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S.: Complexity results for checking equivalence of stratified logic programs
 Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI’07
, 2007
"... Recent research in nonmonotonic logic programming under the answerset semantics focuses on different notions of program equivalence. However, previous results do not address the important classes of stratified programs and its subclass of acyclic (i.e., recursionfree) programs, although they are r ..."
Abstract

Cited by 5 (4 self)
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Recent research in nonmonotonic logic programming under the answerset semantics focuses on different notions of program equivalence. However, previous results do not address the important classes of stratified programs and its subclass of acyclic (i.e., recursionfree) programs, although they are recognized as important tools for knowledge representation and reasoning. In this paper, we consider such programs, possibly augmented with constraints. Our results show that in the propositional setting, where reasoning is wellknown to be polynomial, deciding strong and uniform equivalence is as hard as for arbitrary normal logic programs (and thus coNPcomplete), but is polynomial in some restricted cases. Nonground programs behave similarly. However, exponential lower bounds already hold for small programs (i.e., with constantly many rules). In particular, uniform equivalence is undecidable even for small Horn programs plus a single negative constraint. 1
Characterising equilibrium logic and nested logic programs: Reductions and complexity
, 2009
"... Equilibrium logic is an approach to nonmonotonic reasoning that extends the stablemodel and answerset semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations are permitted in heads and bodies of rules, as special kind ..."
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Cited by 4 (2 self)
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Equilibrium logic is an approach to nonmonotonic reasoning that extends the stablemodel and answerset semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations are permitted in heads and bodies of rules, as special kinds of theories. In this paper, we present polynomial reductions of the main reasoning tasks associated with equilibrium logic and nested logic programs into quantified propositional logic, an extension of classical propositional logic where quantifications over atomic formulas are permitted. Thus, quantified propositional logic is a fragment of secondorder logic, and its formulas are usually referred to as quantified Boolean formulas (QBFs). We provide reductions not only for decision problems, but also for the central semantical concepts of equilibrium logic and nested logic programs. In particular, our encodings map a given decision problem into some QBF such that the latter is valid precisely in case the former holds. The basic tasks we deal with here are the consistency problem, brave reasoning, and skeptical reasoning. Additionally, we also provide encodings for testing equivalence of theories or programs under different notions