An Axiomatic Semantics for RDF, RDF-S, and DAML+OIL (March 2001)

This document provides an axiomatization for the Resource Description Framework (RDF), RDF Schema (RDF-S), and DAML+OIL by specifying a mapping of a set of descriptions in any one of these languages into a logical theory expressed in first-order predicate calculus. The basic claim of this paper is that the logical theory produced by the mapping specified herein of a set of such descriptions is logically equivalent to the intended meaning of that set of descriptions. Providing a means of translating RDF, RDF-S, and DAML+OIL descriptions into a first-order predicate calculus logical theory not only specifies the intended meaning of the descriptions, but also produces a representation of the descriptions from which inferences can automatically be made using traditional automatic theorem provers and problem solvers. For example, the DAML+OIL axioms enable a reasoner to infer from the two statements "Class Male and class Female are disjointWith." and "John is type Male." that the statement "John is type Female." is false. The mapping into predicate calculus consists of a simple rule for translating RDF statements into first-order relational sentences and a set of first-order logic axioms that restrict the allowable interpretations of the non-logical symbols (i.e., relations, functions, and constants) in each language. Since RDF Schema and DAML+OIL are both vocabularies of non-logical symbols added to RDF, the translation of RDF statements is sufficient for translating RDF Schema and DAML+OIL as well. The axioms are written in ANSI Knowledge Interchange Format (KIF)), which is a proposed ANSI standard. The axiomatic semantics are updated as daml+oil evolves and updated versions are available from http://www.ksl.stanford.edu/people/dlm/daml-semantics/abstract-axiomatic-semantics.html. In order to support additional operational usability of the document, we include two additional files: one containing all of the kif axioms and kif theorems in the document.