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153
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
Extending and Implementing the Stable Model Semantics
, 2002
"... A novel logic program like language, weight constraint rules, is developed for answer set programming purposes. It generalizes normal logic programs by allowing weight constraints in place of literals to represent, e.g., cardinality and resource constraints and by providing optimization capabilities ..."
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Cited by 312 (5 self)
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A novel logic program like language, weight constraint rules, is developed for answer set programming purposes. It generalizes normal logic programs by allowing weight constraints in place of literals to represent, e.g., cardinality and resource constraints and by providing optimization capabilities. A declarative semantics is developed which extends the stable model semantics of normal programs. The computational complexity of the language is shown to be similar to that of normal programs under the stable model semantics. A simple embedding of general weight constraint rules to a small subclass of the language called basic constraint rules is devised. An implementation of the language, the smodels system, is developed based on this embedding. It uses a two level architecture consisting of a frontend and a kernel language implementation. The frontend allows restricted use of variables and functions and compiles general weight constraint rules to basic constraint rules. A major part of the work is the development of an ecient search procedure for computing stable models for this kernel language. The procedure is compared with and empirically tested against satis ability checkers and an implementation of the stable model semantics. It offers a competitive implementation of the stable model semantics for normal programs and attractive performance for problems where the new types of rules provide a compact representation.
Tabled Evaluation with Delaying for General Logic Programs
, 1996
"... SLD resolution with negation as finite failure (SLDNF) reflects the procedural interpretation of predicate calculus as a programming language and forms the computational basis for Prolog systems. Despite its advantages for stackbased memory management, SLDNF is often not appropriate for query evalu ..."
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Cited by 260 (27 self)
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SLD resolution with negation as finite failure (SLDNF) reflects the procedural interpretation of predicate calculus as a programming language and forms the computational basis for Prolog systems. Despite its advantages for stackbased memory management, SLDNF is often not appropriate for query evaluation for three reasons: a) it may not terminate due to infinite positive recursion; b) it may not terminate due to infinite recursion through negation; c) it may repeatedly evaluate the same literal in a rule body, leading to unacceptable performance. We address three problems fir a goaloriented query evaluation of general logic programs by presenting tabled evaluation with delaying (SLG resolution).
Stable models and an alternative logic programming paradigm
 In The Logic Programming Paradigm: a 25Year Perspective
, 1999
"... In this paper we reexamine the place and role of stable model semantics in logic programming and contrast it with a least Herbrand model approach to Horn programs. We demonstrate that inherent features of stable model semantics naturally lead to a logic programming system that offers an interesting ..."
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Cited by 250 (18 self)
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In this paper we reexamine the place and role of stable model semantics in logic programming and contrast it with a least Herbrand model approach to Horn programs. We demonstrate that inherent features of stable model semantics naturally lead to a logic programming system that offers an interesting alternative to more traditional logic programming styles of Horn logic programming, stratified logic programming and logic programming with wellfounded semantics. The proposed approach is based on the interpretation of program clauses as constraints. In this setting programs do not describe a single intended model, but a family of stable models. These stable models encode solutions to the constraint satisfaction problem described by the program. Our approach imposes restrictions on the syntax of logic programs. In particular, function symbols are eliminated from the language. We argue that the resulting logic programming system is wellattuned to problems in the class NP, has a welldefined domain of applications, and an emerging methodology of programming. We point out that what makes the whole approach viable is recent progress in implementations of algorithms to compute stable models of propositional logic programs. 1
Logic Programming and Knowledge Representation
 Journal of Logic Programming
, 1994
"... In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and sh ..."
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Cited by 224 (21 self)
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In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and show how each of the added features extends the representational power of the language.
The Alternating Fixpoint of Logic Programs with Negation
, 1995
"... The alternating fixpoint of a logic program with negation is defined constructively. The underlying idea is monotonically to build up a set of negative conclusions until the least fixpoint is reached, using a transformation related to the one that defines stable models. From a fixed set of negative ..."
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Cited by 208 (2 self)
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The alternating fixpoint of a logic program with negation is defined constructively. The underlying idea is monotonically to build up a set of negative conclusions until the least fixpoint is reached, using a transformation related to the one that defines stable models. From a fixed set of negative conclusions, the positive conclusions follow (without deriving any further negative ones), by traditional Horn clause semantics. The union of positive and negative conclusions is called the alternating xpoint partial model. The name "alternating" was chosen because the transformation runs in two passes; the first pass transforms an underestimate of the set of negative conclusions into an (intermediate) overestimate; the second pass transforms the overestimate into a new underestimate; the composition of the two passes is monotonic. The principal contributions of this work are (1) that the alternating fixpoint partial model is identical to the wellfounded partial model, and (2) that alternating xpoint logic is at least as expressive as xpoint logic on all structures. Also, on finite structures, fixpoint logic is as expressive as alternating fixpoint logic.
Stable Semantics for Disjunctive Programs
 New Generation Computing
, 1991
"... We introduce the stable model semantics for disjunctive logic programs and deductive databases, which generalizes the stable model semantics, defined earlier for normal (i.e., nondisjunctive) programs. Depending on whether only total (2valued) or all partial (3valued) models are used we obtain th ..."
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Cited by 163 (2 self)
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We introduce the stable model semantics for disjunctive logic programs and deductive databases, which generalizes the stable model semantics, defined earlier for normal (i.e., nondisjunctive) programs. Depending on whether only total (2valued) or all partial (3valued) models are used we obtain the disjunctive stable semantics or the partial disjunctive stable semantics, respectively. The proposed semantics are shown to have the following properties: ffl For normal programs, the disjunctive (respectively, partial disjunctive) stable semantics coincides with the stable (respectively, partial stable) semantics. ffl For normal programs, the partial disjunctive stable semantics also coincides with the wellfounded semantics. ffl For locally stratified disjunctive programs both (total and partial) disjunctive stable semantics coincide with the perfect model semantics. ffl The partial disjunctive stable semantics can be generalized to the class of all disjunctive logic programs. ffl B...
Preferred Answer Sets for Extended Logic Programs
 ARTIFICIAL INTELLIGENCE
, 1998
"... In this paper, we address the issue of how Gelfond and Lifschitz's answer set semantics for extended logic programs can be suitably modified to handle prioritized programs. In such programs an ordering on the program rules is used to express preferences. We show how this ordering can be used to de ..."
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Cited by 132 (17 self)
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In this paper, we address the issue of how Gelfond and Lifschitz's answer set semantics for extended logic programs can be suitably modified to handle prioritized programs. In such programs an ordering on the program rules is used to express preferences. We show how this ordering can be used to define preferred answer sets and thus to increase the set of consequences of a program. We define a strong and a weak notion of preferred answer sets. The first takes preferences more seriously, while the second guarantees the existence of a preferred answer set for programs possessing at least one answer set. Adding priorities