This is an early and development draft of an ontology of rule systems, being developed by the W3C Rule Interchange Format (RIF) Working Group.
RIFRAF
We need to define several restrictions here, first that the Head and body are exactly defined by a condition and a Litform.
Second, that all ComplexTerms occurring in such a rule are FirstOrderComplexTerms.
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A rule language that can compute any Turing Machine computable function.
Whether a rule language has this property depends on both the inference engine and the syntax and semantics of the language.
In general, for any given well-formed element E of a given formal language, a model-theoretic semantics will assign a value to E that depends upon a) a chosen domain of interpretion, b) the syntactic structure of E, and c) an interpretation function that governs the assignment of members of (a) to E.
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A function from well formed expressions of a formal language to the elements of a given universe of discourse.
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A rule language whose formal semantics is a model-theoretic semantics
The set of all UoDs that have a finite cardinality
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From an abstract formal point of view the key point is that the inference mechanism X can be thought of as a mechanical procedure that can be applied to a set of well formed formulas R of a language, represented X(R) , such that X(R) yields a set of zero of more additional formulas not in R.
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A rule language is a formal language that has an inference procedure or proof-theory associated with it. In practice the nature of the inference mechanism can be quite varied. From an abstract formal point of view the key point is that the inference mechanism X can be thought of as a mechanical procedure that can be applied to a set of rules R (which includes "facts"), represented X(R) , such that X(R) yields a set of zero of more additional formulas not in R.
Formally a rule language has one and only one inference associated procedure.
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A triple consisting of a rule set R, belonging to a given formal language, a Universe of Discourse, U, and an Interpretation Function, I, such that T (true) and F (false) are members of U, and I(r) = T for all w members of r.
The restriction given below do not capture this definition, since the last clause of the definition is not represented. To do that totally iin owl alone we would need to add more properties and create more restrictive subclasses using them and build up from there.
Alternatively we could define rules (axioms) that woud express these complex relationsions.
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This class shoult be a subclass of owl:nothing, i,e. invalid.
An inference procedure X(R) that will always terminate with "an answer." For example, if the "question" is whether r can be inferred from R, and X is decidable, then either X(R) will terminate and contain r or X(R) will terminate and not contain r (which means that r does not follow from R, according to X).
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A set. Intuitively it is the range of an interpretation function in a model-theoretic semantics.
A formally specified and, in principle, mechanically useable set of definitions or rules, for determining "the meaning" of any well formed element in a given formal language.
A specification (or theory) of the "meanings" of symbols in a given language.
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By a formal language we mean a fully specified syntax, including all "terminal symbols" such as logical and non-logical constants, as well as a mechanism that determines whether or not any sequence of terminal symbols belongs to the language.
A formal language should not be confused with a formal language framework. The latter is a system or methodology for creating formal languages. When we say that a formal language "has a semantics" we are, in the first instance, talking about this concept.
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The N3 language, from Tim Berners-Lee (timbl@w3.org)
The cwm Semantic Web reasoner