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28
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 and Negation: A Survey
 JOURNAL OF LOGIC PROGRAMMING
, 1994
"... We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the prooftheoretic and modeltheoretic issues and the relationships between them. ..."
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Cited by 242 (8 self)
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We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the prooftheoretic and modeltheoretic issues and the relationships between them.
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 159 (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...
On the Computational Cost of Disjunctive Logic Programming: Propositional Case
, 1995
"... This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of wellknown semantics, as well as the complexity of deciding whethe ..."
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Cited by 113 (26 self)
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This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of wellknown semantics, as well as the complexity of deciding whether a propositional formula is satised by all models according to a given semantics. We concentrate on nite propositional disjunctive programs with as wells as without integrity constraints, i.e., clauses with empty heads; the problems are located in appropriate slots of the polynomial hierarchy. In particular, we show that the consistency check is P 2 complete for the disjunctive stable model semantics (in the total as well as partial version), the iterated closed world assumption, and the perfect model semantics, and we show that the inference problem for these semantics is P 2 complete; analogous results are derived for the an
Stationary Semantics for Normal and Disjunctive Logic Programs
 Annals of Mathematics and Artificial Intelligence
, 1991
"... this paper we show, however, that stationary expansions can be equivalently defined in terms of classical, 2valued logic. As a byproduct, we obtain a simpler and more natural description of stationary expansions. ..."
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Cited by 70 (13 self)
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this paper we show, however, that stationary expansions can be equivalently defined in terms of classical, 2valued logic. As a byproduct, we obtain a simpler and more natural description of stationary expansions.
Disjunctive Deductive Databases
, 1994
"... Background material is presented on deductive and normal deductive databases. A historical review is presented of work in disjunctive deductive databases, starting from 1982. The semantics of alternative classes of disjunctive databases is reviewed with their model and fixpoint characterizations. Al ..."
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Cited by 57 (7 self)
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Background material is presented on deductive and normal deductive databases. A historical review is presented of work in disjunctive deductive databases, starting from 1982. The semantics of alternative classes of disjunctive databases is reviewed with their model and fixpoint characterizations. Algorithms are developed to compute answers to queries in the alternative theories using the concept of a model tree. Open problems in this area are discussed.
Disjunctive Semantics based upon Partial and BottomUp Evaluation
 Proceedings of the 12th Int. Conf. on Logic Programming
, 1995
"... We present a new and general approach of defining semantics for disjunctive logic programs. Our framework consists of two parts: (1) a semantical , where semantics are defined in an abstract way as the weakest semantics satisfying certain properties, and (2) a procedural, namely a bottomup queryeva ..."
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Cited by 45 (12 self)
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We present a new and general approach of defining semantics for disjunctive logic programs. Our framework consists of two parts: (1) a semantical , where semantics are defined in an abstract way as the weakest semantics satisfying certain properties, and (2) a procedural, namely a bottomup queryevaluation method based on operators working on conditional facts (introduced independently by Bry and Dung/Kanchansut for nondisjunctive programs). As to (1), we concentrate in this paper on a particular set of abstract properties (the most important being the unfolding or partial evaluation property GPPE) and define a new semantics DWFS. Our semantics coincides for normal programs with the wellfounded semantics WFS. For positive disjunctive programs DWFS coincides with the generalized closed world semantics GCWA. As a byproduct, we get new characterizations of WFS and GCWA. DWFS is strongly related to Przymusinski's STATIC semantics: we conjecture that they coincide w.r.t. to the derivati...
Abduction from Logic Programs: Semantics and Complexity
 Theoretical Computer Science
, 1998
"... Abduction from observations and a theory, find using hypotheses an explanation for the observations  gained increasing interest during the last years. This form of reasoning has wide applicability in different areas of computer science; in particular, it has been recognized as an important pr ..."
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Cited by 36 (7 self)
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Abduction from observations and a theory, find using hypotheses an explanation for the observations  gained increasing interest during the last years. This form of reasoning has wide applicability in different areas of computer science; in particular, it has been recognized as an important principle of commonsense reasoning. In this paper, we define a general abduction model for logic programming, where the inference operator (i.e., the semantics to be applied on programs), can be specified by the user. Advanced forms of logic programming have been proposed as valuable tools for knowledge representation and reasoning. We show that logic programming semantics can be more meaningful for abductive reasoning than classical inference by providing examples from the area of knowledge representation and reasoning. The main part of the paper is devoted to an extensive study of the computational complexity of the principal problems in abductive reasoning, which are: Given an inst...
Knowledge Representation with Logic Programs
 DEPT. OF CS OF THE UNIVERSITY OF KOBLENZLANDAU
, 1996
"... In this tutorialoverview, which resulted from a lecture course given by the authors at ..."
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Cited by 32 (6 self)
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In this tutorialoverview, which resulted from a lecture course given by the authors at
Characterizations of the Disjunctive Wellfounded Semantics: Confluent Calculi and Iterated GCWA
 Journal of Automated Reasoning
, 1997
"... . Recently Brass and Dix have introduced the semantics DWFS for general disjunctive logic programs. The interesting feature of this approach is that it is both semantically and prooftheoretically founded. Any program \Phi is associated a normalform res(\Phi), called the residual program, by a non ..."
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Cited by 31 (9 self)
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. Recently Brass and Dix have introduced the semantics DWFS for general disjunctive logic programs. The interesting feature of this approach is that it is both semantically and prooftheoretically founded. Any program \Phi is associated a normalform res(\Phi), called the residual program, by a nontrivial bottomup construction using least fixpoints of two monotonic operators. We show in this paper, that the original calculus, consisting of some simple transformations, has a very strong and appealing property: it is confluent and terminating. This means that all the transformations can be applied in any order: we always arrive at an irreducible program (no more transformation is applicable) and this program is already uniquely determined. Moreover, it coincides with the normalform res(\Phi) of the program we started with. The semantics DWFS can be read off from res(\Phi) immediately. No proper subset of the calculus has these properties  only when we restrict to certain subclasse...