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Translating default logic into standard autoepistemic logic

Authors: Gottlob, G;

Translating default logic into standard autoepistemic logic

Abstract

Since Konolige's translation of default logic into strongly grounded autoepistemic logic, several other variants of Moore's original autoepistemic logic that embody default logic have been studied. All these logics differ significantly from Moore's autoepistemic logic (standard AEL) in that expansions are subject to additional groundedness-conditions. Hence, the question naturally arises whether default logic can be translated into standard AEL at all. We show that a modular translation is not possible. However, we are able to construct a faithful polynomial-time translation from default logic into standard AEL, which is nonmodular. Our translation exploits the self-referentiality of AEL. It uses as an important intermediate step an embedding of Marek's and Truszczyn´ski's nonmonotonic logic N into standard AEL. It follows from our results that the expressive power of standard AEL is strictly greater than that of default logic.

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Keywords

Logic in artificial intelligence, polynomial-time translation, default logic, nonmonotonic logic, Other nonclassical logic, autoepistemic logic, nonmonotonic reasoning, modal logic

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
44
Average
Top 10%
Top 10%
Green