A Model of Decidable Introspective Reasoning with Quantifying-In

Since knowledge is usually incomplete, agents need to introspect on what they know and do not know. The best known models of introspective reasoning suffer from intractability or even undecidability if the underlying language is first-order. To better suit the fact that agents have limited resources, we recently proposed a model of decidable introspective reasoning in first-order knowledge bases (KBs). However, this model is deficient in that it does not allow for quantifying-in, which is needed to distinguish between knowing that and knowing who. In this paper, we extend our earlier work by adding quantifying-in and equality to a model of limited belief that integrates ideas from possible-world semantics and relevance logic.

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

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

[3]  Gerhard Lakemeyer.  Decidable Reasoning in First-Order Knowledge Bases with Perfect Introspection , 1990, AAAI.

[4]  Saul A. Kripke,et al.  Naming and Necessity , 1980 .

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

[6]  Kurt Konolige,et al.  A Computational Theory of Belief Introspection , 1985, IJCAI.

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

[8]  Hector J. Levesque,et al.  Foundations of a Functional Approach to Knowledge Representation , 1984, Artif. Intell..

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

[10]  Alan Mark Frisch.  Knowledge retrieval as specialized inference (artificial intelligence, sorted logic) , 1986 .

[11]  Richard W. Weyhrauch,et al.  A Decidable Fragment of Predicate Calculus , 1984, Theor. Comput. Sci..

[12]  P. Patel-Schneider.  Decidable, logic-based knowledge representation , 1987 .

[13]  Martin D. Davis,et al.  Obvious Logical Inferences , 1981, IJCAI.

[14]  P. T. Geach,et al.  KNOWLEDGE AND BELIEF: An Introduction to the Logic of the Two Notions , 1963 .

[15]  Leonard Linsky,et al.  Reference and modality , 1971 .

[16]  Gerhard Lakemeyer,et al.  A Tractable Knowledge Representation Service with Full Introspection , 1988, TARK.

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

[18]  Robert C. Moore.  Semantical Considerations on Nonmonotonic Logic , 1985, IJCAI.

[19]  Gerhard Lakemeyer.  Steps Towards a First-Order Logic of Explicit and Implicit Belief , 1986, TARK.

[20]  Alan M Frisch.  Knowledge Retrieval as Specialized Inference. , 1987 .