On decidability of concept satisfiability in Description Logic with product semantics

Abstract

The aim of the present paper is to prove that concept validity and positive satisfiability with an empty ontology in the Fuzzy Description Logic IALE, under standard product semantics and with respect to quasi-witnessed models, are decidable. In our framework we are not considering reasoning tasks over ontologies. The proof of our result consists in reducing the problem to a finitary consequence problem in propositional product logic with Monteiro-Baaz delta operator, which is known to be decidable. Product FDL and first order logic are known not to enjoy the finite model property, so we cannot restrict to finite interpretations. Thus, in order to obtain our result, we need to codify infinite interpretations using a finite number of propositional formulas. Such result was conjectured in [10], but the proof given was subsequently found incorrect. In the present work an improved reduction algorithm is proposed and a proof of the same result is provided.