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Intellektik: Technical report 93-12

Possible Worlds Semantics for Default Logics

P. Besnard and T. Schaub

We introduce a uniform semantical framework for various default logics in terms of Kripke structures. This possible worlds approach provides a simple but meaningful instrument for comparing existing default logics in a unified setting. The possible worlds semantics is introduced by means of constrained default logic. Also, it easily deals with Brewka's cumulative default logic. The semantics is then extended to Reiter's original default logic as well as Lukaszewicz' variant. The possible worlds approach remedies several difficulties encountered in former proposals aiming at individual default logics. Notably, it provides the first pure model--theoretic semantics for Lukaszewicz' variant of default logic. Since the semantical framework is presented from the perspective of ``commitment to assumptions'' we also obtain a very natural modal interpretation of the notion of commitment.

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