A Preference Semantics for Ground Nonmonotonic Modal Logics

In this paper we provide a semantic characterization of ground logics, a family of nonmonotonic modal logics obtained by means of a variant of the well known Mc Dermott and Doyle fixed point equation. The term ground logics carries the idea of restricting the negative introspection capabilities of the reasoning agent to the objective (i.e. non modal) part of the theory. This intuition was nicely formalized for modal logic S5 by a semantic definition based on a preference relation on Kripke models, which was obtained as the semantic counterpart to the notion of minimal knowledge initially defined by Halpern and Moses. We have then found a preference relation on Kripke models that both generalizes this notion of minimal knowledge and provides a semantic characterization for a significant subset of ground logics.

[1]  Francesco M. Donini,et al.  Non-first-order features in concept languages , 1995, AI*IA.

[2]  Vladimir Lifschitz.  Minimal Belief and Negation as Failure , 1994, Artif. Intell..

[3]  Victor W. Marek,et al.  Nonmonotonic logic - context-dependent reasoning , 1997, Artificial intelligence.

[4]  Vladimir Lifschitz,et al.  Nonmonotonic Databases and Epistemic Queries , 1991, IJCAI.

[5]  Michael Kaminski.  Embedding a default system into nonmonotonic logics , 1991, Fundam. Informaticae.

[6]  Victor W. Marek,et al.  Autoepistemic logic , 1991, JACM.

[7]  Kurt Konolige,et al.  On the Relation Between Default and Autoepistemic Logic , 1987, Artif. Intell..

[8]  Joseph Y. Halpern,et al.  Towards a Theory of Knowledge and Ignorance: Preliminary Report , 1989, NMR.

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

[10]  Victor W. Marek,et al.  Modal nonmonotonic logics: ranges, characterization, computation , 1991, JACM.

[11]  Grigori Schwarz.  Bounding Introspection in Nonmonotonic Logic , 1992, KR.

[12]  Grigori Schwarz,et al.  Minimal model semantics for nonmonotonic modal logics , 1992, [1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science.

[13]  Miroslaw Truszczynski,et al.  Modal Logic S4F and The Minimal Knowledge Paradigm , 1992, TARK.

[14]  Drew McDermott,et al.  Nonmonotonic Logic II: Nonmonotonic Modal Theories , 1982, JACM.

[15]  Michael Kaminski,et al.  Nonmonotonic default modal logics , 1990, JACM.

[16]  Drew McDermott,et al.  Non-Monotonic Logic I , 1987, Artif. Intell..

[17]  Francesco M. Donini,et al.  Ground Nonmonotonic Modal Logics for Knowledge Representation , 1995, WOCFAI.

[18]  Fangzhen Lin,et al.  A Logic of Knowledge and Justified Assumptions , 1992, Artif. Intell..

[19]  Miroslaw Truszczynzki.  Modal interpretations of default logic , 1991, IJCAI 1991.

[20]  Miroslaw Truszczynski,et al.  Minimal Knowledge Problem: A New Approach , 1994, Artif. Intell..

[21]  Grigori Schwarz.  Autoepistemic Logic of Knowledge , 1991, LPNMR.

[22]  Raymond Reiter,et al.  A Logic for Default Reasoning , 1987, Artif. Intell..

[23]  V. Wiktor Marek,et al.  Nonmonotonic Logic , 1993, Artificial Intelligence.

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

[25]  Yoav Shoham,et al.  Nonmonotonic Logics: Meaning and Utility , 1987, IJCAI.