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242
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 414 (94 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 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 74 (26 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 62 (10 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 57 (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 56 (4 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 55 (9 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 53 (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.
Engineering an Incremental ASP Solver
"... Abstract. Many realworld applications, like planning or model checking, comprise a parameter reflecting the size of a solution. In a propositional formalism like Answer Set Programming (ASP), such problems can only be dealt with in a bounded way, considering one problem instance after another by gr ..."
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Cited by 49 (19 self)
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Abstract. Many realworld applications, like planning or model checking, comprise a parameter reflecting the size of a solution. In a propositional formalism like Answer Set Programming (ASP), such problems can only be dealt with in a bounded way, considering one problem instance after another by gradually increasing the bound on the solution size. We thus propose an incremental approach to both grounding and solving in ASP. Our goal is to avoid redundancy by gradually processing the extensions to a problem rather than repeatedly reprocessing the entire (extended) problem. We start by furnishing a formal framework capturing our incremental approach in terms of module theory. In turn, we take advantage of this framework for guiding the successive treatment of program slices during grounding and solving. Finally, we describe the first integrated incremental ASP system, iclingo, and provide an experimental evaluation. 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 42 (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.