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Some (in)translatability results for normal logic programs and propositional theories
 Journal of Applied NonClassical Logics
, 2006
"... ABSTRACT. In this article, we compare the expressive powers of classes of normal logic programs that are obtained by constraining the number of positive subgoals (n) in the bodies of rules. The comparison is based on the existence/nonexistence of polynomial, faithful, and modular (PFM) translation f ..."
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Cited by 25 (8 self)
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ABSTRACT. In this article, we compare the expressive powers of classes of normal logic programs that are obtained by constraining the number of positive subgoals (n) in the bodies of rules. The comparison is based on the existence/nonexistence of polynomial, faithful, and modular (PFM) translation functions between the classes. As a result, we obtain a strict ordering among the classes under consideration. Binary programs (n ≤ 2) are shown to be as expressive as unconstrained programs but strictly more expressive than unary programs (n ≤ 1) which, in turn, are strictly more expressive than atomic programs (n = 0). We also take propositional theories into consideration and prove them to be strictly less expressive than atomic programs. In spite of the gap in expressiveness, we develop a faithful but nonmodular translation function from normal programs to propositional theories. We consider this as a breakthrough due to subquadratic time complexity (of the order of P   × log 2 Hb(P)). Furthermore, we present a prototype implementation of the translation function and demonstrate its promising performance with SAT solvers using three benchmark problems.
Replacements in nonground answerset programming
 In Proceedings of International Conference on Principles of Knowledge Representation and Reasoning (KR
, 2006
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Hyperequivalence of logic programs with respect to supported models
 PROCEEDINGS OF AAAI 2008
, 2008
"... Recent research in nonmonotonic logic programming has focused on certain types of program equivalence, which we refer to here as hyperequivalence, that are relevant for program optimization and modular programming. So far, most results concern hyperequivalence relative to the stablemodel semantics. ..."
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Cited by 7 (6 self)
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Recent research in nonmonotonic logic programming has focused on certain types of program equivalence, which we refer to here as hyperequivalence, that are relevant for program optimization and modular programming. So far, most results concern hyperequivalence relative to the stablemodel semantics. However, other semantics for logic programs are also of interest, especially the semantics of supported models which, when properly generalized, is closely related to the autoepistemic logic of Moore. In this paper, we consider a family of hyperequivalence relations for programs based on the semantics of supported and supported minimal models. We characterize these relations in modeltheoretic terms. We use the characterizations to derive complexity results concerning testing whether two programs are hyperequivalent relative to supported and supported minimal models.
Embedding General Default Logic into the Logic of GK
"... In this paper, we show that the logic of GK is indeed a general framework for nonmonotonic reasoning by embedding general default logic into it. More importantly, we illustrate that it is also a powerful tool for studying nonmonotonic formalisms. We first show that checking for weak equivalence and ..."
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In this paper, we show that the logic of GK is indeed a general framework for nonmonotonic reasoning by embedding general default logic into it. More importantly, we illustrate that it is also a powerful tool for studying nonmonotonic formalisms. We first show that checking for weak equivalence and strong equivalence between two rule bases in general default logic can both be captured in the logic of GK and the complexities for both problems are coNP complete. Then, we show that each rule base is strongly equivalent to a set of rules of normal form. Finally, we prove that autoepistemic logic is equivalent to a proper subset of general default logic, and the selfintrospection operator in autoepistemic logic indeed plays the same role as the double negationasfailure operator in general default logic.