On finding extensions of default theories
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We study from the computational standpoint the problem of finding an extension of a given default theory, and extend previous results in three directions. We show that all default theories that have no odd cycles (in some precise sense) have an extension, which can he found efficiently. We prove that it is NP-complete to find extensions even for default theories with no prerequisites and at most two literals per default. We also characterize precisely the complexity of finding extensions in general default theories: The problem is ∑ 2 P -complete.
KeywordsLogic Program Conjunctive Normal Form Truth Assignment Extension Problem Default Theory
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