Embedding-based approaches to paraconsistent and temporal description logics

Abstract

In this article, some paraconsistent and temporal description logics are studied based on an embedding-based proof method. A new paraconsistent description logic, PALC, is obtained from the description logic ALC by adding a paraconsistent negation. Two temporal description logics, XALC and BALCl, are introduced by combining and modifying ALC and Prior’s tomorrow tense logic. XALC has the next-time operator, and BALCl has some restricted versions of the next-time, any-time and some-time operators, in which the time domain is bounded by a positive integer l. Some theorems for embedding PALC, XALC and BALCl into ALC are proved in a uniform way, and PALC, XALC and BALCl are shown to be decidable. Three tableau calculi for PALC, XALC and BALCl are introduced, and the completeness theorems for these calculi are proved.