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On Eliminating Disjunctions in Stable Logic Programming
 PROCEEDINGS OF THE 9TH INTERNATIONAL CONFERENCE ON PRINCIPLES OF KNOWLEDGE REPRESENTATION AND REASONING (KR 2004
, 2003
"... Disjunction is generally considered to add expressive power to logic programs under the stable model semantics, which have become a popular programming paradigm for knowledge representation and reasoning. However, disjunction is often not really needed, in that an equivalent program without disju ..."
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Disjunction is generally considered to add expressive power to logic programs under the stable model semantics, which have become a popular programming paradigm for knowledge representation and reasoning. However, disjunction is often not really needed, in that an equivalent program without disjunction can be given. In this paper, we consider the question, given a disjunctive logic program, P , under which conditions does there exist an equivalent normal (i.e., disjunctionfree) logic program P . In fact, we study this problem under different notions of equivalence, viz. for ordinary equivalence (considering the collections of all stable models of the programs) as well as for the more restrictive notions of strong and uniform equivalence. We resolve the issue for propositional programs on which we focus here, and present a simple, appealing semantic criterion from which all disjunctions can be eliminated under strong equivalence; testing this criterion is coNPcomplete, but the class of programs satisfying it has the same complexity as disjunctive logic programs in general. We also show that under ordinary and uniform equivalence, disjunctions can always be eliminated. In all cases, we give constructive methods to achieve this. However, we also provide evidence that disjunctive logic programs are a more succinct knowledge representation formalism than normal logic programs under all these notions of equivalence.
Replacements in nonground answerset programming
 In Proceedings of International Conference on Principles of Knowledge Representation and Reasoning (KR
, 2006
"... ..."
A common view on strong, uniform, and other notions of equivalence in answerset programming. Theory and Practice of Logic Programming
"... Logic programming under the answerset semantics nowadays deals with numerous different notions of program equivalence. This is due to the fact that equivalence for substitution (known as strong equivalence) and ordinary equivalence are different concepts. The former holds, given programs P and Q, i ..."
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Cited by 8 (6 self)
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Logic programming under the answerset semantics nowadays deals with numerous different notions of program equivalence. This is due to the fact that equivalence for substitution (known as strong equivalence) and ordinary equivalence are different concepts. The former holds, given programs P and Q, iff P can be faithfully replaced by Q within any context R, while the latter holds iff P and Q provide the same output, that is, they have the same answer sets. Notions in between strong and ordinary equivalence have been introduced as theoretical tools to compare incomplete programs and are defined by either restricting the syntactic structure of the considered context programs R or by bounding the set A of atoms allowed to occur in R (relativized equivalence). For the latter approach, different A yield properly different equivalence notions, in general. For the former approach, however, it turned out that any “reasonable ” syntactic restriction to R coincides with either ordinary, strong, or uniform equivalence (for uniform equivalence, the context ranges over arbitrary sets of facts, rather than program rules). In this paper, we propose a parameterization for equivalence notions which takes care of both such kinds of restrictions simultaneously by bounding, on the one hand, the atoms which are allowed to occur in the rule heads of the context and, on the other hand, the atoms which are allowed to occur in the rule bodies of the context. We introduce a general semantical characterization which includes known ones as SEmodels (for strong equivalence) or UEmodels (for uniform equivalence) as special cases. Moreover, we provide complexity bounds for the problem in question and sketch a possible implementation method making use of dedicated systems for checking ordinary equivalence. KEYWORDS: Answerset programming, strong equivalence, relativized equivalence.
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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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.
Advanced Preprocessing for Answer Set Solving
"... Abstract. We introduce the first substantial approach to preprocessing in the context of answer set solving. The idea is to simplify a logic program while identifying equivalences among its relevant constituents. These equivalences are then used for building a compact representation of the program ( ..."
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Abstract. We introduce the first substantial approach to preprocessing in the context of answer set solving. The idea is to simplify a logic program while identifying equivalences among its relevant constituents. These equivalences are then used for building a compact representation of the program (in terms of Boolean constraints). We implemented our approach as well as a SATbased technique to reduce Boolean constraints. This allows us to empirically analyze both preprocessing types and to demonstrate their computational impact. 1
S.: Belief revision of logic programs under answer set semantics
 In: KR’08, AAAI
, 2008
"... We address the problem of belief revision in (nonmonotonic) logic programming under answer set semantics: given logic programs P and Q, the goal is to determine a program R that corresponds to the revision of P by Q, denoted P ∗ Q. Unlike previous approaches in logic programming, our formal techniqu ..."
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We address the problem of belief revision in (nonmonotonic) logic programming under answer set semantics: given logic programs P and Q, the goal is to determine a program R that corresponds to the revision of P by Q, denoted P ∗ Q. Unlike previous approaches in logic programming, our formal techniques are analogous to those of distancebased belief revision in propositional logic. In developing our results, we build upon the model theory of logic programs furnished by SE models. Since SE models provide a formal, monotonic chacterisation of logic programs, we can adapt wellknown techniques from the area of belief revision to revision in logic programs. We investigate two specific operators: (logic program) expansion and a revision operator based on the distance between the SE models of logic programs. It proves to be the case that expansion is an interesting operator in its own right, unlike in classical AGMstyle belief revision where it is relatively uninteresting. Expansion and revision are shown to satisfy a suite of interesting properties; in particular, our revision operators satisfy the majority of the AGM postulates for revision. A complexity analysis reveals that our revision operators do not increase the complexity of the base formalism. As a consequence, we present an encoding for computing the revision of a logic program by another, within the same logic programming framework.
Testing strong equivalence of datalog programs  implementation and examples
 In Baral et al
"... Abstract. In this work we describe a system for determining strong equivalence of disjunctive nonground datalog programs under the stable model semantics. The problem is tackled by reducing it to the unsatisfiability problem of firstorder formulas in the BernaysSchönfinkel fragment. We then employ ..."
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Cited by 5 (1 self)
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Abstract. In this work we describe a system for determining strong equivalence of disjunctive nonground datalog programs under the stable model semantics. The problem is tackled by reducing it to the unsatisfiability problem of firstorder formulas in the BernaysSchönfinkel fragment. We then employ a tableauxbased theorem prover, which (unlike most other currently available provers) is guaranteed to terminate for these formulas. To the best of our knowledge, this is the first strong equivalence tester for disjunctive nonground datalog. 1
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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Cited by 4 (0 self)
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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
Extended ASP Tableaux and Rule Redundancy in Normal Logic Programs
 Proceedings of International Conference on Logic Programming, 2007
, 1951
"... Abstract. We introduce an extended tableau calculus for answer set programming (ASP). The proof system is based on the ASP tableaux defined in [Gebser&Schaub, ICLP 2006], with an added extension rule. We investigate the power of Extended ASP Tableaux both theoretically and empirically. We study the ..."
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Cited by 4 (1 self)
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Abstract. We introduce an extended tableau calculus for answer set programming (ASP). The proof system is based on the ASP tableaux defined in [Gebser&Schaub, ICLP 2006], with an added extension rule. We investigate the power of Extended ASP Tableaux both theoretically and empirically. We study the relationship of Extended ASP Tableaux with the Extended Resolution proof system defined by Tseitin for clause sets, and separate Extended ASP Tableaux from ASP Tableaux by giving a polynomial length proof of a family of normal logic programs {Πn} for which ASP Tableaux has exponential length minimal proofs with respect to n. Additionally, Extended ASP Tableaux imply interesting insight into the effect of program simplification on the length of proofs in ASP. Closely related to Extended ASP Tableaux, we empirically investigate the effect of redundant rules on the efficiency of ASP solving. 1
Strong equivalence for logic programs with preferences
 In Proc. IJCAI 2005
, 2005
"... Recently, strong equivalence for Answer Set Programming has been studied intensively, and was shown to be beneficial for modular programming and automated optimization. In this paper we define the novel notion of strong equivalence for logic programs with preferences. Based on this definition we giv ..."
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Cited by 3 (0 self)
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Recently, strong equivalence for Answer Set Programming has been studied intensively, and was shown to be beneficial for modular programming and automated optimization. In this paper we define the novel notion of strong equivalence for logic programs with preferences. Based on this definition we give, for several semantics for preference handling, necessary and sufficient conditions for programs to be strongly equivalent. These results provide a clear picture of the relationship of these semantics with respect to strong equivalence, which differs considerably from their relationship with respect to answer sets. Finally, based on these results, we present for the first time simplification methods for logic programs with preferences. 1