The Paraconsistent Annotated Logic Program EVALPSN and its Application

Abstract

The main purpose of paraconsistent logic is to deal with inconsistency in a framework for consistent logical systems. It has been almost six decades since the first paraconsistent logical system was proposed by [13]. It was four decades later that a family of paraconsistent logic called ‘annotated logics’ was proposed by [6,51]. It can deal with inconsistency by introducing many truth values called ‘annotations’ that should be attached to each atomic formula, although their semantics is basically two-valued.The paraconsistent annotated logic was developed from the viewpoint of logic programming, aiming at application to Computer Science such as the semantics for knowledge bases by [5,14,50]. Furthermore, in order to deal with inconsistency and non-monotonic reasoning in a framework of annotated logic programming, the paraconsistent annotated logic program [5] was developed to have ontological (strong) negation and stable model semantics [10] by [20], and was named Annotated Logic Program with Strong Negation (ALPSN for short). It has been applied to some non-monotonic systems, default logic [48], autoepistemic logic [18] and a non-monotonic ATMS (Assumption Based Truth Maintenance System) [7] as their computational models [21, 39, 40].