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21
Semantical Characterizations and Complexity of Equivalences in Answer Set Programming
 ACM TRANSACTIONS ON COMPUTATIONAL LOGIC
, 2007
"... In recent research on nonmonotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P ∪ R and Q ∪ R have the same answer sets for any other program R. This property strengthens the equivalence of P and Q with respect to answe ..."
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Cited by 31 (12 self)
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In recent research on nonmonotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P ∪ R and Q ∪ R have the same answer sets for any other program R. This property strengthens the equivalence of P and Q with respect to answer sets (which is the particular case for R =∅), and has its applications in program optimization, verification, and modular logic programming. In this article, we consider more liberal notions of strong equivalence, in which the actual form of R may be syntactically restricted. On the one hand, we consider uniform equivalence where R is a set of facts, rather than a set of rules. This notion, which is wellknown in the area of deductive databases, is particularly useful for assessing whether programs P and Q are equivalent as components of a logic program which is modularly structured. On the other hand, we consider relativized notions of equivalence where R ranges over rules over a fixed alphabet, and thus generalize our results to relativized notions of strong and uniform equivalence. For all these notions, we consider disjunctive logic programs in the propositional (ground) case as well as some restricted classes, providing semantical characterizations and analyzing the computational complexity. Our results, which naturally extend to answer set semantics for programs with strong negation, complement the results on strong
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 17 (12 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.
Replacements in nonground answerset programming
 In Proceedings of International Conference on Principles of Knowledge Representation and Reasoning (KR
, 2006
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Logic Programming for Knowledge Representation
, 2007
"... This note provides background information and references to the tutorial on recent research developments in logic programming inspired by need of knowledge representation. ..."
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Cited by 11 (0 self)
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This note provides background information and references to the tutorial on recent research developments in logic programming inspired by need of knowledge representation.
Complexity results for answer set programming with bounded predicate arities and implications
, 2007
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Answer set programming for the semantic web
 TUTORIAL AT 3RD EUROPEAN SEMANTIC WEB CONFERENCE (ESWC’06
, 2006
"... The purpose of this tutorial is to get the audience familiar with the Answer Set Programming (ASP) Paradigm in the perspective of its fruitful usage for Semantic Web applications. ASP is a declarative programming paradigm with its roots in Knowledge Representation and Logic Programming. Systems and ..."
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Cited by 8 (5 self)
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The purpose of this tutorial is to get the audience familiar with the Answer Set Programming (ASP) Paradigm in the perspective of its fruitful usage for Semantic Web applications. ASP is a declarative programming paradigm with its roots in Knowledge Representation and Logic Programming. Systems and languages based on ASP are ready for tackling many of the challenges the Semantic Web offers, and in particular, are good candidates for solving a variety of issues which have been delegated to the Rule/Logic Layers in the Semantic Web vision. ASP systems are scalable, allow to mix monotonic with nonmonotonic reasoning, permit to combine rules with ontologies, and can interface external reasoners. Moreover, ASP is especially tailored at solving configuration and matchmaking problems involving reasoning with preferences by featuring easy to use, fully declarative soft & hard constraint specification languages. We introduce the attendees to the ASP basics and its principal extensions tailored at Semantic Web applications. We discuss the current impact of Answer Set Programming in the Semantic Web Area and possible future directions. Applications and exercises are presented. The attendees will practice through an online interface using one of the stateoftheart ASP solvers and some of its extensions.
Data integration and answer set programming
 In Proc. LPNMR’05, number 3662 in LNCS
, 2005
"... Abstract. The rapid expansion of the Internet and World Wide Web led to growing interest in data and information integration, which should be capable to deal with inconsistent and incomplete data. Answer Set solvers have been considered as a tool for data integration systems by different authors. We ..."
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Abstract. The rapid expansion of the Internet and World Wide Web led to growing interest in data and information integration, which should be capable to deal with inconsistent and incomplete data. Answer Set solvers have been considered as a tool for data integration systems by different authors. We discuss why data integration can be an interesting model application of Answer Set programming, reviewing valuable features of nonmonotonic logic programs in this respect, and emphasizing the role of the application for driving research. 1
Equivalences in answerset programming by countermodels in the logic of hereandthere
 of Lecture Notes in Computer Science
, 2008
"... Abstract. Different notions of equivalence, such as the prominent notions of strong and uniform equivalence, have been studied in AnswerSet Programming, mainly for the purpose of identifying programs that can serve as substitutes without altering the semantics, for instance in program optimization. ..."
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Abstract. Different notions of equivalence, such as the prominent notions of strong and uniform equivalence, have been studied in AnswerSet Programming, mainly for the purpose of identifying programs that can serve as substitutes without altering the semantics, for instance in program optimization. Such semantic comparisons are usually characterized by various selections of models in the logic of HereandThere (HT). For uniform equivalence however, correct characterizations in terms of HTmodels can only be obtained for finite theories, respectively programs. In this article, we show that a selection of countermodels in HT captures uniform equivalence also for infinite theories. This result is turned into coherent characterizations of the different notions of equivalence by countermodels, as well as by a mixture of HTmodels and countermodels (socalled equivalence interpretations). Moreover, we generalize the socalled notion of relativized hyperequivalence for programs to propositional theories, and apply the same methodology in order to obtain a semantic characterization which is amenable to infinite settings. This allows for a lifting of the results to firstorder theories under a very general semantics given in terms of a quantified version of HT. We thus obtain a general framework for the study of various notions of equivalence for theories under answerset semantics. Moreover, we prove an expedient property that allows for a simplified
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 ..."
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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
ModelBased Recasting in AnswerSet Programming
"... Abstract. As wellknown, answerset programs do not satisfy the replacement property in general, i.e., programs P and Q that are equivalent may cease to be so when they are put in the context of some other program R, i.e., R ∪ P and R ∪ Q may have different (sets of) answer sets. Pearce et al. thus ..."
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Cited by 4 (2 self)
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Abstract. As wellknown, answerset programs do not satisfy the replacement property in general, i.e., programs P and Q that are equivalent may cease to be so when they are put in the context of some other program R, i.e., R ∪ P and R ∪ Q may have different (sets of) answer sets. Pearce et al. thus introduced strong equivalence for contextindependent equivalence, and proved that such equivalence holds between given programs P and Q iff P and Q are equivalent theories in the monotonic logic of hereandthere. In this article, we consider a related question: given a program P, does there exist some program Q from a certain class C of programs such that P and Q are equivalent under a given notion of equivalence? Furthermore, if the answer to this question is positive, how can we recast P to an equivalent program from C (i.e., construct such a Q)? In particular, we consider classes of programs that emerge by (dis)allowing disjunction and/or negation, and as equivalence notions we consider strong, uniform, and ordinary equivalence. Based on general modeltheoretic properties and a novel form of canonical programs, we develop semantic characterisations for the existence of such a program Q, determine the computational complexity of checking existence, and provide (local) rewriting rules for recasting.