A Fully Model-Theoretic Semantics for Model-Preference Default Systems

Propositional systems of default inference based on the dyadic relation of preference between models have recently been proposed by Selman and Kautz to provide a computationally tractable mechanism for the generation of vivid knowledge bases. In this paper we argue that the formalism proposed, albeit endowed with a semantic flavour, is not a model-theoretic (or denotational) semantics, as no ontology which is independent of the existence of the knowledge representation language is postulated. Consistently with good model-theoretic practice we carry on to postulate a language-independent ontology and to use it in the subsequent definition of a fully model-theoretic semantics for model-preference default systems. This semantics is instrumental in providing guidelines for the development of algorithms that reason on model-preference default systems, and for comparing this with other “preferential” nonmonotonic formalisms recently proposed in the literature.

[1]  Alexander Borgida,et al.  Vivid Knowledge and Tractable Reasoning , 1989, IJCAI.

[2]  Matthew L. Ginsberg,et al.  Readings in Nonmonotonic Reasoning , 1987, AAAI 1987.

[3]  Erik Sandewall,et al.  The Semantics of Non-Monotonic Entailment Defined Using Partial Interpretations , 1988, NMR.

[4]  P. Johnson-Laird Mental models , 1989 .

[5]  Henry Kautz,et al.  Vivid Knowledge and Tractable Reasoning: Preliminary Report , 1989, IJCAI 1989.

[6]  J. McCarthy Circumscription|a Form of Nonmonotonic Reasoning , 1979 .

[7]  Hector J. Levesque Making Believers out of Computers , 1989 .

[8]  Grigoris Antoniou,et al.  Nonmonotonic reasoning , 1997 .

[9]  Kurt Konolige,et al.  On the Relation Between Default Theories and Autoepistemic Logic , 1987, IJCAI.

[10]  H. Levesque Logic and the complexity of reasoning , 1988 .

[11]  Saul A. Kripke,et al.  Semantical Analysis of Modal Logic I Normal Modal Propositional Calculi , 1963 .

[12]  Bart Selman,et al.  The Complexity of Model-Preference Default Theories , 1988, NMR.

[13]  John McCarthy,et al.  Circumscription - A Form of Non-Monotonic Reasoning , 1980, Artif. Intell..

[14]  Yoav Shoham,et al.  A semantical approach to nonmonotonic logics , 1987, LICS 1987.

[15]  John McCarthy,et al.  Applications of Circumscription to Formalizing Common Sense Knowledge , 1987, NMR.

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

[17]  Yoav Shoham,et al.  New Results on Semantical Non-Monotonic Reasoning , 1988, NMR.

[18]  Piotr Rychlik,et al.  The Generalized Theory of Model Preference (Preliminary Report) , 1990 .