On decidability of concept satisfiability in Description Logic with product semantics

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