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KGC
1993
Springer

Nonmonotonic Reasoning is Sometimes Simpler

14 years 3 months ago
Nonmonotonic Reasoning is Sometimes Simpler
We establish the complexity of decision problems associated with the nonmonotonic modal logic S4. We prove that the problem of existence of an S4-expansion for a given set A of premises is P 2 -complete. Similarly, we show that for a given formula ' and a set A of premises, it is P 2 complete to decide whether ' belongs to at least one S4-expansion for A, and it is P 2 -complete to decide whether ' belongs to all S4-expansions for A. This refutes a conjecture of Gottlob that these problems are PSPACE-complete. An interesting aspect of these results is that reasoning (testing satis ability and provability) in the monotonic modal logic S4 is PSPACE-complete. To the best of our knowledge, the nonmonotonic logic S4 is the rst example of a nonmonotonic formalism which is computationally easier than the monotonic logic that underlies it (assuming PSPACE does not collapse to P 2 ).
Grigori Schwarz, Miroslaw Truszczynski
Added 10 Aug 2010
Updated 10 Aug 2010
Type Conference
Year 1993
Where KGC
Authors Grigori Schwarz, Miroslaw Truszczynski
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