Deriving inference rules for terminological logics

Abstract

Terminological Logics can be investigated under different perspectives. The aim of this paper is to provide the basis for a tighter combination of theoretical investigations with issues arising in the actual implementation of terminological representation systems. We propose to use inference rules, derived via the sequent calculus, as a new method for specifying terminological inference algorithms. This approach combines the advantages of the tableaux methods and the normalize-combine algorithms that have been predominant in terminological proof theory so far. We first show how a completeness proof for the inference rules of a relatively restricted terminological logic can be given. We then show how these inference rules can be used to construct normalize-compare algorithms and prove their completeness. Furthermore, these rules can be used in two ways for the characterization of terminological representation systems: first, the incompleteness of of systems can be documented by listing those rules that have not been implemented; second, the reasoning strategy can be described by spesifying which rules are applied forward and which backward.

This work was supported by the Commission of the European Communities and is part of the ESPRIT Project 5210 AIMS which involves the following participants: Datamont (I), eria (E), Non Standard Logics (F), Technische Universität Berlin (D), Deutsches Herzzentrum Berlin (D), Onera-Cert (F), Quinary (I), Universidad del Pais Vasco (E).