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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 455 (100 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 with Ordered Disjunction
 In Proceedings of AAAI02
, 2002
"... Logic programs with ordered disjunction (LPODs) combine ideas underlying Qualitative Choice Logic (Brewka, Benferhat, & Le Berre 2002) and answer set programming. Logic programming under answer set semantics is extended with a new connective called ordered disjunction. The new connective allows ..."
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Cited by 95 (8 self)
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Logic programs with ordered disjunction (LPODs) combine ideas underlying Qualitative Choice Logic (Brewka, Benferhat, & Le Berre 2002) and answer set programming. Logic programming under answer set semantics is extended with a new connective called ordered disjunction. The new connective allows us to represent alternative, ranked options for problem solutions in the heads of rules: A &times; B intuitively means: if possible A, but if A is not possible then at least B. The semantics of logic programs...
Declarative ProblemSolving Using the DLV System
"... The need for representing indefinite information led to disjunctive deductive databases, which also fertilized work on disjunctive logic programming. Based on this paradigm, the DLV system has been designed and implemented as a tool for declarative knowledge representation. In this paper, we focus o ..."
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Cited by 70 (27 self)
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The need for representing indefinite information led to disjunctive deductive databases, which also fertilized work on disjunctive logic programming. Based on this paradigm, the DLV system has been designed and implemented as a tool for declarative knowledge representation. In this paper, we focus on the usage of DLV for solving problems in a declarative manner and report on experiments that we have run on a suite of benchmark problems. We discuss how problems can be solved in a natural way using a "Guess&Check"paradigm where solutions are guessed and verified by parts of the program. Furthermore, we describe various frontends that can be used for solving problems in specific applications. The experiments show that due to the ongoing implementation efforts, which include finetuning of the underlying algorithms, successive and significant performance improvements have been achieved during the last two years. The results indicate that DLV is capable of solving some complex problems quite efficiently.
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
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 51 (10 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.
Smodels: A system for answer set programming
 In Proceedings of the 8th International Workshop on NonMonotonic Reasoning
, 2000
"... ..."
Satbased answer set programming
 In Proc. AAAI04
, 2004
"... The relation between answer set programming (ASP) and propositional satisfiability (SAT) is at the center of many research papers, partly because of the tremendous performance boost of SAT solvers during last years. Various translations from ASP to SAT are known but the resulting SAT formula either ..."
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Cited by 45 (12 self)
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The relation between answer set programming (ASP) and propositional satisfiability (SAT) is at the center of many research papers, partly because of the tremendous performance boost of SAT solvers during last years. Various translations from ASP to SAT are known but the resulting SAT formula either includes many new variables or may have an unpractical size. There are also well known results showing a onetoone correspondence between the answer sets of a logic program and the models of its completion. Unfortunately, these results only work for specific classes of problems. In this paper we present a SATbased decision procedure for answer set programming that (i) deals with any (non disjunctive) logic program, (ii) works on a SAT formula without additional variables, and (iii) is guaranteed to work in polynomial space. Further, our procedure can be extended to compute all the answer sets still working in polynomial space. The experimental results of a prototypical implementation show that the approach can pay off sometimes by orders of magnitude.
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.
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.