Technical Report CS0793

TR#:CS0793
Class:CS
Title: A MODAL LOGIC FOR SUBJECTIVE DEFAULT REASONING.
Authors: S. Ben-David and R. Ben-Eliyahu
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Abstract:

We introduce a logic endowed with a two-place modal connective that has the intended meaning of ``If \alpha, then normally \beta''. On top of providing a well-defined tool for analyzing common default reasoning, such a logic allows nesting of the default operator. Once the syntax of this new logic is defined, we go on to present a semantic framework in which many of the known default proof systems can be naturally characterized. We prove soundness and completeness theorems for several such proof systems. Our semantics is a ``neighborhood modal semantics''. It has an appealing intuitive interpretation and may be viewed as a set-theoretic generalization of the probabilistic interpretations of default reasoning. We show that our semantics is most general in the sense that any modal semantics that is sound for the basic axioms for default reasoning is a special case of our semantics. Such a generality result may serve to provide a semantical analysis of the relative strength of different proof systems and to show the nonexistence of semantics with certain properties.

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