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260
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 456 (102 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
Potassco: The Potsdam Answer Set Solving Collection
, 2011
"... This paper gives an overview of the open source project Potassco, the Potsdam Answer Set Solving Collection, bundling tools for Answer Set Programming developed at the University of Potsdam. ..."
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Cited by 98 (15 self)
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This paper gives an overview of the open source project Potassco, the Potsdam Answer Set Solving Collection, bundling tools for Answer Set Programming developed at the University of Potsdam.
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 91 (11 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
Logic Programs with ConsistencyRestoring Rules
 International Symposium on Logical Formalization of Commonsense Reasoning, AAAI 2003 Spring Symposium Series
, 2003
"... We present an extension of language AProlog by consistencyrestoring rules with preferences, give the semantics of the new language, CRProlog, and show how the language can be used to formalize various types of commonsense knowledge and reasoning. ..."
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Cited by 77 (29 self)
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We present an extension of language AProlog by consistencyrestoring rules with preferences, give the semantics of the new language, CRProlog, and show how the language can be used to formalize various types of commonsense knowledge and reasoning.
Stable Models and Circumscription
, 2007
"... The definition of a stable model has provided a declarative semantics for Prolog programs with negation as failure and has led to the development of answer set programming. In this paper we propose a new definition of that concept, which covers many constructs used in answer set programming (includ ..."
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Cited by 71 (37 self)
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The definition of a stable model has provided a declarative semantics for Prolog programs with negation as failure and has led to the development of answer set programming. In this paper we propose a new definition of that concept, which covers many constructs used in answer set programming (including disjunctive rules, choice rules and conditional literals) and, unlike the original definition, refers neither to grounding nor to fixpoints. Rather, it is based on a syntactic transformation, which turns a logic program into a formula of secondorder logic that is similar to the formula familiar from John McCarthy’s definition of circumscription.
What Is Answer Set Programming?
, 2008
"... Answer set programming (ASP) is a form of declarative programming oriented towards difficult search problems. As an outgrowth of research on the use of nonmonotonic reasoning in knowledge representation, it is particularly useful in knowledgeintensive applications. ASP programs consist of rules tha ..."
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Cited by 67 (9 self)
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Answer set programming (ASP) is a form of declarative programming oriented towards difficult search problems. As an outgrowth of research on the use of nonmonotonic reasoning in knowledge representation, it is particularly useful in knowledgeintensive applications. ASP programs consist of rules that look like Prolog rules, but the computational mechanisms used in ASP are different: they are based on the ideas that have led to the creation of fast satisfiability solvers for propositional logic.
Answer set programming based on propositional satisfiability
 Journal of Automated Reasoning, 36:345–377, Gelfond
"... Abstract. Answer Set Programming (ASP) emerged in the late 1990s as a new logic programming paradigm which has been successfully applied in various application domains. Also motivated by the availability of efficient solvers for propositional satisfiability (SAT), various reductions from logic pro ..."
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Cited by 63 (9 self)
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Abstract. Answer Set Programming (ASP) emerged in the late 1990s as a new logic programming paradigm which has been successfully applied in various application domains. Also motivated by the availability of efficient solvers for propositional satisfiability (SAT), various reductions from logic programs to SAT were introduced in the past. All these reductions either are limited to a subclass of logic programs, or introduce new variables, or may produce exponentially bigger propositional formulas. In this paper, we present a SATbased procedure, called ASPSAT, that (i) deals with any (non disjunctive) logic program, (ii) works on a propositional formula without additional variables (except for those possibly introduced by the clause form transformation), and (iii) is guaranteed to work in polynomial space. From a theoretical perspective, we prove soundness and completeness of ASPSAT. From a practical perspective, we have (i) implemented ASPSAT in Cmodels, (ii) extended the basic procedures in order to incorporate the most popular SAT reasoning strategies, and (iii) conducted an extensive comparative analysis involving also other stateoftheart answer set solvers. The experimental analysis shows that our solver is competitive with the other solvers we considered, and that the reasoning strategies that work best on “small but hard ” problems are ineffective on “big but easy” problems and vice versa.
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 62 (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
Loop Formulas for Disjunctive Logic Programs
 In Proc. ICLP03
, 2003
"... We extend Clark's de nition of a completed program and the de nition of a loop formula due to Lin and Zhao to disjunctive logic programs. Our main result, generalizing the Lin/Zhao theorem, shows that answer sets for a disjunctive program can be characterized as the models of its completi ..."
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Cited by 59 (10 self)
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We extend Clark's de nition of a completed program and the de nition of a loop formula due to Lin and Zhao to disjunctive logic programs. Our main result, generalizing the Lin/Zhao theorem, shows that answer sets for a disjunctive program can be characterized as the models of its completion that satisfy the loop formulas. The concept of a tight program and Fages' theorem are extended to disjunctive programs as well.
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 54 (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.