A Semantics for Reasoning Consistently in the Presence of Inconsistency

Abstract 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.

[1]  Craig Boutilier,et al.  Inaccessible Worlds and Irrelevance: Preliminary Report , 1991, IJCAI.

[2]  J. Dunn,et al.  Intuitive semantics for first-degree entailments and ‘coupled trees’ , 1976 .

[3]  Hector J. Levesque,et al.  A Logic of Implicit and Explicit Belief , 1984, AAAI.

[4]  Nuel D. Belnap,et al.  Entailment : the logic of relevance and necessity , 1975 .

[5]  Jinxin Lin.  Frameworks for dealing with conflicting information and applications , 1996 .

[6]  J. M. Dunn,et al.  Modern Uses of Multiple-Valued Logic , 1977 .

[7]  Graham Priest,et al.  Minimally inconsistent LP , 1991, Stud Logica.

[8]  Fangzhen Lin,et al.  Reasoning in the Presence of Inconsistency , 1987, AAAI.

[9]  G. Lakemeyer.  Models of belief for decidable reasoning in incomplete knowledge bases , 1992 .

[10]  Joseph Y. Halpern.  Reasoning About Knowledge: An Overview , 1986, TARK.

[11]  Hector J. Levesque,et al.  All I Know: A Study in Autoepistemic Logic , 1990, Artif. Intell..

[12]  Gerhard Lakemeyer.  Tractable Meta-Reasoning in Propositional Logics of Belief , 1987, IJCAI.

[13]  Melvin Fitting,et al.  First-Order Logic and Automated Theorem Proving , 1990, Graduate Texts in Computer Science.

[14]  Ronald Fagin,et al.  A model-theoretic analysis of knowledge , 1991, JACM.

[15]  Moshe Y. Vardi.  On Epistemic Logic and Logical Omniscience , 1986, TARK.

[16]  L. I. Rozonoer,et al.  On interpretation of inconsistent theories , 1989, Inf. Sci..

[17]  Jinxin Lin,et al.  Consistent Belief Reasoning in the Presence of Inconsistency , 1994, TARK.

[18]  Alberto O. Mendelzon,et al.  Updates and Subjunctive Queries , 1995, Inf. Comput..

[19]  Jinxin Lin,et al.  Integration of Weighted Knowledge Bases , 1996, Artif. Intell..

[20]  Nuel D. Belnap,et al.  A Useful Four-Valued Logic , 1977 .

[21]  Gerhard Lakemeyer,et al.  On the Relation between Explicit and Implicit Belief , 1991, KR.

[22]  Ronald Fagin,et al.  A Nonstandard Approach to the Logical Omniscience Problem , 1990, Artif. Intell..

[23]  Ronald Fagin,et al.  Belief, Awareness, and Limited Reasoning. , 1987, Artif. Intell..

[24]  Michael Kifer,et al.  RI: a logic for reasoning with inconsistency , 1989, [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science.

[25]  Joseph Y. Halpern,et al.  A Guide to the Modal Logics of Knowledge and Belief: Preliminary Draft , 1985, IJCAI.

[26]  Joseph Y. Halpern,et al.  A Guide to Completeness and Complexity for Modal Logics of Knowledge and Belief , 1992, Artif. Intell..