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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.
An Abstract, ArgumentationTheoretic Approach to Default Reasoning
, 1997
"... We present an abstract framework for default reasoning, which includes Theorist, default logic, logic programming, autoepistemic logic, nonmonotonic modal logics, and certain instances of circumscription as special cases. The framework can be understood as a generalisation of Theorist. The generali ..."
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Cited by 162 (23 self)
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We present an abstract framework for default reasoning, which includes Theorist, default logic, logic programming, autoepistemic logic, nonmonotonic modal logics, and certain instances of circumscription as special cases. The framework can be understood as a generalisation of Theorist. The generalisation allows any theory formulated in a monotonic logic to be extended by a defeasible set of assumptions. An assumption can be defeated (or "attacked") if its "contrary" can be proved, possibly with the aid of other conflicting assumptions. We show that, given such a framework, the standard semantics of most logics for default reasoning can be understood as sanctioning a set of assumptions, as an extension of a given theory, if and only if the set of assumptions is conflictfree (in the sense that it does not attack itself) and it attacks every assumption not in the set. We propose a more liberal, argumentationtheoretic semantics, based upon the notion of admissible extension in logic pro...
An AssumptionBased Framework for NonMonotonic Reasoning
 Proc. 2nd International Workshop on Logic Programming and Nonmonotonic Reasoning
, 1993
"... The notion of assumptionbased framework generalises and refines the use of abduction to give a formalisation of nonmonotonic reasoning. In this framework, a sentence is a nonmonotonic consequence of a theory if it can be derived monotonically from a theory extended by means of acceptable assumpti ..."
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Cited by 59 (15 self)
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The notion of assumptionbased framework generalises and refines the use of abduction to give a formalisation of nonmonotonic reasoning. In this framework, a sentence is a nonmonotonic consequence of a theory if it can be derived monotonically from a theory extended by means of acceptable assumptions. The notion of acceptability for such assumptions is formulated in terms of their ability successfully to "counterattack" any "attacking" set of assumptions. One set of assumptions is said to "attack" another if the first set monotonically implies a consequence which is inconsistent with an assumption in the second set. This argumentationtheoretic criterion of acceptability is based on notions first introduced for logic programming and used to give a unified account of such diverse semantics for logic programming as stable models, partial stable models, preferred extensions, stable theories, wellfounded semantics, and stationary semantics. The new framework makes it possible to general...
ACLP: Abductive Constraint Logic Programming
, 2000
"... This paper presents the framework of Abductive Constraint Logic Programming (ACLP), which integrates Abductive Logic Programming (ALP) and Constraint Logic Programming (CLP). In ACLP, the task of abduction is supported and enhanced by its nontrivial integration with constraint solving. This int ..."
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Cited by 52 (5 self)
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This paper presents the framework of Abductive Constraint Logic Programming (ACLP), which integrates Abductive Logic Programming (ALP) and Constraint Logic Programming (CLP). In ACLP, the task of abduction is supported and enhanced by its nontrivial integration with constraint solving. This integration of constraint solving into abductive reasoning facilitates a general form of constructive abduction and enables the application of abduction to computationally demanding problems
Deterministic and NonDeterministic Stable Models
 Journal of Logic and Computation
, 1997
"... Stable models have been first introduced in the domain of total interpretations (T stable models), where the existence of multiple Tstable models for the same program provides a powerful mechanism to express nondeterminism. Stable models have been later extended to the domain of partial interpre ..."
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Cited by 26 (6 self)
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Stable models have been first introduced in the domain of total interpretations (T stable models), where the existence of multiple Tstable models for the same program provides a powerful mechanism to express nondeterminism. Stable models have been later extended to the domain of partial interpretations (Pstable models). In this paper, we show that the presence of multiple Pstable models need not be a direct manifestation of nondeterminism, for it can be instead an expression of assorted degrees of undefinedness. To separate the two factors, nondeterminism and undefinedness, this paper introduces the notion of deterministic stable models and strictly nondeterministic ones. Deterministic stable models form an interesting family, having a lattice structure where the wellfounded model serves as the bottom; the top of the lattice, the maximum deterministic stable model, resolves differences between any two Pstable models in the family. On the other hand, every two models in a fam...
On The Correctness Of Unfold/fold Transformation Of Normal And Extended Logic Programs
 JOURNAL OF LOGIC PROGRAMMING
, 1995
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On the Partial Semantics for Disjunctive Deductive Databases
, 1997
"... this paper, a characterization of partial stable models for disjunctive datalog programs is given using a suitable extension of the notion of unfounded set. Two interesting subclasses of partial stable models, Mstable (Maximalstable) (also called regular models, preferred extension, and maximal ..."
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Cited by 21 (5 self)
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this paper, a characterization of partial stable models for disjunctive datalog programs is given using a suitable extension of the notion of unfounded set. Two interesting subclasses of partial stable models, Mstable (Maximalstable) (also called regular models, preferred extension, and maximal stable classes) and Lstable (Least undefinedstable) models, are then extended from normal to disjunctive datalog programs. Lstable models are shown to be the natural relaxation of the notion of total stable model; on the other hand the less strict Mstable models, endowed with a nice modularity property, may be appealing from the programming and computational point of view. Mstable and Lstable models are also compared with the regular models for disjunctive datalog programs recently proposed in the literature. 1 Introduction Deductive dat
A Unifying View for Logic Programming with NonMonotonic Reasoning
, 1997
"... We provide a simple formulation of a framework where some extensions of logic programming with nonmonotonic reasoning are treated uniformly, namely two kinds of negation and abduction. The resulting semantics is purely modeltheoretic, and gives meaning to any noncontradictory abductive logic pr ..."
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Cited by 18 (11 self)
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We provide a simple formulation of a framework where some extensions of logic programming with nonmonotonic reasoning are treated uniformly, namely two kinds of negation and abduction. The resulting semantics is purely modeltheoretic, and gives meaning to any noncontradictory abductive logic program. Moreover, it embeds and generalizes some existing semantics which deal with negation and abduction. The framework is equipped with a correct topdown proof procedure. Keywords: Programming languages, Logic programming, Nonmonotonic reasoning, Negation, Abduction. Dipartimento di Informatica, Universit`a di Pisa, Corso Italia 40, Pisa, Italy. brogi@di.unipi.it y DEIS, Universit`a di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy. elamma@deis.unibo.it z Dipartimento di Informatica, Universit`a di Pisa, Corso Italia 40, Pisa, Italy. paolo@di.unipi.it x DEIS, Universit`a di Ferrara, Via Saragat, 41100 Ferrara, Italy. pmello@ing.unife.it Contents 1 Introduction and Motiva...
Expressive Power and Complexity of Partial Models for Disjunctive Deductive Databases
, 1999
"... This paper investigates the expressive power and complexity of partial model semantics for disjunctive deductive databases. In particular,... ..."
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Cited by 17 (7 self)
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This paper investigates the expressive power and complexity of partial model semantics for disjunctive deductive databases. In particular,...
An Abductive Semantics for Disjunctive Logic Programs and its Proof Procedure
 In Proceedings of the International Conference on the Foundations of Software Technology and Theoretical Computer Science
, 1997
"... . While it is wellknown how normal logic programs may be viewed as a form of abduction and argumentation, the problem of how disjunctive programs may be used for abductive reasoning is rarely discussed. In this paper we propose an abductive semantics for disjunctive logic programs with default nega ..."
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Cited by 1 (0 self)
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. While it is wellknown how normal logic programs may be viewed as a form of abduction and argumentation, the problem of how disjunctive programs may be used for abductive reasoning is rarely discussed. In this paper we propose an abductive semantics for disjunctive logic programs with default negation and show that Eshghi and Kowalski 's abductive proof procedure for normal programs can be adopted to compute abductive solutions for disjunctive programs. 1 Introduction In the simplest form abduction is the problem: From A and A / B, infer B as a possible explanation of A. Nonmonotonic reasoning has been explored as a form of abductive reasoning. In particular, default assumptions in logic programs have been treated as abductive hypotheses and a number of reasoning mechanisms and semantics have been proposed [7, 10, 16, 18, 19]. Chief among these is Eshghi and Kowalski's formulation of an elegant abductive proof procedure for normal programs where default assumptions are viewed as a...