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Complexity of Consistent Query Answering in Databases under CardinalityBased and Incremental Repair Semantics
 In ICDT
, 2007
"... Abstract. Consistent Query Answering (CQA) is the problem of computing from a database the answers to a query that are consistent with respect to certain integrity constraints that the database, as a whole, may fail to satisfy. Consistent answers have been characterized as those that are invariant u ..."
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Cited by 30 (9 self)
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Abstract. Consistent Query Answering (CQA) is the problem of computing from a database the answers to a query that are consistent with respect to certain integrity constraints that the database, as a whole, may fail to satisfy. Consistent answers have been characterized as those that are invariant under certain minimal forms of restoration of the database consistency. In this paper we investigate algorithmic and complexity theoretic issues of CQA under database repairs that minimally departwrt the cardinality of the symmetric difference from the original database. Research on this kind of repairs has been suggested in the literature, but no systematic study had been done. Here we obtain first tight complexity bounds. We also address, considering for the first time a dynamic scenario for CQA, the problem of incremental complexity of CQA, that naturally occurs when an originally consistent database becomes inconsistent after the execution of a sequence of update operations. Tight bounds on incremental complexity are provided for various semantics under denial constraints, e.g. (a) minimum tuplebased repairs wrt cardinality, (b) minimal tuplebased repairs wrt set inclusion, and (c) minimum numerical aggregation of attributebased repairs. Fixed parameter tractability is also investigated in this dynamic context, where the size of the update sequence becomes the relevant parameter. 1
Integrating answer set programming and constraint logic programming
 Annals of Mathematics and Artificial Intelligence
, 2008
"... We introduce a knowledge representation language AC(C) extending the syntax and semantics of ASP and CRProlog, give some examples of its use, and present an algorithm, ACsolver, for computing answer sets of AC(C) programs. The algorithm does not require full grounding of a program and combines “cla ..."
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Cited by 28 (0 self)
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We introduce a knowledge representation language AC(C) extending the syntax and semantics of ASP and CRProlog, give some examples of its use, and present an algorithm, ACsolver, for computing answer sets of AC(C) programs. The algorithm does not require full grounding of a program and combines “classical” ASP solving methods with constraint logic programming techniques and CRProlog based abduction. The AC(C) based approach often allows to solve problems which are impossible to solve by more traditional ASP solving techniques. We belief that further investigation of the language and development of more efficient and reliable solvers for its programs can help to substantially expand the domain of applicability of the answer set programming paradigm. 1
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 27 (11 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
Disjunctive Answer Set Programming via Satisfiability
 Logic Programming and Nonmonotonic Reasoning — 8th International Conference, LPNMR’05, Diamante, Italy, September 2005, Proceedings. Volume 3662 of Lecture Notes in Computer Science
, 2005
"... Abstract. Using SAT solvers as inference engines in answer set programming systems showed to be a promising approach in building efficient systems. Nowadays SAT based answer set programming systems successfully work with nondisjunctive programs. This paper proposes a way to use SAT solvers for findi ..."
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Cited by 26 (2 self)
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Abstract. Using SAT solvers as inference engines in answer set programming systems showed to be a promising approach in building efficient systems. Nowadays SAT based answer set programming systems successfully work with nondisjunctive programs. This paper proposes a way to use SAT solvers for finding answer sets for disjunctive logic programs. We implement two different ways of SAT solver invocation used in nondisjunctive answer set programming. The algorithms are based on the definition of completion for disjunctive programs and the extension of loop formula to the disjunctive case. We propose the necessary modifications to the algorithms known for nondisjunctive programs in order to adapt them to the disjunctive case and demonstrate their implementation based on system CMODELS. 1
The first answer set programming system competition
 Proceedings of the 9th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2007, LNAI
, 2007
"... Abstract. This paper gives a summary of the First Answer Set Programming System Competition that was held in conjunction with the Ninth International Conference on Logic Programming and Nonmonotonic Reasoning. The aims of the competition were twofold: first, to collect challenging benchmark problems ..."
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Cited by 26 (7 self)
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Abstract. This paper gives a summary of the First Answer Set Programming System Competition that was held in conjunction with the Ninth International Conference on Logic Programming and Nonmonotonic Reasoning. The aims of the competition were twofold: first, to collect challenging benchmark problems, and second, to provide a platform to assess a broad variety of Answer Set Programming systems. The competition was inspired by similar events in neighboring fields, where regular benchmarking has been a major factor behind improvements in the developed systems and their ability to address practical applications. 1
Modularity Aspects of Disjunctive Stable Models
, 2007
"... Practically all programming languages used in software engineering allow to split a program into several modules. For fully declarative and nonmonotonic logic programming languages, however, the modular structure of programs is hard to realise, since the output of an entire program cannot in general ..."
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Cited by 26 (8 self)
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Practically all programming languages used in software engineering allow to split a program into several modules. For fully declarative and nonmonotonic logic programming languages, however, the modular structure of programs is hard to realise, since the output of an entire program cannot in general be composed from the output of its component programs in a direct manner. In this paper, we consider these aspects for the stablemodel semantics of disjunctive logic programs (DLPs). We define the notion of a DLPfunction, where a welldefined input/output interface is provided, and establish a novel module theorem enabling a suitable compositional semantics for modules. The module theorem extends the wellknown splittingset theorem and allows also a generalisation of a shifting technique for splitting shared disjunctive rules among components.
Enhancing the MagicSet Method for Disjunctive Datalog Programs
 In Proc. 20th International Conference on Logic Programming (ICLP 04), Springer LNCS 3132
, 2004
"... Abstract. We present a new technique for the optimization of (partially) bound queries over disjunctive datalog programs. The technique exploits the propagation of query bindings, and extends the MagicSet optimization technique (originally defined for nondisjunctive programs) to the disjunctive ca ..."
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Cited by 25 (5 self)
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Abstract. We present a new technique for the optimization of (partially) bound queries over disjunctive datalog programs. The technique exploits the propagation of query bindings, and extends the MagicSet optimization technique (originally defined for nondisjunctive programs) to the disjunctive case, substantially improving on previously defined approaches. MagicSettransformed disjunctive programs frequently contain redundant rules. We tackle this problem and propose a method for preventing the generation of such superfluous rules during the MagicSet transformation. In addition, we provide an efficient heuristic method for the identification of redundant rules, which can be applied in general, even if MagicSets are not used. We implement all proposed methods in the DLV system – the stateoftheart implementation of disjunctive datalog – and perform some experiments. The experimental results confirm the usefulness of MagicSets for disjunctive datalog, and they highlight the computational gain obtained by our method, which outperforms significantly the previously proposed MagicSet method for disjunctive datalog programs. 1
A Reductive Semantics for Counting and Choice in Answer Set Programming
"... In a recent paper, Ferraris, Lee and Lifschitz conjectured that the concept of a stable model of a firstorder formula can be used to treat some answer set programming expressions as abbreviations. We follow up on that suggestion and introduce an answer set programming language that defines the mean ..."
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Cited by 25 (16 self)
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In a recent paper, Ferraris, Lee and Lifschitz conjectured that the concept of a stable model of a firstorder formula can be used to treat some answer set programming expressions as abbreviations. We follow up on that suggestion and introduce an answer set programming language that defines the meaning of counting and choice by reducing these constructs to firstorder formulas. For the new language, the concept of a safe program is defined, and its semantic role is investigated. We compare the new language with the concept of a disjunctive program with aggregates introduced by Faber, Leone and Pfeifer, and discuss the possibility of implementing a fragment of the language by translating it into the input language of the answer set solver DLV. The language is also compared with cardinality constraint programs defined by Syrjänen.
Magic Sets and their Application to Data Integration
 In Proc. International Conference on Database Theory (ICDT 05), Springer LNCS 3363, 2005
, 2005
"... Abstract. We propose a generalization of the wellknown Magic Sets technique to Datalog ¬ programs with (possibly unstratified) negation under stable model semantics. Our technique produces a new program whose evaluation is generally more efficient (due to a smaller instantiation), while preserving ..."
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Cited by 24 (4 self)
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Abstract. We propose a generalization of the wellknown Magic Sets technique to Datalog ¬ programs with (possibly unstratified) negation under stable model semantics. Our technique produces a new program whose evaluation is generally more efficient (due to a smaller instantiation), while preserving soundness under cautious reasoning. Importantly, if the original program is consistent, then full queryequivalence is guaranteed for both brave and cautious reasoning, which turn out to be sound and complete. In order to formally prove the correctness of our Magic Sets transformation, we introduce a novel notion of modularity for Datalog ¬ under the stable model semantics, which is relevant per se. We prove that a module can be evaluated independently from the rest of the program, while preserving soundness under cautious reasoning. For consistent programs, both soundness and completeness are guaranteed for brave reasoning and cautious reasoning as well. Our Magic Sets optimization constitutes an effective method for enhancing the performance of dataintegration systems in which queryanswering is carried out by means of cautious reasoning over Datalog ¬ programs. In fact, preliminary results of experiments in the EU project INFOMIX, show that Magic Sets are fundamental for the scalability of the system. 1