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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 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.
SLDNFA: an abductive procedure for normal abductive programs
 Proc. of the International Joint Conference and Symposium on Logic Programming
, 1992
"... A family of extensions of SLDNFresolution for normal abductive programs is presented. The main difference between our approach and existing procedures is the treatment of nonground abductive goals. A completion semantics is given and the soundness and completeness of the procedures has been proven ..."
Abstract

Cited by 64 (15 self)
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A family of extensions of SLDNFresolution for normal abductive programs is presented. The main difference between our approach and existing procedures is the treatment of nonground abductive goals. A completion semantics is given and the soundness and completeness of the procedures has been proven. The research presented here, provides a simple framework of abductive procedures, in which a number of parameters can be set, in order to fit the abduction procedure to the application under consideration.
Logic Programs with ConsistencyRestoring Rules
 International Symposium on Logical Formalization of Commonsense Reasoning, AAAI 2003 Spring Symposium Series
, 2003
"... We present an extension of language AProlog by consistencyrestoring rules with preferences, give the semantics of the new language, CRProlog, and show how the language can be used to formalize various types of commonsense knowledge and reasoning. ..."
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Cited by 64 (24 self)
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We present an extension of language AProlog by consistencyrestoring rules with preferences, give the semantics of the new language, CRProlog, and show how the language can be used to formalize various types of commonsense knowledge and reasoning.
Negation As Failure In The Head
, 1998
"... The class of logic programs with negation as failure in the head is a subset of the logic of MBNF introduced by Lifschitz and is an extension of the class of extended disjunctive programs. An interesting feature of such programs is that the minimality of answer sets does not hold. This paper conside ..."
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Cited by 61 (2 self)
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The class of logic programs with negation as failure in the head is a subset of the logic of MBNF introduced by Lifschitz and is an extension of the class of extended disjunctive programs. An interesting feature of such programs is that the minimality of answer sets does not hold. This paper considers the class of {\em general extended disjunctive programs\/} (GEDPs) as logic programs with negation as failure in the head. First, we discuss that the class of GEDPs is useful for representing knowledge in various domains in which the principle of minimality is too strong. In particular, the class of abductive programs is properly included in the class of GEDPs. Other applications include the representation of inclusive disjunctions and circumscription with fixed predicates. Secondly, the semantic nature of GEDPs is analyzed by the syntax of programs. In acyclic programs, negation as failure in the head can be shifted to the body without changing the answer sets of the program. On the other hand, supported sets of any program are always preserved by the same transformation. Thirdly, the computational complexity of the class of GEDPs is shown to remain in the same complexity class as normal disjunctive programs. Through the simulation of negation as failure in the head, computation of answer sets and supported sets is realized using any proof procedure for extended or positive disjunctive programs. Finally, a simple translation of GEDPs into autoepistemic logic is presented.
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...
Abduction in WellFounded Semantics and Generalized Stable Models via Tabled Dual Programs
 THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2004
"... Abductive logic programming oers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled logic programming oers a computational mechanism that provides a level of declarativity superior to that of Prolog, and wh ..."
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Cited by 42 (30 self)
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Abductive logic programming oers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled logic programming oers a computational mechanism that provides a level of declarativity superior to that of Prolog, and which has supported successful applications in elds such as parsing, program analysis, and model checking. In this paper we show how to use tabled logic programming to evaluate queries to abductive frameworks with integrity constraints when these frameworks contain both default and explicit negation. The result is the ability to compute abduction over wellfounded semantics with explicit negation and answer sets. Our approach consists of a transformation and an evaluation method. The transformation adjoins to each objective literal O in a program, an objective literal not(O) along with rules that ensure that not(O) will be true if and only if O is false. We call the resulting program a dual program. The evaluation method, Abdual, then operates on the dual program. Abdual is sound and complete for evaluating queries to abductive frameworks whose entailment method is based on either the wellfounded semantics with explicit negation, or on answer sets. Further, Abdual is asymptotically as ecient as any known method for either class of problems. In addition, when abduction is not desired, Abdual operating on a dual program provides a novel tabling method for evaluating queries to ground extended programs whose complexity and termination properties are similar to those of the best tabling methods for the wellfounded semantics. A publicly available metainterpreter has been developed for Abdual using the XSB system.
Approaches to Abductive Reasoning  An Overview
 ARTIFICIAL INTELLIGENCE REVIEW
, 1993
"... Abduction is a form of nonmonotonic reasoning that has gained increasing interest in the last few years. The key idea behind it can be represented by the following inference rule
$$O = \mathop C\limits_  N = \mathop P\limits_^  O  \mathop C\limits_^  .$$
i.e., from an occurrence of ohgr an ..."
Abstract

Cited by 40 (1 self)
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Abduction is a form of nonmonotonic reasoning that has gained increasing interest in the last few years. The key idea behind it can be represented by the following inference rule
$$O = \mathop C\limits_  N = \mathop P\limits_^  O  \mathop C\limits_^  .$$
i.e., from an occurrence of ohgr and the rule ldquophiv implies ohgrrdquo, infer an occurrence of phiv as aplausible hypothesis or explanation for ohgr. Thus, in contrast to deduction, abduction is as well as induction a form of ldquodefeasiblerdquo inference, i.e., the formulae sanctioned are plausible and submitted to verification.
In this paper, a formal description of current approaches is given. The underlying reasoning process is treated independently and divided into two parts. This includes a description of methods for hypotheses generation and methods for finding the best explanations among a set of possible ones. Furthermore, the complexity of the abductive task is surveyed in connection with its relationship to default reasoning. We conclude with the presentation of applications of the discussed approaches focusing on plan recognition and plan generation.
A Fixpoint Characterization Of Abductive Logic Programs
, 1996
"... this paper, we generalize the program transformation techniques of [17] for nonabductive programs to deal with abductive frameworks. We introduce a new translation from an abductive logic program into a positive disjunctive program, and show that the belief models of an abductive program can be cha ..."
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Cited by 38 (8 self)
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this paper, we generalize the program transformation techniques of [17] for nonabductive programs to deal with abductive frameworks. We introduce a new translation from an abductive logic program into a positive disjunctive program, and show that the belief models of an abductive program can be characterized by the fixpoint closure of the transformed disjunctive program. In the transformation, both negative hypotheses through negation as failure and positive hypotheses from the abducibles are dealt with uniformly. This fixpoint characterization is further extended to a fixpoint semantics for abductive extended disjunctive programs, i.e., abductive programs that permit classical negation as well as disjunctions. For a procedural aspect of our fixpoint semantics, we also show that a model generation procedure for positive disjunctive programs can be used as a sound and complete procedure for computing belief models for functionfree and rangerestricted programs.
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 37 (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...