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Sequent calculi for skeptical reasoning in predicate default logic and other nonmonotonic logics

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Sequent calculi for skeptical consequence in predicate default logic, predicate stable model logic programming, and infinite autoepistemic theories are presented and proved sound and complete. While skeptical consequence is decidable in the finite propositional case of all three formalisms, the move to predicate or infinite theories increases the complexity of skeptical reasoning to being Π 11 -complete. This implies the need for sequent rules with countably many premises, and such rules are employed.

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Correspondence to Robert Saxon Milnikel.

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AMS subject classification

03B42, 68N17, 68T27

This paper grew directly out of the author’s dissertation, written under the direction of Anil Nerode.

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Milnikel, R.S. Sequent calculi for skeptical reasoning in predicate default logic and other nonmonotonic logics. Ann Math Artif Intell 44, 1–34 (2005).

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