Paraconsistent Reasoning with Quasi-classical Semantic in $\mathcal{ALC}$

Abstract

Description logics are a family of knowledge representation formalism which descended from semantic networks. During the past decade, the important reasoning problems such as satisfiability and subsumption have been handled by tableau-like algorithms. Description logics are practical monotonic logics which, though imparting strong and conclusive reasoning mechanisms, lack the flexibility of non-monotonic reasoning mechanisms. In recent years, the study of inconsistency handling in description logics becomes more and more important. Some technologies are being applied to handle inconsistency in description logic. Quasi-classical logic, which allows the derivation of nontrivial classical inferences from inconsistent information, supports many important proof rules such as modus tollens, modus ponens, and disjunctive syllogism. In this paper, we consider the characters of $\mathcal{ALC}$ with Quasi-classical semantics and develop a sound and complete tableau algorithm for paraconsistent reasoning in $\mathcal{ALC}$.