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Answer Sets
, 2007
"... This chapter is an introduction to Answer Set Prolog a language for knowledge representation and reasoning based on the answer set/stable model semantics of logic programs [44, 45]. The language has roots in declarative programing [52, 65], the syntax and semantics of standard Prolog [24, 23], disj ..."
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Cited by 59 (5 self)
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This chapter is an introduction to Answer Set Prolog a language for knowledge representation and reasoning based on the answer set/stable model semantics of logic programs [44, 45]. The language has roots in declarative programing [52, 65], the syntax and semantics of standard Prolog [24, 23], disjunctive databases [66, 67] and nonmonotonic logic
Uniform Equivalence of Logic Programs under the Stable Model Semantics
, 2003
"... 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 stable models for any other program R. This property strengthens equivalence of P and Q with respect to sta ..."
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Cited by 56 (14 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 stable models for any other program R. This property strengthens equivalence of P and Q with respect to stable models (which is the particular case for R = ;), and has an application in program optimization. In this paper, we consider the more liberal notion of uniform equivalence, in which R ranges only over the sets of facts rather than all sets of rules. This notion, which is wellknown, is particularly useful for assessing whether programs P and Q are equivalent as components in a logic program which is modularly structured. We provide semantical characterizations of uniform equivalence for disjunctive logic programs and some restricted classes, and analyze the computational cost of uniform equivalence in the propositional (ground) case. Our results, which naturally extend to answer set semantics, complement the results on strong equivalence of logic programs and pave the way for optimizations in answer set solvers as a tool for inputbased problem solving.
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 44 (9 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 43 (10 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.
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 42 (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
The CIFF Proof Procedure for Abductive Logic Programming with Constraints
 In Proceedings JELIA04
, 2004
"... We introduce a new proof procedure for abductive logic programming and present two soundness results. Our procedure extends that of Fung and Kowalski by integrating abductive reasoning with constraint solving and by relaxing the restrictions on allowed inputs for which the procedure can operate ..."
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Cited by 41 (20 self)
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We introduce a new proof procedure for abductive logic programming and present two soundness results. Our procedure extends that of Fung and Kowalski by integrating abductive reasoning with constraint solving and by relaxing the restrictions on allowed inputs for which the procedure can operate correctly. An implementation of our proof procedure is available and has been applied successfully in the context of multiagent systems.
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 41 (12 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
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
"... 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 answe ..."
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Cited by 36 (2 self)
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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.
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 33 (10 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
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 32 (8 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