The Complexity of Reasoning for Fragments of Default Logic

Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified the complexity of the extension existence problem for propositional default logic as \SigmaPtwo-complete, and the complexity of the credulous and skeptical reasoning problem as SigmaP2-complete, resp. PiP2-complete. Additionally, he investigated restrictions on the default rules, i.e., semi-normal default rules. Selman made in 1992 a similar approach with disjunction-free and unary default rules. In this paper we systematically restrict the set of allowed propositional connectives. We give a complete complexity classification for all sets of Boolean functions in the meaning of Post's lattice for all three common decision problems for propositional default logic. We show that the complexity is a hexachotomy (SigmaP2-, DeltaP2-, NP-, P-, NL-complete, trivial) for the extension existence problem, while for the credulous and skeptical reasoning problem we obtain similar classifications without trivial cases.Comment: Corrected versio

Reactive preferential structures and nonmonotonic consequence

We introduce information bearing systems (IBRS) as an abstraction of many logical systems. We define a general semantics for IBRS, and show that IBRS generalize in a natural way preferential semantics and solve open representation problems

Set-Theoretic Completeness for Epistemic and Conditional Logic

The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of formulas in the language (the semantics), a collection of axioms and rules of inference characterizing reasoning (the proof theory), and then relate the proof theory to the semantics via soundness and completeness results. Here we consider an approach that is more common in the economics literature, which works purely at the semantic, set-theoretic level. We provide set-theoretic completeness results for a number of epistemic and conditional logics, and contrast the expressive power of the syntactic and set-theoretic approachesComment: This is an expanded version of a paper that appeared in AI and Mathematics, 199