use {...} to denote a set of argument/value pairs.
Here {...} denotes a bag of attribute/value pairs.
Note that, by definition, External(t) is well formed only if t is an instance of an external schema. Furthermore, by the definition of coherent sets of external schemas, t can be an instance of at most one such schema, so I(External(t)) is well-defined.
The effect of data types. The data types in DTS impose the following restrictions. If dt is a symbol space identifier of a data type, 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 Data Types of RIF-FLD). Then the following must hold:
That is, IC must map the constants of a data type dt in accordance with Ldt.
RIF-BLD does not impose restrictions on IC for constants in the lexical spaces that do not correspond to primitive datatypes in DTS. ☐
Definition (Truth valuation). Truth valuation for well-formed formulas in RIF-BLD is determined using the following function, denoted TValI:
To ensure that the operator ## is transitive, i.e., c1 ## c2 and c2 ## c3 imply c1 ## c3, the following is required:
To ensure that all members of a subclass are also members of the superclass, i.e., o # cl and cl ## scl implies o # scl, the following is required:
Since the bag of attribute/value pairs represents the conjunctions of all the pairs, the following is required:
Note that, by definition, External(t) is well-formed only if t is an instance of an external schema. Furthermore, by the definition of coherent sets of external schemas, t can be an instance of at most one such schema, so I(External(t)) is well-defined.
The empty conjunction is treated as a tautology, so TValI(And()) = t.
The empty disjunction is treated as a contradiction, so TValI(Or()) = f.
Here I* is a semantic structure of the form <TV, DTS, D, Dind, Dfunc, IC, I*V, IF, Iframe, ISF, Isub, Iisa, I=, Iexternsl, Itruth>, which is exactly like I, except that the mapping I*V, is used instead of IV. I*V is defined to coincide with IV on all variables except, possibly, on ?v1,...,?vn.
If Γ is a group formula of the form Group φ (ρ1 ... ρn) or Group (ρ1 ... ρn) then
This means that a group of rules is treated as a conjunction. The metadata is ignored for purposes of the RIF-BLD semantics.
A model of a group of rules,formula, Γ, is a
semantic structure I such that
TValI(Γ) = t. In this case, we
write I |= Γ. ☐
Note that although metadata associated with RIF-BLD formulas is ignored by the semantics, it can be extracted by XML tools. Since metadata is represented by frame terms, it can be reasoned with by RIF-BLD rules.
Document formulas are interpreted using semantic multi-structures.
Definition (Semantic multi-structures). A semantic multi-structure is a tuple (I1, ..., In), n>0, where I1, ..., In are semantic structures, which are identical in all respects except that the mappings I1C, ..., InC may differ on the constants in Const that belong to the rif:local symbol space. ☐
Definition (Imported document). Let Δ be a document
formula and Import(t) be one of its import directives,
which references another document formula, Δ'. In this
case, we same that Δ' is directly imported
into Δ.
A document formula Δ' is said to be imported into Δ if it is either directly imported into Δ or it is imported (directly or not) into another formula, which is directly imported into Δ. ☐
With the help of semantic multi-structures we can now explain the semantics of RIF documents.
Definition (Truth valuation of document formulas). Let Δ be a document formula and let Δ1, ..., Δk be all the RIF-BLD document formulas that are imported (directly or indirectly, according to the previous definition) into Δ. Let Γ, Γ1, ..., Γk denote the respective group formulas associated with these documents. If any of these Γi is missing (which is a possibility, since every part of a document is optional), assume that it is a tautology, such as a = a, so that every TVal function maps such a Γi to the truth value t. Let I = (I0, I1, ..., In) be a semantic multi-structure such that n≥k. Then we define:
Note that this definition considers only those document formulas that are reachable via the one-argument import directives. Two argument import directives are ignored here. Their semantics is defined by the document RIF RDF and OWL Compatibility. ☐
The above definitions make the intent behind the rif:local
constants clear: rif:local constants that occur in
different documents can be interpreted differently even if they
have the same name. Therefore, each document can choose the names
for the rif:local constants freely and without regard to
the names of such constants used in the imported documents.
A model of a document formula Δ is a semantic multi-structure I such that TValI(Δ) = t. In this case, we write I |= Δ.
We now define what it means for a set of RIF-BLD rules (such as a group or a document formula) to entail a RIF-BLD condition. We say that a RIF-BLD condition formula φ is existentially closed, if and only if every variable, ?V, in φ occurs in a subformula of the form Exists ...?V...(ψ).
Definition (Logical entailment). Let Γ be a RIF-BLD group or document formula and φ an existentially closed RIF-BLD condition formula. We say that Γ entails φ, written as Γ |= φ, if and only if for every model of Γ it is the case that TValI(φ) = t.
Equivalently, we can say that Γ |= φ holds iff whenever I |= Γ it follows that also I |= φ. ☐
Editor's Note: The XML syntax, including the element tags, is being discussed by the Working Group. Input is welcome. See Issue-49
The XML serialization for RIF-BLD is alternating or fully
striped [ANF01]. A fully striped serialization views XML documents as
objects and divides all XML tags into class descriptors, called
type tags, and property descriptors, called role
tags. We use capitalized names for type tags and lowercase
names for role tags.
The all-uppercase classes in the presentation syntax, such as FORMULA, become XML Schema groups in Appendix XML Schema for BLD. They act like macros and are not visible in instance markup. The other classes as well as non-terminals and symbols (such as Exists or =) become XML elements with optional attributes, as shown below.
XML serialization of the presentation syntax of Section EBNF for RIF-BLD Condition Language uses the following tags.
- And (conjunction) - Or (disjunction) - Exists (quantified formula for 'Exists', containing declare and formula roles) - declare (declare role, containing a Var) - formula (formula role, containing a FORMULA) - Atom (atom formula, positional or with named arguments) - External (external call, containing a content role) - content (content role, containing an Atom, for predicates, or Expr, for functions) - Member (member formula) - Subclass (subclass formula) - Frame (Frame formula) - object (Member/Frame role, containing a TERM or an object description) - op (Atom/Expr role for predicates/functions as operations) - arg (positional argument role) - upper (Member/Subclass upper class role) - lower (Member/Subclass lower instance/class role) - slot (Atom/Expr/Frame slot role, containing a Prop) - Prop (Property, prefix version of slot infix '->') - key (Prop key role, containing a Const) - val (Prop val role, containing a TERM) - Equal (prefix version of term equation '=') - Expr (expression formula, positional or with named arguments) - side (Equal left-hand side and right-hand side role) - Const (individual, function, or predicate symbol, with optional 'type' attribute) - Name (name of named argument) - Var (logic variable)
For the XML Schema Definition (XSD) of the RIF-BLD condition language see Appendix XML Schema for BLD.
The XML syntax for symbol spaces utilizes the type attribute associated with XML term elements such as Const. For instance, a literal in the xsd:dateTime data type can be represented as <Const type="xsd:dateTime">2007-11-23T03:55:44-02:30</Const>.
Example 4 (A RIF condition and its XML serialization).
This example illustrates XML serialization for RIF conditions. As before, the compact URI notation is used for better readability.
Compact URI prefixes: bks expands into http://example.com/books# cpt expands into http://example.com/concepts# curr expands into http://example.com/currencies#
RIF condition And (Exists ?Buyer ("cpt:purchase"^^rif:iri(?Buyer ?Seller "cpt:book"^^rif:iri(?Author "bks:LeRif"^^rif:iri) "curr:USD"^^rif:iri("49"^^xsd:integer))) ?Seller=?Author ) XML serialization <And> <formula> <Exists> <declare><Var>Buyer</Var></declare> <formula> <Atom> <op><Const type="rif:iri">cpt:purchase</Const></op> <arg><Var>Buyer</Var></arg> <arg><Var>Seller</Var></arg> <arg> <Expr> <op><Const type="rif:iri">cpt:book</Const></op> <arg><Var>Author</Var></arg> <arg><Const type="rif:iri">bks:LeRif</Const></arg> </Expr> </arg> <arg> <Expr> <op><Const type="rif:iri">curr:USD</Const></op> <arg><Const type="xsd:integer">49</Const></arg> </Expr> </arg> </Atom> </formula> </Exists> </formula> <formula> <Equal> <side><Var>Seller</Var></side> <side><Var>Author</Var></side> </Equal> </formula> </And>
Example 5 (A RIF condition with named arguments and its XML
serialization).
This example illustrates XML serialization of RIF conditions that involve terms with named arguments.
Compact URI prefixes: bks expands into http://example.com/books#authexpandsintohttp://example.com/authors#cpt expands into http://example.com/concepts# curr expands into http://example.com/currencies#
RIF condition: And (Exists ?Buyer ?P ( And (?P#"cpt:purchase"^^rif:iri ?P["cpt:buyer"^^rif:iri->?Buyer "cpt:seller"^^rif:iri->?Seller "cpt:item"^^rif:iri->"cpt:book"^^rif:iri(cpt:author->?Author cpt:title->"bks:LeRif"^^rif:iri) "cpt:price"^^rif:iri->"49"^^xsd:integer "cpt:currency"^^rif:iri->"curr:USD"^^rif:iri])) ?Seller=?Author) XML serialization: <And> <formula> <Exists> <declare><Var>Buyer</Var></declare> <declare><Var>P</Var></declare> <formula> <And> <formula> <Member> <lower><Var>P</Var></lower> <upper><Const type="rif:iri">cpt:purchase</Const></upper> </Member> </formula> <formula> <Frame> <object> <Var>P</Var> </object> <slot> <Prop> <key><Const type="rif:iri">cpt:buyer</Const></key> <val><Var>Buyer</Var></val> </Prop> </slot> <slot> <Prop> <key><Const type="rif:iri">cpt:seller</Const></key> <val><Var>Seller</Var></val> </Prop> </slot> <slot> <Prop> <key><Const type="rif:iri">cpt:item</Const></key> <val> <Expr> <op><Const type="rif:iri">cpt:book</Const></op> <slot> <Prop> <key><Name>cpt:author</Name></key> <val><Var>Author</Var></val> </Prop> </slot> <slot> <Prop> <key><Name>cpt:title</Name></key> <val><Const type="rif:iri">bks:LeRif</Const></val> </Prop> </slot> </Expr> </val> </Prop> </slot> <slot> <Prop> <key><Const type="rif:iri">cpt:price</Const></key> <val><Const type="xsd:integer">49</Const></val> </Prop> </slot> <slot> <Prop> <key><Const type="rif:iri">cpt:currency</Const></key> <val><Const type="rif:iri">curr:USD</Const></val> </Prop> </slot> </Frame> </formula> </And> </formula> </Exists> </formula> <formula> <Equal> <side><Var>Seller</Var></side> <side><Var>Author</Var></side> </Equal> </formula> </And>
We now extend the RIF-BLD serialization from Section XML for RIF-BLD Condition Language by including rules as described in Section EBNF for RIF-BLD Rule Language. The extended serialization uses the following additional tags.
- Document (document, containing directives and optional payload annotated with metadata) - directive (directive role, containing Import) - payload (payload role, containing Group) - Import (importation, containing address and optional manner) - address (address role, containing IRI) - manner (manner role, containing PROFILE) - Group (nested collection of sentences annotated with metadata) - meta (meta role, containing metadata, which is represented as a Frame) - sentence (sentence role, containing RULE or Group) - Forall (quantified formula for 'Forall', containing declare and formula roles) - Implies (implication, containing if and then roles) - if (antecedent role, containing FORMULA) - then (consequent role, containing ATOMIC)
The XML Schema Definition of RIF-BLD is given in Appendix XML Schema for BLD.
Example 6 (Serializing a RIF-BLD group annotated with
metadata).
This example shows a serialization for the group from Example 3. For convenience, the group is reproduced at the top and then is followed by its serialization.
Compact URI prefixes: bks expands into http://example.com/books# auth expands into http://example.com/authors# cpt expands into http://example.com/concepts# dc expands intohttp://dublincore.org/documents/dces/http://purl.org/dc/terms/ w3 expands into http://www.w3.org/
Presentation syntax: 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) ) ) XML syntax: <Group> <meta> <Frame> <object> <Const type="rif:iri">http://sample.org</Const> </object> <slot> <Prop> <key><Const type="rif:iri">dc:publisher</Const></key> <val><Const type="rif:iri">w3:W3C</Const></val> </Prop> </slot> <slot> <Prop> <key><Const type="rif:iri">dc:date</Const></key> <val><Const type="xsd:date">2008-04-04</Const></val> </Prop> </slot> </Frame> </meta> <sentence> <Forall> <declare><Var>item</Var></declare> <declare><Var>deliverydate</Var></declare> <declare><Var>scheduledate</Var></declare> <declare><Var>diffduration</Var></declare> <declare><Var>diffdays</Var></declare> <formula> <Implies> <if> <And> <formula> <Atom> <op><Const type="rif:iri">cpt:perishable</Const></op> <arg><Var>item</Var></arg> </Atom> </formula> <formula> <Atom> <op><Const type="rif:iri">cpt:delivered</Const></op> <arg><Var>item</Var></arg> <arg><Var>deliverydate</Var></arg> <arg><Const type="rif:iri">ppl:John</Const></arg> </Atom> </formula> <formula> <Atom> <op><Const type="rif:iri">cpt:scheduled</Const></op> <arg><Var>item</Var></arg> <arg><Var>scheduledate</Var></arg> </Atom> </formula> <formula> <External> <content> <Atom> <op><Const type="rif:iri">fn:subtract-dateTimes-yielding-dayTimeDuration</Const></op> <arg><Var>deliverydate</Var></arg> <arg><Var>scheduledate</Var></arg> <arg><Var>diffduration</Var></arg> </Atom> </content> </External> </formula> <formula> <External> <content> <Atom> <op><Const type="rif:iri">fn:get-days-from-dayTimeDuration</Const></op> <arg><Var>diffduration</Var></arg> <arg><Var>diffdays</Var></arg> </Atom> </content> </External> </formula> <formula> <External> <content> <Atom> <op><Const type="rif:iri">op:numeric-greater-than</Const></op> <arg><Var>diffdays</Var></arg> <arg><Const type="xsd:long">10</Const></arg> </Atom> </content> </External> </formula> </And> </if> <then> <Atom> <op><Const type="xsd:long">reject</Const></op> <arg><Const type="rif:iri">ppl:John</Const></arg> <arg><Var>item</Var></arg> </Atom> </then> </Implies> </formula> </Forall> </sentence> <sentence> <Forall> <declare><Var>item</Var></declare> <formula> <Implies> <if> <Atom> <op><Const type="rif:iri">cpt:unsolicited</Const></op> <arg><Var>item</Var></arg> </Atom> </if> <then> <Atom> <op><Const type="rif:iri">cpt:reject</Const></op> <arg><Const type="rif:iri">ppl:Fred</Const></arg> <arg><Var>item</Var></arg> </Atom> </then> </Implies> </formula> </Forall> </sentence> </Group>
We now show how to translate between the presentation and XML syntaxes of RIF-BLD.
Editor's Note: This XML syntax translation table is expected to be made more formal in future versions of this draft.
The translation between the presentation syntax and the XML syntax of the RIF-BLD Condition Language is specified by the table below. Since the presentation syntax of RIF-BLD is context sensitive, the translation must differentiate between the terms that occur in the position of the individuals from terms that occur as atomic formulas. To this end, in the translation table, the positional and named argument terms that occur in the context of atomic formulas are denoted by the expressions of the form pred(...) and the terms that occur as individuals are denoted by expressions of the form func(...).
The prime symbol (for instance, variable') indicates that the translation function defined by the table must be applied recursively (i.e., to variable in our example).
Presentation Syntax | XML Syntax |
---|---|
And ( conjunct1 . . . conjunctn ) |
<And> <formula>conjunct1'</formula> . . . <formula>conjunctn'</formula> </And> |
Or ( disjunct1 . . . disjunctn ) |
<Or> <formula>disjunct1'</formula> . . . <formula>disjunctn'</formula> </Or> |
Exists variable1 . . . variablen ( body ) |
<Exists> <declare>variable1'</declare> . . . <declare>variablen'</declare> <formula>body'</formula> </Exists> |
pred ( argument1 . . . argumentn ) |
<Atom> <op>pred'</op> <arg>argument1'</arg> . . . <arg> argumentn'</arg> </Atom> |
External ( |
<External> <content> |
func ( argument1 . . . argumentn ) |
<Expr> <op>func'</op> <arg>argument1'</arg> . . . <arg> argumentn'</arg> </Expr> |
pred ( unicodestring1 -> filler1 . . . unicodestringn -> fillern ) |
<Atom> <op>pred'</op> <slot> <Prop> <key><Name>unicodestring1</Name></key> <val>filler1'</val> </Prop> </slot> . . . <slot> <Prop> <key><Name>unicodestringn</Name></key> <val>fillern'</val> </Prop> </slot> </Atom> |
func ( unicodestring1 -> filler1 . . . unicodestringn -> fillern ) |
<Expr> <op>func'</op> <slot> <Prop> <key><Name>unicodestring1</Name></key> <val>filler1'</val> </Prop> </slot> . . . <slot> <Prop> <key><Name>unicodestringn</Name></key> <val>fillern'</val> </Prop> </slot> </Expr> |
inst [ key1 -> filler1 . . . keyn -> fillern ] |
<Frame> <object>inst'</object> <slot> <Prop> <key>key1'</key> <val>filler1'</val> </Prop> </slot> . . . <slot> <Prop> <key>keyn'</key> <val>fillern'</val> </Prop> </slot> </Frame> |
inst # class |
<Member> <lower>inst'</lower> <upper>class'</upper> </Member> |
sub ## super |
<Subclass> <lower>sub'</lower> <upper>super'</upper> </Subclass> |
left = right |
<Equal> <side>left'</side> <side>right'</side> </Equal> |
unicodestring^^space |
<Const type="space">unicodestring</Const> |
?unicodestring |
<Var>unicodestring</Var> |
The translation between the presentation syntax and the XML syntax of the RIF-BLD Rule Language is given by the table below, which extends the translation table of Section Translation of RIF-BLD Condition Language.
Presentation Syntax | XML Syntax |
---|---|
Group ( clause1 . . . clausen ) |
<Group> <sentence>clause1'</sentence> . . . <sentence>clausen'</sentence> </Group> |
Group metaframe ( clause1 . . . clausen ) |
<Group> <meta>metaframe'</meta> <sentence>clause1'</sentence> . . . <sentence>clausen'</sentence> </Group> |
Forall variable1 . . . variablen ( rule ) |
<Forall> <declare>variable1'</declare> . . . <declare>variablen'</declare> <formula>rule'</formula> </Forall> |
conclusion :- condition |
<Implies> <if>condition'</if> <then>conclusion'</then> </Implies> |
This normative section describes RIF-BLD by specializing RIF-FLD. The reader is assumed to be familiar with RIF-FLD as described in RIF Framework for Logic-Based Dialects. The reader who is not interested in how RIF-BLD is derived from the framework can skip this section.
This section defines the precise relationship between the syntax of RIF-BLD and the syntactic framework of RIF-FLD.
The syntax of the RIF Basic Logic Dialect is defined by specialization from the syntax of the RIF Syntactic Framework for Logic Dialects. Section Syntax of a RIF Dialect as a Specialization of the RIF Framework in that document lists the parameters of the syntactic framework in mathematical English, which we will now specialize for RIF-BLD.
The signature set of RIF-BLD contains the following signatures:
The signature individual{ } represents the context
in which individual objects (but not atomic formulas) can
appear.
The signature atomic{ } represents the context where
atomic formulas can occur.
These represent function and predicate symbols of arity n (each of the above cases has n individuals as arguments inside the parentheses).
Thus, in RIF-BLD each constant symbol can be either an individual, a function of one particular arity or with certain argument names, a predicate of one particular arity or with certain argument names, an externally defined function of one particular arity, or an externally defined predicate symbol of one particular arity -- it is not possible for the same symbol to play more than one role.
This means that equality can compare only those terms whose signature is individual; it cannot compare predicate names or function symbols. Equality terms are also not allowed to occur inside other terms, since the above signature implies that any term of the form t = s has signature atomic and not individual.
Note that this precludes the possibility that a frame term might occur as an argument to a predicate, a function, or inside some other term.
Note that this precludes the possibility that a membership term might occur as an argument to a predicate, a function, or inside some other term.
As with frames and membership terms, this precludes the possibility that a subclass term might occur inside some other term.
RIF-BLD uses no special syntax for declaring signatures. Instead, the author specifies signatures contextually. That is, since RIF-BLD requires that each symbol is associated with a unique signature, the signature is determined from the context in which the symbol is used. If a symbol is used in more than one context, the parser must treat this as a syntax error. If no errors are found, all terms and atomic formulas are guaranteed to be well-formed. Thus, signatures are not part of the RIF-BLD language, and individual and atomic are not reserved keywords in RIF-BLD.
RIF-BLD supports all the symbol spaces defined in Section Symbol Spaces of the syntactic framework:
RIF-BLD supports the following types of formulas (see Well-formed Terms and Formulas for the definitions):
A RIF-BLD condition is an atomic formula, a conjunctive or disjunctive combination of atomic formulas with optional existential quantification of variables, or an external atomic formula.
A RIF-BLD rule is a universally quantified RIF-FLD rule with the following restrictions:
A RIF-BLD group is a RIF-FLD group that contains only RIF-BLD rules and RIF-BLD groups.
Recall that negation (classical or default) is not supported by RIF-BLD in either the rule head or the body.
Editor's Note: The list of supported symbol spaces will move to another document, Data Types and Built-Ins. Any existing discrepancies will be fixed at that time.
This normative section defines the precise relationship between the semantics of RIF-BLD and the semantic framework of RIF-FLD. Specification of the semantics that does not rely on RIF-FLD is given in Section Direct Specification of RIF-BLD Semantics.
The semantics of the RIF Basic Logic Dialect is defined by specialization from the semantics of the Semantic Framework for Logic Dialects of RIF. Section Semantics of a RIF Dialect as a Specialization of the RIF Framework in that document lists the parameters of the semantic framework, which one need to specialize. Thus, for RIF-BLD, we need to look at the following parameters:
RIF-BLD does not support negation. This is the only obvious simplification with respect to RIF-FLD as far as the semantics is concerned. The restrictions on the signatures of symbols in RIF-BLD do not affect the semantics in a significant way.
The set TV of truth values in RIF-BLD consists of just two values, t and f such that f <t t. The order <t is total.
RIF-BLD supports all the data types listed in Section Primitive Data Types of RIF-FLD:
Recall that logical entailment in RIF-FLD is defined with respect to an unspecified set of intended semantic structures and that dialects of RIF must make this notion concrete. For RIF-BLD, this set is defined in one of the two following equivalent ways:
These two definitions are equivalent for entailment of existentially closed RIF-BLD conditions by RIF-BLD sets of formulas, since all rules in RIF-BLD are Horn -- it is a classical result of Van Emden and Kowalski [vEK76].
Editor's Note: The list of supported data types will move to another document, Data Types and Built-Ins. Any existing discrepancies will be fixed at that time.
The namespace of RIF is http://www.w3.org/2007/rif#.
XML schemas for the RIF-BLD sublanguages are available below and online, with examples.
<?xml version="1.0" encoding="UTF-8"?> <xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns="http://www.w3.org/2007/rif#" targetNamespace="http://www.w3.org/2007/rif#" elementFormDefault="qualified" version="Id: BLDCond.xsd,v 0.8 2008-04-14 dhirtle/hboley"> <xs:annotation> <xs:documentation> This is the XML schema for the Condition Language as defined by Working Draft 2 of the RIF Basic Logic Dialect. The schema is based on the following EBNF for the RIF-BLD Condition Language: FORMULA ::= 'And' '(' FORMULA* ')' | 'Or' '(' FORMULA* ')' | 'Exists' Var+ '(' FORMULA ')' | ATOMIC | 'External' '(' ATOMIC ')' ATOMIC ::= 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 ::= Const | Var | Expr | 'External' '(' Expr ')' Expr ::= UNITERM Const ::= '"' UNICODESTRING '"^^' SYMSPACE Name ::= UNICODESTRING Var ::= '?' UNICODESTRING </xs:documentation> </xs:annotation> <xs:group name="FORMULA"> <xs:choice> <xs:element ref="And"/> <xs:element ref="Or"/> <xs:element ref="Exists"/> <xs:group ref="ATOMIC"/> <xs:element name="External" type="External-FORMULA.type"/> </xs:choice> </xs:group> <xs:complexType name="External-FORMULA.type"> <xs:sequence> <xs:element name="content" type="content-FORMULA.type"/> </xs:sequence> </xs:complexType> <xs:complexType name="content-FORMULA.type"> <xs:sequence> <xs:group ref="ATOMIC"/> </xs:sequence> </xs:complexType> <xs:element name="And"> <xs:complexType> <xs:sequence> <xs:element ref="formula" minOccurs="0" maxOccurs="unbounded"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Or"> <xs:complexType> <xs:sequence> <xs:element ref="formula" minOccurs="0" maxOccurs="unbounded"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Exists"> <xs:complexType> <xs:sequence> <xs:element ref="declare" minOccurs="1" maxOccurs="unbounded"/> <xs:element ref="formula"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="formula"> <xs:complexType> <xs:sequence> <xs:group ref="FORMULA"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="declare"> <xs:complexType> <xs:sequence> <xs:element ref="Var"/> </xs:sequence> </xs:complexType> </xs:element> <xs:group name="ATOMIC"> <xs:choice> <xs:element ref="Atom"/> <xs:element ref="Equal"/> <xs:element ref="Member"/> <xs:element ref="Subclass"/> <xs:element ref="Frame"/> </xs:choice> </xs:group> <xs:element name="Atom"> <xs:complexType> <xs:sequence> <xs:group ref="UNITERM"/> </xs:sequence> </xs:complexType> </xs:element> <xs:group name="UNITERM"> <xs:sequence> <xs:element ref="op"/> <xs:choice> <xs:element ref="arg" minOccurs="0" maxOccurs="unbounded"/> <xs:element name="slot" type="slot-UNITERM.type" minOccurs="0" maxOccurs="unbounded"/> </xs:choice> </xs:sequence> </xs:group> <xs:element name="op"> <xs:complexType> <xs:sequence> <xs:element ref="Const"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="arg"> <xs:complexType> <xs:sequence> <xs:group ref="TERM"/> </xs:sequence> </xs:complexType> </xs:element> <xs:complexType name="slot-UNITERM.type"> <xs:sequence> <xs:element name="Prop" type="Prop-UNITERM.type"/> </xs:sequence> </xs:complexType> <xs:complexType name="Prop-UNITERM.type"> <xs:sequence> <xs:element name="key" type="key-UNITERM.type"/> <xs:element ref="val"/> </xs:sequence> </xs:complexType> <xs:complexType name="key-UNITERM.type"> <xs:sequence> <xs:element ref="Name"/> </xs:sequence> </xs:complexType> <xs:element name="val"> <xs:complexType> <xs:sequence> <xs:group ref="TERM"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Equal"> <xs:complexType> <xs:sequence> <xs:element ref="side"/> <xs:element ref="side"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="side"> <xs:complexType> <xs:sequence> <xs:group ref="TERM"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Member"> <xs:complexType> <xs:sequence> <xs:element ref="lower"/> <xs:element ref="upper"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Subclass"> <xs:complexType> <xs:sequence> <xs:element ref="lower"/> <xs:element ref="upper"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="lower"> <xs:complexType> <xs:sequence> <xs:group ref="TERM"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="upper"> <xs:complexType> <xs:sequence> <xs:group ref="TERM"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Frame"> <xs:complexType> <xs:sequence> <xs:element ref="object"/> <xs:element name="slot" type="slot-Frame.type" minOccurs="0" maxOccurs="unbounded"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="object"> <xs:complexType> <xs:sequence> <xs:group ref="TERM"/> </xs:sequence> </xs:complexType> </xs:element> <xs:complexType name="slot-Frame.type"> <xs:sequence> <xs:element name="Prop" type="Prop-Frame.type"/> </xs:sequence> </xs:complexType> <xs:complexType name="Prop-Frame.type"> <xs:sequence> <xs:element name="key" type="key-Frame.type"/> <xs:element ref="val"/> </xs:sequence> </xs:complexType> <xs:complexType name="key-Frame.type"> <xs:sequence> <xs:group ref="TERM"/> </xs:sequence> </xs:complexType> <xs:group name="TERM"> <xs:choice> <xs:element ref="Const"/> <xs:element ref="Var"/> <xs:element ref="Expr"/> <xs:element name="External" type="External-TERM.type"/> </xs:choice> </xs:group> <xs:complexType name="External-TERM.type"> <xs:sequence> <xs:element name="content" type="content-TERM.type"/> </xs:sequence> </xs:complexType> <xs:complexType name="content-TERM.type"> <xs:sequence> <xs:element ref="Expr"/> </xs:sequence> </xs:complexType> <xs:element name="Expr"> <xs:complexType> <xs:sequence> <xs:group ref="UNITERM"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Const"> <xs:complexType mixed="true"> <xs:sequence/> <xs:attribute name="type" type="xs:string" use="required"/> </xs:complexType> </xs:element> <xs:element name="Name" type="xs:string"> </xs:element> <xs:element name="Var" type="xs:string"> </xs:element> </xs:schema>
<?xml version="1.0" encoding="UTF-8"?> <xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns="http://www.w3.org/2007/rif#" targetNamespace="http://www.w3.org/2007/rif#" elementFormDefault="qualified" version="Id: BLDRule.xsd,v 0.8 2008-04-09 dhirtle/hboley"> <xs:annotation> <xs:documentation> This is the XML schema for the Rule Language as defined by Working Draft 2 of the RIF Basic Logic Dialect. The schema is based on the following EBNF for the RIF-BLD Rule Language: Document ::= Group Group ::= 'Group' IRIMETA? '(' (RULE | Group)* ')' IRIMETA ::= Frame RULE ::= 'Forall' Var+ '(' CLAUSE ')' | CLAUSE CLAUSE ::= Implies | ATOMIC Implies ::= ATOMIC ':-' FORMULA Note that this is an extension of the syntax for the RIF-BLD Condition Language (BLDCond.xsd). </xs:documentation> </xs:annotation> <xs:include schemaLocation="BLDCond.xsd"/> <xs:element name="Document"> <xs:complexType> <xs:sequence> <xs:element ref="Group"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Group"> <xs:complexType> <xs:sequence> <xs:element ref="meta" minOccurs="0" maxOccurs="1"/> <xs:element ref="sentence" minOccurs="0" maxOccurs="unbounded"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="meta"> <xs:complexType> <xs:sequence> <xs:group ref="IRIMETA"/> </xs:sequence> </xs:complexType> </xs:element> <xs:group name="IRIMETA"> <xs:sequence> <xs:element ref="Frame"/> </xs:sequence> </xs:group> <xs:element name="sentence"> <xs:complexType> <xs:choice> <xs:element ref="Group"/> <xs:group ref="RULE"/> </xs:choice> </xs:complexType> </xs:element> <xs:group name="RULE"> <xs:choice> <xs:element ref="Forall"/> <xs:group ref="CLAUSE"/> </xs:choice> </xs:group> <xs:element name="Forall"> <xs:complexType> <xs:sequence> <xs:element ref="declare" minOccurs="1" maxOccurs="unbounded"/> <xs:element name="formula"> <xs:complexType> <xs:group ref="CLAUSE"/> </xs:complexType> </xs:element> </xs:sequence> </xs:complexType> </xs:element> <xs:group name="CLAUSE"> <xs:choice> <xs:element ref="Implies"/> <xs:group ref="ATOMIC"/> </xs:choice> </xs:group> <xs:element name="Implies"> <xs:complexType> <xs:sequence> <xs:element ref="if"/> <xs:element ref="then"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="if"> <xs:complexType> <xs:sequence> <xs:group ref="FORMULA"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="then"> <xs:complexType> <xs:sequence> <xs:group ref="ATOMIC"/> </xs:sequence> </xs:complexType> </xs:element> </xs:schema>