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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.
The Appendix: List of Builtins is currently kept as an external link.
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This document develops RIF-BLD (the Basic Logic Dialect of the Rule Interchange Format) based on a set of foundational concepts that are supposed to be shared by all logic-based RIF dialects.
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, internationalized resource identifiers (or IRIs, defined by RFC 3987 [RFC 3987]) as identifiers for concepts, and XML Schema data types. The last two features make RIF-BLD into a Web 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. First, it is defined as a specialization of RIF-FLD, the RIF Framework for Logic-based Dialects; it is a very short description, but it requires familiarity with RIF-FLD. RIF-FLD provides a general framework -- both syntactic and semantic -- for defining RIF dialects. With this framework, one can extend RIF-BLD with default negation, higher-order features, and so on. Then RIF-BLD is described independently of the RIF Framework, for the benefit of those who desire a quicker path to RIF-BLD and are not interested in the extensibility issues.
One fragment of RIF is called the Condition Language. It defines the syntax and semantics for the bodies of the rules in RIF-BLD. However, it is envisioned that this fragment will have a wider use in RIF. In particular, it will be used as queries, constraints, and in the conditional part in production rules (see RIF PRD), reactive rules, and normative rules.
The current document is the third draft of the RIF-BLD specification. A number of extensions are planned to support built-ins, additional primitive XML data types, the notion of RIF compliance, and so on. Tool support for RIF-BLD is forthcoming. 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.
This section defines the precise relationship between the syntax of RIF-BLD and the syntactic framework of RIF-FLD. The other sections describe RIF-BLD largely independently of RIF-FLD.
The syntax of the RIF Basic Logic Dialect is defined by specialization from the syntax of the Syntactic Framework for Logic Dialects of RIF. Section Syntax of a RIF Dialect as a Specialization of RIF-FLD in that document lists the parameters of the syntactic framework, which we will now specialize for RIF-BLD.
Recall that negation (classical or default) is not supported by RIF-BLD in either the rule head or the body.
In order to make this document self-contained, we will now define the syntax of RIF-BLD with no references to RIF-FLD -- except for Symbol Spaces whose definition we do not duplicate here.
The alphabet of RIF-BLD consists of a countably infinite set of constant symbols Const, a countably infinite set of variable symbols Var (disjoint from Const), a countably infinite set of argument names, ArgNames (disjoint from Const and Var), connective symbols And and Or, quantifiers Exists and Forall, the symbols =, #, ##, ->, :-, and auxiliary symbols, such as "(" and ")". The set of connective symbols, quantifiers, =, etc., is disjoint from Const and Var. Variables are written as Unicode strings preceded with the symbol "?". The syntax for constant symbols is given in Section Symbol Spaces of RIF-FLD.
The language of RIF-BLD is the set of formulas constructed using the above alphabet according to the rules spelled out below.
RIF-BLD supports several kinds of terms: constants and variables, positional terms, terms with named arguments, equality, membership, and subclass terms, and frames. The word "term" will be used to refer to any kind of terms. Formally, terms are defined as follows:
Membership, subclass, and frame terms are used to describe objects in object-based logics like F-logic [KLW95]. These terms can be readily mixed both with positional terms and terms with named arguments: p(?X q#r[v(1,2)->s] t(d->e f->g)).
The set of all symbols, Const, is partitioned into positional predicate symbols, predicate symbols with named arguments, positional function symbols, function symbols with named arguments, and individuals. Each positional predicate and function symbol has precisely one arity, which is a non-negative integer that tells how many arguments the symbol can take. An arity for terms with named arguments (of a symbol with named arguments) is a bag {s1 ... sk} of argument names (si ∈ ArgNames). Each predicate or function symbol with named arguments has precisely one arity (for terms with named arguments).
The arity of a symbol (or whether it is a predicate, a function, or an individual) is not specified explicitly in RIF-BLD. Instead, it is inferred as follows. Each constant symbol in a RIF-BLD formula (or a set of formulas) is expected to occur in at most one context: as an individual, a function symbol of a particular arity, a predicate symbol of a particular arity, or an individual. The arity of the symbol and its type is then determined by its context. If a symbol from Const occurs in more than one context, the formula (or a set of formulas) is not considered to be well-formed in RIF-BLD.
Any term (positional or with named arguments) of the form p(...), where p is a predicate symbol, is also an atomic formula. Equality, membership, subclass, and frame terms are also atomic formula. Simple terms (constants and variables) are not formulas. Not all atomic formulas are well-formed -- see Section Well-formedness. A well-formed atomic formula is an atomic formula that is also a well-formed term.
More general formulas are constructed out of the atomic formulas with the help of logical connectives. A formula is a statement that can have one of the following forms:
Formulas constructed using the above definitions are called RIF-BLD conditions. RIF-BLD rules are defined as follows:
So far, the syntax of RIF-BLD was specified in Mathematical English. Tool developers, however, prefer the more formal EBNF notation, which we will give next. Several points should be kept in mind regarding this notation.
The Condition Language represents formulas that can be used in the body of the RIF-BLD rules. It is supposed to be a common part of a number of RIF dialects, including RIF PRD. The EBNF grammar for a superset of the RIF-BLD condition language is as follows.
CONDITION ::= 'And' '(' CONDITION* ')' | 'Or' '(' CONDITION* ')' | 'Exists' Var+ '(' CONDITION ')' | COMPOUND COMPOUND ::= Uniterm | Equal | Member | Subclass | Frame Uniterm ::= Const '(' (TERM* | (Const '->' TERM)*) ')' Equal ::= TERM '=' TERM Member ::= TERM '#' TERM Subclass ::= TERM '##' TERM Frame ::= TERM '[' (TERM '->' TERM)* ']' TERM ::= Const | Var | COMPOUND Const ::= LITERAL '^^' SYMSPACE Var ::= '?' VARNAME
The production rule for the non-terminal CONDITION 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 CONDITION. RIF-BLD conditions permit only existential variables, but RIF-FLD syntax allows arbitrary quantification, which can be used in some dialects. A CONDITION can also be a COMPOUND term, i.e. a Uniterm, Equal, Member, Subclass, or Frame. The production for the non-terminal TERM defines RIF-BLD terms -- constants, variables, or COMPOUND terms.
The RIF-BLD presentation syntax does not commit to any
particular vocabulary for the names of variables or for the
literals used in constant symbols. In the examples, variables are
denoted by Unicode character sequences beginning with
a ?-sign.a ?-sign. Constant symbols have the form:
LITERAL^^SYMSPACE, where SYMSPACE is an IRI
string that identifies the symbol space of the constant and
LITERAL is a Unicode string from the lexical space of that
symbol space. Equality, membership, and subclass terms are
self-explanatory. Uniterms (Universal terms) are terms that
can be either positional or with named arguments. A frame term is a
term composed of an object Id and a collection of attribute-value
pairs.
Example 1 shows conditions that are composed of uniterms, frames, and existentials. The examples of the frames show that variables can occur in the syntactic positions of object Ids, object properties, or property values.
Example 1 (RIF-BLD conditions) We use the prefix bks to abbreviate http://example.com/books# and the prefix auth for http://example.com/authors#. Positional terms: book^^rif:local(auth:rifwg^^rif:iri bks:LeRif^^rif:iri) Exists ?X (book^^rif:local(?X LeRif^^rif:local)) Terms with named arguments: book^^rif:local(author^^rif:local->auth:rifwg^^rif:iri title^^rif:local->bks:LeRif^^rif:iri) Exists ?X (book^^rif:local(author^^rif:local->?X title^^rif:local->bks:LeRif^^rif:iri)) Frames: wd1^^rif:local[author^^rif:local->auth:rifwg^^rif:iri title^^rif:local->bks:LeRif^^rif:iri ] Exists ?X (wd2^^rif:local[author^^rif:local->?X title^^rif:local->bks:LeRif^^rif:iri ]) Exists ?X (wd2^^rif:local#book^^rif:local[author^^rif:local->?X title^^rif:local->bks:LeRif^^rif:iri]) Exists ?I ?X (?I[author^^rif:local->?X title^^rif:local->bks:LeRif^^rif:iri]) Exists ?I ?X (?I#book^^rif:local[author^^rif:local->?X title^^rif:local->bks:LeRif^^rif:iri]) Exists ?S (wd2^^rif:local[author^^rif:local->auth:rifwg^^rif:iri ?S->bks:LeRif^^rif:iri]) Exists ?X ?S (wd2^^rif:local[author^^rif:local->?X ?S->bks:LeRif^^rif:iri]) Exists ?I ?X ?S (?I#book^^rif:local[author->?X ?S->bks:LeRif^^rif:iri])
The presentation syntax for Horn rules extends the syntax in Section EBNF for RIF-BLD Condition Language with the following productions.
Ruleset ::= RULE* RULE ::= 'Forall' Var+ '(' RULE ')' | Implies | COMPOUND Implies ::= COMPOUND ':-' CONDITION
A Ruleset is a set of RIF rules. Rules are generated by the Implies production, with optional Forall-quantification. Var, COMPOUND, and CONDITION were defined as part of the syntax for positive conditions in Section EBNF for RIF-BLD Condition Language. Note that COMPOUND terms are treated as rules with an empty condition part -- they are usually called facts. Note that, by a definition in Section Formulas, atomic formulas that correspond to builtin predicates (i.e., formulas with signature bi_atomic) are not allowed in the conclusion part of a rule. This restriction is not reflected in the EBNF syntax.
The document RIF Use Cases and Requirements includes a use case "Negotiating eBusiness Contracts Across Rule Platforms", which discusses a business rule slightly modified here:
If an item is perishable and it is delivered to John more than 10 days after the scheduled delivery date then the item will be rejected by him.
In the Presentation EBNF Syntax used throughout this document, this rule can be written in one of these two equivalent ways:
Example 2 (RIF-BLD rules) Here we use the prefix ppl as an abbreviation for http://example.com/people#. The prefix op is used for a yet-to-be-determined IRI, which will be used for RIF builtin predicates. a. Universal form: Forall ?item ?deliverydate ?scheduledate ?diffduration ?diffdays ( reject^^rif:local(ppl:John^^rif:iri ?item) :- And(perishable^^rif:local(?item) delivered^^rif:local(?item ?deliverydate ppl:John^^rif:iri) scheduled^^rif:local(?item ?scheduledate) fn:subtract-dateTimes-yielding-dayTimeDuration(?deliverydate ?scheduledate ?diffduration) fn:get-days-from-dayTimeDuration(?diffduration ?diffdays) op:numeric-greater-than(?diffdays 10)) ) b. Universal-existential form: Forall ?item ( reject^^rif:local(ppl#John^^rif:iri ?item ) :- Exists ?deliverydate ?scheduledate ?diffduration ?diffdays ( And(perishable^^rif:local(?item) delivered^^rif:local(?item ?deliverydate ppl:John^^rif:iri) scheduled^^rif:local(?item ?scheduledate) fn:subtract-dateTimes-yielding-dayTimeDuration(?deliverydate ?scheduledate ?diffduration) fn:get-days-from-dayTimeDuration(?diffduration ?diffdays) op:numeric-greater-than(?diffdays 10)) ) )
The XML serialization for RIF-BLD presentation syntax given in this section is alternating or fully striped (e.g., Alternating Normal Form). Positional information is optionally exploited only for the arg role elements. For example, role elements (declare and formula) are explicit within the Exists element. Following the examples of Java and RDF, we use capitalized names for class elements and names that start with lowercase for role elements.
The all-uppercase classes in the presentation syntax, such as CONDITION, become XML entities. 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.
We now serialize the syntax of Section EBNF for RIF-BLD Condition Language in XML.
Classes, roles and their intended meaning - 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 CONDITION formula) - Uniterm (term or atomic formula, positional or with named arguments) - Member (member formula) - Subclass (subclass formula) - Frame (Frame formula) - object (Member/Frame role containing a TERM or an object description) - op (Uniterm role for predicates/functions as operations) - arg (argument role) - upper (Member/Subclass upper class role) - lower (Member/Subclass lower instance/class role) - slot (Uniterm/Frame slot role, prefix version of slot infix ' -> ') - Equal (prefix version of term equation '=') - side (Equal left-hand side and right-hand side role) - Const (slot, individual, function, or predicate symbol, with optional 'type' attribute) - Var (logic variable)
For the XML Schema Definition (XSD) of the RIF-BLD condition language see Appendix Specification.
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>.
The following example illustrates XML serialization of RIF conditions.
Example 3 (A RIF condition and its XML serialization): We use the prefix bks as an abbreviation for http://example.com/books# and curr for http://example.com/currencies# a. RIF condition And ( Exists ?Buyer ( purchase^^rif:local ( ?Buyer ?Seller book^^rif:local ( ?Author bks:LeRif^^rif:iri ) curr:USD^^rif:iri ( 49^^xsd:integer ) ) ?Seller=?Author ) b. XML serialization <And> <formula> <Exists> <declare><Var>Buyer</Var></declare> <formula> <Uniterm> <op><Const type="rif:local">purchase</Const></op> <arg><Var>Buyer</Var></arg> <arg><Var>Seller</Var></arg> <arg> <Uniterm> <op><Const type="rif:local">book</Const></op> <arg><Var>Author</Var></arg> <arg><Const type="rif:iri">bks:LeRif</Const></arg> </Uniterm> </arg> <arg> <Uniterm> <op><Const type="rif:iri">curr:USD</Const></op> <arg><Const type="xsd:integer">49</Const></arg> </Uniterm> </arg> </Uniterm> </formula> </Exists> </formula> <formula> <Equal> <side><Var>Seller</Var></side> <side><Var>Author</Var></side> </Equal> </formula> </And>
The following example illustrates XML serialization of RIF conditions that involve terms with named arguments.
Example 4 (A RIF condition and its XML serialization): We use the prefix bks to abbreviate http://example.com/books#, the prefix auth for http://example.com/authors#, and curr for http://example.com/currencies#, a. RIF condition: And ( Exists ?Buyer ?P ( ?P # purchase^^rif:local [ buyer^^rif:local -> ?Buyer seller^^rif:local -> ?Seller item^^rif:local -> book^^rif:local ( author^^rif:local -> ?Author title^^rif:local -> bks:LeRif^^rif:iri ) price^^rif:local -> 49^^xsd:integer currency^^rif:local -> curr:USD^^rif:iri ] ) ?Seller=?Author ) b. XML serialization: <And> <formula> <Exists> <declare><Var>Buyer</Var></declare> <declare><Var>P</Var></declare> <formula> <Frame> <object> <Member> <lower><Var>P</Var></lower> <upper><Const type="rif:local">purchase</Const></upper> </Member> </object> <slot><Const type="rif:local">buyer</Const><Var>Buyer</Var></slot> <slot><Const type="rif:local">seller</Const><Var>Seller</Var></slot> <slot> <Const type="rif:local">item</Const> <Uniterm> <op><Const type="rif:local">book</Const></op> <slot><Const type="rif:local">author</Const><Var>Author</Var></slot> <slot><Const type="rif:local">title</Const><Const type="rif:iri">bks:LeRif</Const></slot> </Uniterm> </slot> <slot><Const type="rif:local">price</Const><Const type="xsd:integer">49</Const></slot> <slot><Const type="rif:local">currency</Const><Const type="rif:iri">curr:USD</Const></slot> </Frame> </formula> </Exists> </formula> <formula> <Equal> <side><Var>Seller</Var></side> <side><Var>Author</Var></side> </Equal> </formula> </And>
The following extends the XML syntax in Section XML for RIF-BLD Condition Language, by serializing the syntax of Section EBNF for RIF-BLD Rule Language in XML. The Forall element contains the role elements declare and formula, which were earlier used within the Exists element in Section XML for RIF-BLD Condition Language. The Implies element contains the role elements if and then to designate these two parts of a rule.
Classes, roles and their intended meaning - Ruleset (rule collection, containing rule roles) - Forall (quantified formula for 'Forall', containing declare and formula roles) - Implies (implication, containing if and then roles) - if (antecedent role, containing CONDITION) - then (consequent role, containing a Uniterm, Equal, or Frame)
For the XML Schema Definition (XSD) of the RIF-BLD Horn rule language see Appendix Specification.
For instance, the rule in Example 5a can be serialized in XML as shown below as the first element of a rule set whose second element is a business rule for Fred.
Example 5 (A RIF rule set in XML syntax) <Ruleset> <rule> <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> <Uniterm> <op><Const type="rif:local">perishable</Const></op> <arg><Var>item</Var></arg> </Uniterm> </formula> <formula> <Uniterm> <op><Const type="rif:local">delivered</Const></op> <arg><Var>item</Var></arg> <arg><Var>deliverydate</Var></arg> <arg><Const type="rif:iri">ppl:John</Const></arg> </Uniterm> </formula> <formula> <Uniterm> <op><Const type="rif:local">scheduled</Const></op> <arg><Var>item</Var></arg> <arg><Var>scheduledate</Var></arg> </Uniterm> </formula> <formula> <Uniterm> <op><Const type="rif:local">fn:subtract-dateTimes-yielding-dayTimeDuration</Const></op> <arg><Var>deliverydate</Var></arg> <arg><Var>scheduledate</Var></arg> <arg><Var>diffduration</Var></arg> </Uniterm> </formula> <formula> <Uniterm> <op><Const type="rif:local">fn:get-days-from-dayTimeDuration</Const></op> <arg><Var>diffduration</Var></arg> <arg><Var>diffdays</Var></arg> </Uniterm> </formula> <formula> <Uniterm> <op><Const type="rif:iri">op:numeric-greater-than</Const></op> <arg><Var>diffdays</Var></arg> <arg><Const type="xsd:long">10</Const></arg> </Uniterm> </formula> </And> </if> <then> <Uniterm> <op><Const type="xsd:long">reject</Const></op> <arg><Const type="rif:iri">ppl:John</Const></arg> <arg><Var>item</Var></arg> </Uniterm> </then> </Implies> </formula> </Forall> </rule> <rule> <Forall> <declare><Var>item</Var></declare> <formula> <Implies> <if> <Uniterm> <op><Const type="rif:local">unsolicited</Const></op> <arg><Var>item</Var></arg> </Uniterm> </if> <then> <Uniterm> <op><Const type="rif:local">reject</Const></op> <arg><Const type="rif:iri">ppl:Fred</Const></arg> <arg><Var>item</Var></arg> </Uniterm> </then> </Implies> </formula> </Forall> </rule> </Ruleset>
We now show how to translate between the presentation and XML syntaxes of RIF-BLD.
The translation between the presentation syntax and the XML syntax of the RIF-BLD Condition Language is given by a table as follows.
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> |
predfunc ( argument1 . . . argumentn ) |
<Uniterm> <op>predfunc</op> <arg>argument1</arg> . . . <arg> argumentn</arg> </Uniterm> |
predfunc ( key1 -> filler1 . . . keyn -> fillern ) |
<Uniterm> <op>predfunc</op> <slot>key1 filler1</slot> . . . <slot>keyn fillern</slot> </Uniterm> |
inst [ key1 -> filler1 . . . keyn -> fillern ] |
<Frame> <object>inst</object> <slot>key1 filler1</slot> . . . <slot>keyn fillern</slot> </Frame> |
inst # class [ key1 -> filler1 . . . keyn -> fillern ] |
<Frame> <object> <Member> <lower>inst</lower> <upper>class</upper> </Member> </object> <slot>key1 filler1</slot> . . . <slot>keyn fillern</slot> </Frame> |
sub ## super [ key1 -> filler1 . . . keyn -> fillern ] |
<Frame> <object> <Subclass> <lower>sub</lower> <upper>super</upper> </Subclass> </object> <slot>key1 filler1</slot> . . . <slot>keyn fillern</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> |
name^^space |
<Const type="space">name</Const> |
?name |
<Var>name</Var> |
The translation between the presentation syntax and the XML syntax of the RIF-BLD Rule Language is given by a table that extends the translation table of Section Translation of RIF-BLD Condition Language as follows.
Presentation Syntax | XML Syntax |
---|---|
Ruleset ( clause1 . . . clausen ) |
<Ruleset> <rule>clause1</rule> . . . <rule>clausen</rule> </Ruleset> |
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> |
|
The syntactic structure of RIF-BLD suggests several useful subdialects:
|
This section defines the precise relationship between the semantics of RIF-BLD and the semantic framework of RIF-FLD. The remaining sections describe the semantics of RIF-BLD without referring to the general framework -- except for Primitive Data Types whose definition is not duplicated here.
The semantics of the RIF Basic Logic Dialect is defined by specialization from the semantics of the [:FLD/Semantics:Semantic Framework for Logic Dialects] of RIF. Section [:FLD/Semantics#sec-rif-dialect-semantics:Semantics of a RIF Dialect as a Specialization of RIF-FLD] in that document lists the parameters of the semantic framework, which we need to specialize for RIF-BLD.
Recall that the semantics of a dialect is derived from these notions by specializing the following parameters.
These two definitions are equivalent for entailment of RIF-BLD conditions by RIF-BLD rulesets, since all rules in RIF-BLD are Horn -- it is a classical result of Van Emden and Kowalski [vEK76].
The set TV of truth values in RIF-BLD consists of just two values, t and f. This set has a total order, called truth order, such that f <t t.
A semantic structure, I, is a tuple of the form <TV, DTS, D, IC, IV, IF, Iframe, ISF, Isub, Iisa, I=, ITruth>. Here D is a non-empty set of elements called the domain of I, and there is a proper subset, Dind ⊂D, which is used to interpret individuals. We use Const to refer to the set of all constant symbols and Var to refer to 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).
The other components of I are total mappings defined as follows:
If a constant, c ∈ Const, occurs in the position of an individual then it is required that IC(c) ∈ Dind.
Bags are used here because the order of the attribute/value pairs in a frame is immaterial and pairs may repeat. For instance, o[a->b a->b].
We also define the following mapping I : :
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.
Truth valuation for well-formed formulas in RIF-BLD is determined using the following function, denoted TValI:
Here maxt (respectively, mint) is taken over all interpretations I* of the form <TV, DTS, D, IC, I*V, IF, Iframe, ISF, Isub, Iisa, ITruth>, which are 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.
A model of a set Ψ of formulas is a semantic structure I such that TValI(φ) = t for every φ∈Ψ. In this case, we write I |= Ψ.
We now define what it means for a set of RIF-BLD rules to entail a RIF-BLD condition.
Let R be a set of RIF-BLD rules and φ an existentially closed RIF-BLD condition formula. We say that R entails φ, written as R |= φ, if and only if for every semantic structure I of R and every ψ ∈ R, it is the case that TValI(ψ) ≤ TValI(φ).
Equivalently, we can say that R |= φ holds iff whenever I |= R it follows that also I |= φ.
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 0.7 2008-02-12 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: CONDITION ::= 'And' '(' CONDITION* ')' | 'Or' '(' CONDITION* ')' | 'Exists' Var+ '(' CONDITION ')' | COMPOUND COMPOUND ::= Uniterm | Equal | Member | Subclass | Frame Uniterm ::= Const '(' (TERM* | (Const '->' TERM)*) ')' Equal ::= TERM '=' TERM Member ::= TERM '#' TERM Subclass ::= TERM '##' TERM Frame ::= TERM '[' (TERM '->' TERM)* ']' TERM ::= Const | Var | COMPOUND Const ::= LITERAL '^^' SYMSPACE Var ::= '?' VARNAME </xs:documentation> </xs:annotation> <xs:group name="CONDITION"> <!-- CONDITION ::= 'And' '(' CONDITION* ')' | 'Or' '(' CONDITION* ')' | 'Exists' Var+ '(' CONDITION ')' | COMPOUND --> <xs:choice> <xs:element ref="And"/> <xs:element ref="Or"/> <xs:element ref="Exists"/> <xs:group ref="COMPOUND"/> </xs:choice> </xs:group> <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="CONDITION"/> </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="COMPOUND"> <!-- COMPOUND ::= Uniterm | Equal | Member | Subclass | Frame --> <xs:choice> <xs:element ref="Uniterm"/> <xs:element ref="Equal"/> <xs:element ref="Member"/> <xs:element ref="Subclass"/> <xs:element ref="Frame"/> </xs:choice> </xs:group> <xs:element name="Uniterm"> <!-- Uniterm ::= Const '(' (TERM* | (Const '->' TERM)*) ')' --> <xs:complexType> <xs:sequence> <xs:element ref="op"/> <xs:choice> <xs:element ref="arg" minOccurs="0" maxOccurs="unbounded"/> <xs:element ref="slot" minOccurs="0" maxOccurs="unbounded"/> </xs:choice> </xs:sequence> </xs:complexType> </xs:element> <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:element name="slot"> <xs:complexType> <xs:sequence> <xs:element ref="Const"/> <xs:group ref="TERM"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Equal"> <!-- Equal ::= TERM '=' TERM --> <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"> <!-- Member ::= TERM '#' TERM --> <xs:complexType> <xs:sequence> <xs:element ref="lower"/> <xs:element ref="upper"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Subclass"> <!-- Subclass ::= TERM '##' TERM --> <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"> <!-- Frame ::= TERM '[' (TERM '->' TERM)* ']' --> <xs:complexType> <xs:sequence> <xs:element ref="object"/> <xs:element name="slot" minOccurs="0" maxOccurs="unbounded"> <!-- note difference from slot in Uniterm --> <xs:complexType> <xs:sequence> <xs:group ref="TERM"/> <xs:group ref="TERM"/> </xs:sequence> </xs:complexType> </xs:element> </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:group name="TERM"> <!-- TERM ::= Const | Var | COMPOUND --> <xs:choice> <xs:element ref="Const"/> <xs:element ref="Var"/> <xs:group ref="COMPOUND"/> </xs:choice> </xs:group> <xs:element name="Const"> <!-- Const ::= LITERAL '^^' SYMSPACE --> <xs:complexType mixed="true"> <xs:sequence/> <xs:attribute name="type" type="xs:string" use="required"/> </xs:complexType> </xs:element> <xs:element name="Var" type="xs:string"> <!-- Var ::= '?' VARNAME --> </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 0.7 2008-02-12 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 ::= Ruleset* Ruleset ::= RULE* RULE ::= 'Forall' Var+ '(' RULE ')' | Implies | COMPOUND Implies ::= COMPOUND ':-' CONDITION Note that this is an extension of the syntax for the RIF-BLD Condition Language (BLDCond.xsd). </xs:documentation> </xs:annotation> <!-- The Rule Language includes the Condition Language--> <xs:include schemaLocation="BLDCond.xsd"/> <xs:element name="Document"> <!-- Document ::= Ruleset* --> <xs:complexType> <xs:sequence> <xs:element ref="Ruleset" minOccurs="0" maxOccurs="unbounded"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Ruleset"> <!-- Ruleset ::= RULE* --> <xs:complexType> <xs:sequence> <xs:element ref="rule" minOccurs="0" maxOccurs="unbounded"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="rule"> <xs:complexType> <xs:sequence> <xs:group ref="RULE"/> </xs:sequence> </xs:complexType> </xs:element> <xs:group name="RULE"> <!-- RULE ::= 'Forall' Var+ '(' RULE ')' | Implies | COMPOUND --> <xs:choice> <xs:element ref="Forall"/> <xs:element ref="Implies"/> <xs:group ref="COMPOUND"/> </xs:choice> </xs:group> <xs:element name="Forall"> <xs:complexType> <xs:sequence> <xs:element ref="declare" minOccurs="1" maxOccurs="unbounded"/> <!-- note different from formula in And, Or and Exists --> <xs:element name="formula"> <xs:complexType> <xs:group ref="RULE"/> </xs:complexType> </xs:element> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Implies"> <!-- Implies ::= COMPOUND ':-' CONDITION --> <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="CONDITION"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="then"> <xs:complexType> <xs:sequence> <xs:group ref="COMPOUND"/> </xs:sequence> </xs:complexType> </xs:element> </xs:schema>