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2009
Springer

The Complexity of Reasoning for Fragments of Default Logic

8 years 11 months ago
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 Σp 2-complete, and the complexity of the credulous and skeptical reasoning problem as Σp 2-complete, resp. Πp 2complete. 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 trichotomy (Σp 2-, NP-complete, trivial) for the extension existence problem, whereas for the credulous and sceptical reasoning problem we get a finer classification down to NL-complete cases.
Olaf Beyersdorff, Arne Meier, Michael Thomas, Heri
Added 27 May 2010
Updated 27 May 2010
Type Conference
Year 2009
Where SAT
Authors Olaf Beyersdorff, Arne Meier, Michael Thomas, Heribert Vollmer
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