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Abduction in Logic Programming
"... Abduction in Logic Programming started in the late 80s, early 90s, in an attempt to extend logic programming into a framework suitable for a variety of problems in Artificial Intelligence and other areas of Computer Science. This paper aims to chart out the main developments of the field over th ..."
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Cited by 538 (74 self)
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Abduction in Logic Programming started in the late 80s, early 90s, in an attempt to extend logic programming into a framework suitable for a variety of problems in Artificial Intelligence and other areas of Computer Science. This paper aims to chart out the main developments of the field over the last ten years and to take a critical view of these developments from several perspectives: logical, epistemological, computational and suitability to application. The paper attempts to expose some of the challenges and prospects for the further development of the field.
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 245 (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.
Consistency of Clark's Completion and Existence of Stable Models
, 1994
"... The most general notion of canonical model for a logic program with negation is the one of stable model [9]. In [7] the stable models of a logic program are characterized by the wellsupported Herbrand models of the program, and a new fixed point semantics that formalizes the bottomup truth mainten ..."
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Cited by 142 (2 self)
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The most general notion of canonical model for a logic program with negation is the one of stable model [9]. In [7] the stable models of a logic program are characterized by the wellsupported Herbrand models of the program, and a new fixed point semantics that formalizes the bottomup truth maintenance procedure of [4] is based on that characterization. Here we focus our attention on the abstract notion of wellsupportedness in order to derive sufficient conditions for the existence of stable models. We show that if a logic program \Pi is positiveorderconsistent (i.e. there is no infinite decreasing chain w.r.t. the positive dependencies in the atom dependency graph of \Pi) then the Herbrand models of comp(\Pi) coincide with the stable models of \Pi. From this result and the ones of [10] [17] [2] on the consistency of Clark's completion, we obtain sufficient conditions for the existence of stable models for positiveorderconsistent programs. Then we show that a negative cycle free ...
A new perspective on stable models
 In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI
, 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 (includi ..."
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Cited by 66 (31 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 the definition of circumscription. 1
The meaning of negative premises in transition system specifications II
 THE JOURNAL OF LOGIC AND ALGEBRAIC PROGRAMMING
, 2004
"... ..."
Generalized Metrics and Uniquely Determined Logic Programs
 Theoretical Computer Science
"... The introduction of negation into logic programming brings the benefit of enhanced syntax and expressibility, but creates some semantical problems. Specifically, certain operators which are monotonic in the absence of negation become nonmonotonic when it is introduced, with the result that standard ..."
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Cited by 28 (17 self)
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The introduction of negation into logic programming brings the benefit of enhanced syntax and expressibility, but creates some semantical problems. Specifically, certain operators which are monotonic in the absence of negation become nonmonotonic when it is introduced, with the result that standard approaches to denotational semantics then become inapplicable. In this paper, we show how generalized metric spaces can be used to obtain fixedpoint semantics for several classes of programs relative to the supported model semantics, and investigate relationships between the underlying spaces we employ. Our methods allow the analysis of classes of programs which include the acyclic, locally hierarchical, and acceptable programs, amongst others, and draw on fixedpoint theorems which apply to generalized ultrametric spaces and to partial metric spaces.
Paraconsistent Stable Semantics for Extended Disjunctive Programs
 Journal of Logic and Computation
, 1995
"... This paper presents declarative semantics of possibly inconsistent disjunctive logic programs. We introduce the paraconsistent minimal and stable model semantics for extended disjunctive programs, which can distinguish inconsistent information from others in a program. These semantics are based ..."
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Cited by 24 (0 self)
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This paper presents declarative semantics of possibly inconsistent disjunctive logic programs. We introduce the paraconsistent minimal and stable model semantics for extended disjunctive programs, which can distinguish inconsistent information from others in a program. These semantics are based on latticestructured multivalued logics, and are characterized by a new fixpoint semantics of extended disjunctive programs. Applications of the paraconsistent semantics for reasoning in inconsistent programs are also presented. Keywords: Extended disjunctive programs, inconsistency, multivalued logic, paraconsistent stable model semantics. 3 Journal of Logic and Computation 5: 265285, Oxford University Press, 1995. 1 1
Twelve Definitions of a Stable Model
"... This is a review of some of the definitions of the concept of a stable model that have been proposed in the literature. These definitions are equivalent to each other, at least when applied to traditional Prologstyle programs, but there are reasons why each of them is valuable and interesting. A n ..."
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Cited by 18 (1 self)
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This is a review of some of the definitions of the concept of a stable model that have been proposed in the literature. These definitions are equivalent to each other, at least when applied to traditional Prologstyle programs, but there are reasons why each of them is valuable and interesting. A new characterization of stable models can suggest an alternative picture of the intuitive meaning of logic programs; or it can lead to new algorithms for generating stable models; or it can work better than others when we turn to generalizations of the traditional syntax that are important from the perspective of answer set programming; or it can be more convenient for use in proofs; or it can be interesting simply because it demonstrates a relationship between seemingly unrelated ideas.