A semantics for reasoning consistently in the presence of inconsistency

摘要

A great deal of research has been devoted to nontrivial reasoning in the presence of inconsistency. However, previous formalisms on this account do not permit consistent reasoning in the presence of inconsistency—they may conclude a statement on one hand and the negation of the statement on the other. In this paper, we propose a logic that allows an agent to reason consistently, even though there are inconsistencies in the agent's beliefs. We first give the semantics of the logic and then present a simple, sound and complete axiomatization for the logic, thus forming the formal basis of reasoning consistently in the presence of inconsistency.