Automatic Theorem Proving in Paraconsistent Logics: Theory and Implementation

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.

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