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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 320 (78 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 us t ..."
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Cited by 75 (7 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 × 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 62 (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.
Smodels: a system for answer set programming
 In Proceedings of the 8th International Workshop on NonMonotonic Reasoning
, 2000
"... The Smodels system implements the stable model semantics for normal logic programs. It handles a subclass of programs which contain no function symbols and are domainrestricted but supports extensions including builtin functions as well as cardinality and weight constraints. On top of this core en ..."
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Cited by 42 (6 self)
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The Smodels system implements the stable model semantics for normal logic programs. It handles a subclass of programs which contain no function symbols and are domainrestricted but supports extensions including builtin functions as well as cardinality and weight constraints. On top of this core engine more involved systems can be built. As an example, we have implemented total and partial stable model computation for disjunctive logic programs. An interesting application method is based on answer set programming, i.e., encoding an application problem as a set of rules so that its solutions are captured by the stable models of the rules. Smodels has been applied to a number of areas including planning, model checking, reachability analysis, product configuration, dynamic constraint satisfaction, and feature interaction. General Information The Smodels system is written in C++ and the source code, test cases and documentation are available at
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 33 (6 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.
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 32 (8 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.
Implementing Ordered Disjunction Using Answer Set Solvers for Normal Programs
"... Logic programs with ordered disjunction (LPODs) add a new connective to logic programming. This connective allows us to represent alternative, ranked options for problem solutions in the heads of rules: AB intuitively means: if possible A, but if A is not possible, then at least B. The semantics ..."
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Cited by 32 (7 self)
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Logic programs with ordered disjunction (LPODs) add a new connective to logic programming. This connective allows us to represent alternative, ranked options for problem solutions in the heads of rules: AB intuitively means: if possible A, but if A is not possible, then at least B. The semantics of logic programs with ordered disjunction is based on a preference relation on answer sets. In this paper we show how LPODs can be implemented using answer set solvers for normal programs. The implementation is based on a generator which produces candidate answer sets and a tester which checks whether a given candidate is maximally preferred and produces a better candidate if it is not.
S.: Modularity aspects of disjunctive stable models
 LPNMR 2007. LNCS (LNAI
, 2007
"... Practically all programming languages allow the programmer to split a program into several modules which brings along several advantages in software development. In this paper, we are interested in the area of answerset programming where fully declarative and nonmonotonic languages are applied. In ..."
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Cited by 27 (9 self)
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Practically all programming languages allow the programmer to split a program into several modules which brings along several advantages in software development. In this paper, we are interested in the area of answerset programming where fully declarative and nonmonotonic languages are applied. In this context, obtaining a modular structure for programs is by no means straightforward since the output of an entire program cannot in general be composed from the output of its components. To better understand the effects of disjunctive information on modularity we restrict the scope of analysis to the case of disjunctive logic programs (DLPs) subject to stablemodel semantics. We define the notion of a DLPfunction, where a welldefined input/output interface is provided, and establish a novel module theorem which indicates the compositionality of stablemodel semantics for DLPfunctions. The module theorem extends the wellknown splittingset theorem and enables the decomposition of DLPfunctions given their strongly connected components based on positive dependencies induced by rules. In this setting, it is also possible to split shared disjunctive rules among components using a generalized shifting technique. The concept of modular equivalence is introduced for the mutual comparison of DLPfunctions using a generalization of a translationbased verification method. 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
"... Abstract. 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 findi ..."
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Cited by 26 (2 self)
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Abstract. 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. 1