Decidable Reasoning in a Logic of Limited Belief with Function Symbols

A principled way to study limited forms of reasoning for expressive knowledge bases is to specify the reasoning problem within a suitable logic of limited belief. Ideally such a logic comes equipped with a perspicuous semantics, which provides insights into the nature of the belief model and facilitates the study of the reasoning problem. While a number of such logics were proposed in the past, none of them is able to deal with function symbols except perhaps for the special case of logical constants. In this paper we propose a logic of limited belief with arbitrary function symbols. Among other things, we demonstrate that this form of limited belief has desirable properties such as eventual completeness for a large class of formulas and that it serves as a specification of a form of decidable reasoning for very expressive knowledge bases.

[1]  Hector J. Levesque,et al.  Tractable Reasoning in First-Order Knowledge Bases with Disjunctive Information , 2005, AAAI.

[2]  K. Konolige.  A deduction model of belief , 1986 .

[3]  Philip Hugly,et al.  There Is A Problem with Substitutional Quantification , 2008 .

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

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

[6]  Hector J. Levesque,et al.  Towards Tractable Inference for Resource-Bounded Agents , 2015, AAAI Spring Symposia.

[7]  Peter F. Patel-Schneider,et al.  A decidable first-order logic for knowledge representation , 1985, Journal of Automated Reasoning.

[8]  Gerhard Lakemeyer.  Evaluation-Based Reasoning with Disjunctive Information in First-Order Knowledge Bases , 2002, KR.

[9]  Gerhard Lakemeyer,et al.  Decidable Reasoning in a Logic of Limited Belief with Introspection and Unknown Individuals , 2013, IJCAI.

[10]  Marco Schaerf,et al.  Approximate Reasoning and Non-Omniscient Agents , 1992, TARK.

[11]  Gerhard Lakemeyer,et al.  Decidable Reasoning in a Fragment of the Epistemic Situation Calculus , 2014, KR.

[12]  Dana S. Scott,et al.  Advice on Modal Logic , 1970 .

[13]  Saul Kripke,et al.  A completeness theorem in modal logic , 1959, Journal of Symbolic Logic.

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

[15]  Gerhard Lakemeyer,et al.  The logic of knowledge bases , 2000 .

[16]  Jaakko Hintikka,et al.  Impossible possible worlds vindicated , 1975, J. Philos. Log..

[17]  James P. Delgrande,et al.  A FRAMEWORK FOR LOGICS OF EXPLICIT BELIEF , 1995, Comput. Intell..

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

[19]  Hector J. Levesque,et al.  Efficient Reasoning in Proper Knowledge Bases with Unknown Individuals , 2011, IJCAI.

[20]  Gerhard Lakemeyer,et al.  A Logic of Limited Belief for Reasoning with Disjunctive Information , 2004, KR.

[21]  Gerhard Lakemeyer,et al.  A semantic characterization of a useful fragment of the situation calculus with knowledge , 2011, Artif. Intell..

[22]  Vito F. Sinisi,et al.  Entailment: The Logic of Relevance and Necessity , 1996 .

[23]  Moshe Y. Vardi,et al.  On Epistemic Logic and Logical Omniscience. , 1988 .

[24]  Hector J. Levesque.  A Completeness Result for Reasoning with Incomplete First-Order Knowledge Bases , 1998, KR.

[25]  Alan M. Frisch.  Inference without Chaining , 1987, IJCAI.

[26]  J. Armstrong.  Knowledge and Belief , 1953 .

[27]  Gerhard Lakemeyer,et al.  Limited Reasoning in First-Order Knowledge Bases with Full Introspection , 1996, Artif. Intell..