Details
| Original language | English |
|---|---|
| Title of host publication | Theory and Applications of Satisfiability Testing - SAT 2009, 12th International Conference, SAT 2009, Swansea, UK, June 30 - July 3, 2009. Proceedings |
| Editors | Oliver Kullmann |
| Pages | 51-64 |
| Number of pages | 14 |
| Volume | 5584 |
| Publication status | Published - 28 Aug 2008 |
Publication series
| Name | Lecture Notes in Computer Science |
|---|---|
| Publisher | Springer |
Abstract
Keywords
- cs.CC, cs.LO, F.2.2; F.4.1; I.2.3; I.2.4
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Theory and Applications of Satisfiability Testing - SAT 2009, 12th International Conference, SAT 2009, Swansea, UK, June 30 - July 3, 2009. Proceedings. ed. / Oliver Kullmann. Vol. 5584 2008. p. 51-64 (Lecture Notes in Computer Science).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - The Complexity of Reasoning for Fragments of Default Logic
AU - Beyersdorff, Olaf
AU - Meier, Arne
AU - Thomas, Michael
AU - Vollmer, Heribert
PY - 2008/8/28
Y1 - 2008/8/28
N2 - 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.
AB - 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.
KW - cs.CC
KW - cs.LO
KW - F.2.2; F.4.1; I.2.3; I.2.4
U2 - 10.1007/978-3-642-02777-27
DO - 10.1007/978-3-642-02777-27
M3 - Conference contribution
VL - 5584
T3 - Lecture Notes in Computer Science
SP - 51
EP - 64
BT - Theory and Applications of Satisfiability Testing - SAT 2009, 12th International Conference, SAT 2009, Swansea, UK, June 30 - July 3, 2009. Proceedings
A2 - Kullmann, Oliver
ER -