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Title: Representing "Recursive" Default Logic in Modal Logic
Authors: Brown, Frank
Keywords: Recursive Definition of Default Logic
Modal Logic
Nonmonotonic Logic
Issue Date: 2004
Publisher: Institute of Information Theories and Applications FOI ITHEA
Abstract: The "recursive" definition of Default Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the "recursive" fixed-point equation of Default Logic with an initial set of axioms and defaults if and only if the meaning of the fixed-point is logically equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in those defaults. This is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and because unlike the original "recursive" definition of Default Logic, it is easily generalized to the case where quantified variables may be shared across the scope of the components of the defaults.
ISSN: 1313-0463
Appears in Collections:Volume 11 Number 4

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