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15
Facts do not Cease to Exist Because They are Ignored: Relativised Uniform Equivalence with AnswerSet Projection
 In Proceedings of the 22nd National Conference on Artificial Intelligence (AAAI 2007
, 2007
"... Recent research in answerset programming (ASP) focuses on different notions of equivalence between programs which are relevant for program optimisation and modular programming. Prominent among these notions is uniform equivalence, which checks whether two programs have the same semantics when joine ..."
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Cited by 13 (10 self)
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Recent research in answerset programming (ASP) focuses on different notions of equivalence between programs which are relevant for program optimisation and modular programming. Prominent among these notions is uniform equivalence, which checks whether two programs have the same semantics when joined with an arbitrary set of facts. In this paper, we study a family of more finegrained versions of uniform equivalence, where the alphabet of the added facts as well as the projection of answer sets is taken into account. The latter feature, in particular, allows the removal of auxiliary atoms in computation, which is important for practical programming aspects. We introduce novel semantic characterisations for the equivalence problems under consideration and analyse the computational complexity for checking these problems. We furthermore provide efficient reductions to quantified propositional logic, yielding a rapidprototyping system for equivalence checking.
SELP  a system for studying strong equivalence between logic programs
 In Proceedings of the 8th International Conference on Logic Programming and Nonmonotonic Reasoning(LPNMR 2005
, 2005
"... Abstract. This paper describes a system called SELP for studying strong equivalence in answer set logic programming. The basic function of the system is to check if two given ground disjunctive logic programs are equivalent, and if not, return a counterexample. This allows us to investigate some in ..."
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Cited by 12 (1 self)
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Abstract. This paper describes a system called SELP for studying strong equivalence in answer set logic programming. The basic function of the system is to check if two given ground disjunctive logic programs are equivalent, and if not, return a counterexample. This allows us to investigate some interesting properties of strong equivalence, such as a complete characterization for a rule to be strongly equivalent to another one, and checking whether a given set of rules is strongly equivalent to another, perhaps simpler set of rules. 1
Replacements in nonground answerset programming
 In Proceedings of International Conference on Principles of Knowledge Representation and Reasoning (KR
, 2006
"... ..."
Discovering theorems in game theory: Twoperson games with unique pure Nash equilibrium payoffs
, 2007
"... In this paper we provide a logical framework for using computers to discover theorems in twoperson finite games in strategic form, and apply it to discover classes of games that have unique pure Nash equilibrium payoffs. We consider all possible classes of games that can be expressed by a conjuncti ..."
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Cited by 8 (4 self)
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In this paper we provide a logical framework for using computers to discover theorems in twoperson finite games in strategic form, and apply it to discover classes of games that have unique pure Nash equilibrium payoffs. We consider all possible classes of games that can be expressed by a conjunction of two binary clauses, and our program rediscovered Kats and Thisse’s class of weakly unilaterally competitive twoperson games, and came up with several other classes of games that have unique pure Nash equilibrium payoffs. It also came up with new classes of strict games that have unique pure Nash equilibria, where a game is strict if for both player different profiles have different payoffs.
Minimal logic programs
"... Abstract. bb We consider the problem of obtaining a minimal logic program strongly equivalent (under the stable models semantics) to a given arbitrary propositional theory. We propose a method consisting in the generation of the set of prime implicates of the original theory, starting from its set o ..."
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Cited by 7 (2 self)
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Abstract. bb We consider the problem of obtaining a minimal logic program strongly equivalent (under the stable models semantics) to a given arbitrary propositional theory. We propose a method consisting in the generation of the set of prime implicates of the original theory, starting from its set of countermodels (in the logic of HereandThere), in a similar vein to the QuineMcCluskey method for minimisation of boolean functions. As a side result, we also provide several results about fundamental rules (those that are not tautologies and do not contain redundant literals) which are combined to build the minimal programs. In particular, we characterise their form, their corresponding sets of countermodels, as well as necessary and sufficient conditions for entailment and equivalence among them.
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 6 (5 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.
Computing Loops with at Most One External Support Rule for Disjunctive Logic Programs
"... Abstract. We extend to disjunctive logic programs our previous work on computing loop formulas of loops with at most one external support. We show that for these logic programs, loop formulas of loops with no external support can be computed in polynomial time, and if the given program has no constr ..."
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Cited by 4 (1 self)
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Abstract. We extend to disjunctive logic programs our previous work on computing loop formulas of loops with at most one external support. We show that for these logic programs, loop formulas of loops with no external support can be computed in polynomial time, and if the given program has no constraints, an iterative procedure based on these formulas, the program completion, and unit propagation computes the least fixed point of a simplification operator used by DLV. We also relate loops with no external supports to the unfounded sets and the wellfounded semantics of disjunctive logic programs by Wang and Zhou. However, the problem of computing loop formulas of loops with at most one external support rule is NPhard for disjunctive logic programs. We thus propose a polynomial algorithm for computing some of these loop formulas, and show experimentally that this polynomial approximation algorithm can be effective in practice. 1
On Modular Translations and Strong Equivalence
 Proceedings of the 8th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR05), volume 3552 of LNCS, 79–91
"... Abstract. Given two classes of logic programs, we may be interested in modular translations from one class into the other that are sound wth respect to the answer set semantics. The main theorem of this paper characterizes the existence of such a translation in terms of strong equivalence. The theor ..."
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Cited by 4 (0 self)
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Abstract. Given two classes of logic programs, we may be interested in modular translations from one class into the other that are sound wth respect to the answer set semantics. The main theorem of this paper characterizes the existence of such a translation in terms of strong equivalence. The theorem is used to study the expressiveness of several classes of programs, including the comparison of cardinality constraints with monotone cardinality atoms. 1
A.: Minimal logic programs (extended report) (2007) Technical report available at http://www.dc.fi.udc.es/~cabalar/ minlpext.pdf
"... Abstract. aa We consider the problem of obtaining a minimal logic program strongly equivalent (under the stable models semantics) to a given arbitrary propositional theory. We propose a method consisting in the generation of the set of prime implicates of the original theory, starting from its set o ..."
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Cited by 2 (2 self)
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Abstract. aa We consider the problem of obtaining a minimal logic program strongly equivalent (under the stable models semantics) to a given arbitrary propositional theory. We propose a method consisting in the generation of the set of prime implicates of the original theory, starting from its set of countermodels (in the logic of HereandThere), in a similar vein to the QuineMcCluskey method for minimisation of boolean functions. As a side result, we also provide several results about fundamental rules (those that are not tautologies and do not contain redundant literals) which are combined to build the minimal programs. In particular, we characterise their form, their corresponding sets of countermodels, as well as necessary and sufficient conditions for entailment and equivalence among them.
FinitelyVerifiable Classes of Sentences
, 2007
"... This paper proposes a notion of finitelyverifiable classes of sentences. Informally, a class of sentences is finitelyverifiable if whether a sentence in this class is a theorem of a given theory can be checked with respect to a finite set of models of the theory. The usefulness of this notion is i ..."
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Cited by 2 (2 self)
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This paper proposes a notion of finitelyverifiable classes of sentences. Informally, a class of sentences is finitelyverifiable if whether a sentence in this class is a theorem of a given theory can be checked with respect to a finite set of models of the theory. The usefulness of this notion is illustrated using examples from arithmetics, firstorder logic, game theory, and planning.