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315
The DLV System for Knowledge Representation and Reasoning
 ACM Transactions on Computational Logic
, 2002
"... Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely believ ..."
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Cited by 330 (80 self)
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Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely believed assumptions, DLP is strictly more expressive than normal (disjunctionfree) logic programming, whose expressiveness is limited to properties decidable in NP. Importantly, apart from enlarging the class of applications which can be encoded in the language, disjunction often allows for representing problems of lower complexity in a simpler and more natural fashion. This paper presents the DLV system, which is widely considered the stateoftheart implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, functionfree disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to ∆P 3complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of
Logic Programming and Knowledge Representation  the AProlog perspective
 Artificial Intelligence
, 2002
"... In this paper we give a short introduction to logic programming approach to knowledge representation and reasoning. The intention is to help the reader to develop a 'feel' for the field's history and some of its recent developments. The discussion is mainly limited to logic programs u ..."
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Cited by 85 (0 self)
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In this paper we give a short introduction to logic programming approach to knowledge representation and reasoning. The intention is to help the reader to develop a 'feel' for the field's history and some of its recent developments. The discussion is mainly limited to logic programs under the answer set semantics. For understanding of approaches to logic programming build on wellfounded semantics, general theories of argumentation, abductive reasoning, etc., the reader is referred to other publications.
A uniform integration of higherorder reasoning and external evaluations in answerset programming
 In Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI05
, 2005
"... We introduce HEX programs, which are nonmonotonic logic programs admitting higherorder atoms as well as external atoms, and we extend the wellknown answerset semantics to this class of programs. Higherorder features are widely acknowledged as useful for performing metareasoning, among other task ..."
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Cited by 66 (29 self)
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We introduce HEX programs, which are nonmonotonic logic programs admitting higherorder atoms as well as external atoms, and we extend the wellknown answerset semantics to this class of programs. Higherorder features are widely acknowledged as useful for performing metareasoning, among other tasks. Furthermore, the possibility to exchange knowledge with external sources in a fully declarative framework such as AnswerSet Programming (ASP) is nowadays important, in particular in view of applications in the Semantic Web area. Through external atoms, HEX programs can model some important extensions to ASP, and are a useful KR tool for expressing various applications. Finally, complexity and implementation issues for a preliminary prototype are discussed. 1
Probabilistic reasoning with answer sets
 In Proceedings of LPNMR7
, 2004
"... Abstract. We give a logic programming based account of probability and describe a declarative language Plog capable of reasoning which combines both logical and probabilistic arguments. Several nontrivial examples illustrate the use of Plog for knowledge representation. 1 ..."
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Cited by 63 (9 self)
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Abstract. We give a logic programming based account of probability and describe a declarative language Plog capable of reasoning which combines both logical and probabilistic arguments. Several nontrivial examples illustrate the use of Plog for knowledge representation. 1
clasp: A conflictdriven answer set solver
 In LPNMR’07
, 2007
"... Abstract. We describe the conflictdriven answer set solver clasp, whichis based on concepts from constraint processing (CSP) and satisfiability checking (SAT). We detail its system architecture and major features, and provide a systematic empirical evaluation of its features. 1 ..."
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Cited by 62 (7 self)
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Abstract. We describe the conflictdriven answer set solver clasp, whichis based on concepts from constraint processing (CSP) and satisfiability checking (SAT). We detail its system architecture and major features, and provide a systematic empirical evaluation of its features. 1
Ultimate Wellfounded and Stable Semantics for Logic Programs With Aggregates (Extended Abstract)
 In Proceedings of ICLP01, LNCS 2237
, 2001
"... is relatively straightforward. Another advantage of the ultimate approximation is that in cases where TP is monotone the ultimate wellfounded model will be 2valued and will coincide with the least fixpoint of TP . This is not the case for the standard wellfounded semantics. For example in the sta ..."
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Cited by 45 (7 self)
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is relatively straightforward. Another advantage of the ultimate approximation is that in cases where TP is monotone the ultimate wellfounded model will be 2valued and will coincide with the least fixpoint of TP . This is not the case for the standard wellfounded semantics. For example in the standard wellfounded model of the program: # p. p. p is undefined while the associated TP operator is monotone and p is true in the ultimate wellfounded model. One disadvantage of using the ultimate semantics is that it has a higher computational cost even for programs without aggregates. The complexity goes one level higher in the polynomial hierarchy to # 2 for the wellfounded model and to 2 for a stable model which is also complete for this class [2]. Fortunately, by adding aggregates the complexity does not increase further. To give an example of a logic program with aggregates we consider the problem of computing the length of the shortest path between two nodes in a direc
Aggregate Functions in Disjunctive Logic Programming: Semantics, . . .
"... Disjunctive Logic Programming (DLP) is a very expressive formalism: it allows to express every property of nite structures that is decidable in the complexity class ). Despite the high expressiveness of DLP, there are some simple properties, often arising in realworld applications, which ..."
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Cited by 41 (4 self)
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Disjunctive Logic Programming (DLP) is a very expressive formalism: it allows to express every property of nite structures that is decidable in the complexity class ). Despite the high expressiveness of DLP, there are some simple properties, often arising in realworld applications, which cannot be encoded in a simple and natural manner. Among these, properties requiring to apply some arithmetic operators (like sum, times, count) on a set of elements satisfying some conditions, cannot be naturally expressed in DLP. To overcome this de ciency, in this paper we extend DLP by aggregate functions. We formally de ne the semantics of the new language, named DLP . We show the usefulness of the new constructs on relevant knowledgebased problems. We analyze the computational complexity of DLP , showing that the addition of aggregates does not bring a higher cost in that respect. We provide an implementation of the DLP language in DLV{ the stateoftheart DLP system { and report on experiments which con rm the usefulness of the proposed extension also for the eciency of the computation.
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 37 (18 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.
Answer set optimization
 PROC. IJCAI03
, 2003
"... We investigate the combination of answer set programming and qualitative optimization techniques. Answer set optimization programs (ASO programs) have two parts. The generating program produces answer sets representing possible solutions. The preference program expresses user preferences. It induces ..."
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Cited by 35 (7 self)
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We investigate the combination of answer set programming and qualitative optimization techniques. Answer set optimization programs (ASO programs) have two parts. The generating program produces answer sets representing possible solutions. The preference program expresses user preferences. It induces a preference relation on the answer sets of based on the degree to which rules are satisfied. We discuss possible applications of ASO programming, give complexity results and propose implementation techniques. We also analyze the relationship between A SO programs and CPnetworks.
Simplifying logic programs under uniform and strong equivalence
 In LPNMR’04
, 2004
"... Abstract. We consider the simplification of logic programs under the stablemodel semantics, with respect to the notions of strong and uniform equivalence between logic programs, respectively. Both notions have recently been considered for nonmonotonic logic programs (the latter dates back to the 198 ..."
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Cited by 35 (21 self)
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Abstract. We consider the simplification of logic programs under the stablemodel semantics, with respect to the notions of strong and uniform equivalence between logic programs, respectively. Both notions have recently been considered for nonmonotonic logic programs (the latter dates back to the 1980s, though) and provide semantic foundations for optimizing programs with input. Extending previous work, we investigate syntactic and semantic rules for program transformation, based on proper notions of consequence. We furthermore provide encodings of these notions in answerset programming, and give characterizations of programs which are semantically equivalent to positive and Horn programs, respectively. Finally, we investigate the complexity of program simplification and determining semantical equivalence, showing that the problems range between coNP and Π P 2 complexity, and we present some tractable cases. 1