Automatic theorem proving in paraconsistent logics: Theory and implementation

Abstract

Databases and knowledge bases may be inconsistent in many ways. However, a database that is inconsistent may, nonetheless, contain a great deal of useful information. Classical logic, however, would deem such a database as useless. Paraconsistent logics are a family of logics introduced by da Costa. A family of paraconsistent logics called annotated logics were proposed by Subrahmanian in [17]. Subsequently, these logics found use in reasoning about logic programs that contained inconsistent and/or erroneous information, as well as in the study of inheritance hierarchies and object oriented databases. However, no full-fledged study of automatic theorem proving in these logics has been carried out to date. In this paper, we develop a linear resolution style proof procedure for mechanical reasoning in these paraconsistent logics.KeywordsLogic ProgramTheorem ProveComplete LatticeVariable AssignmentParaconsistent LogicThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.