Knowledge Systems Laboratory
Stanford University

Abstract: "An Axiomatic Semantics for RDF, RDF Schema, and DAML+OIL"

Richard Fikes and Deborah L. McGuinness. ``An Axiomatic Semantics for RDF, RDF Schema, and DAML+OIL'' KSL Technical Report KSL-01-01, 2001. Updated August, 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 full paper is available in word, html, and text forms. In order to support additional operational use of the document, we include two additional files: one containing all of the

kif axioms and
kif theorems

in the document. This replaces the previous axiomatic semantics for DAML+OIL and the previous axiomatic semantics for DAML-ONT which are available from here.

The main differences in this version over the previous version are listed below:

The theorems in the document have been significantly revised to facilitate the use of the axioms for automatic reasoning. In the new version, the theorems are all either (1) KIF representations of RDF statements that one can assume to be included in any knowledge base, (2) KIF versions of Horn clauses with RDF statements or evaluable constraints as atoms, or (3) implications in which a conjunction of atoms (i.e., KIF representations of RDF statements or evaluable constraints) implies FALSE. For example, these theorems could be used by a forward chaining mechanism to infer additional assertions or logical inconsistencies while a DAML+OIL knowledge base is being loaded.
A file containing only the axioms and a file containing only the theorems has been linked to the primary document to facilitate loading the axioms and theorems into a reasoner.
The numbering scheme for the axioms and theorems was changed so that the number associated with an axiom or theorem does not change every time an axiom or theorem is added to or deleted from the document.
Bugs and redundancies in the axioms and theorems that were reported to us were fixed.

Publications of Richard Fikes,
Selected Publications of Deborah L. McGuinness.