## Abduction in Logic Programming

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### BibTeX

@MISC{Denecker_abductionin,

author = {Marc Denecker and Antonis Kakas},

title = {Abduction in Logic Programming},

year = {}

}

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### Abstract

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.

### Citations

7316 |
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible
- Pearl
- 1988
(Show Context)
Citation Context ... includes logic programs, belief networks, Markov decision processes and the strategic form of a game as special cases. In particular, it has been shown that it is closelyrelated to Bayesian networks =-=[80]-=-, where all uncertaintyis represented as probabilities. An independent choice logic theoryis made up of two parts: – a choice space consisting of disjoint sets of ground atoms. The elements of a choic... |

1876 |
Foundations of Logic Programming
- Lloyd
- 1987
(Show Context)
Citation Context ...ell-founded model semantics [116]. The following ALP frameworks use these semantics for their underlying LP framework. SLDNFA and ID-logic. SLDNFA [17,20] is an abductive extension of SLDNFresolution =-=[68]-=-, suitable for abductive reasoning in the context of (possibly recursive) abductive logic programs under the completion semantics. It was proven sound and, under certain restrictions, complete with re... |

1520 | The stable model semantics for logic programming
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ...2]. 4.2 Approaches under Stable and Well-Founded Semantics In Logic Programming other semantics have been proposed as refinements of the completion semantics. These include the stable model semantics =-=[38]-=- and the well-founded model semantics [116]. The following ALP frameworks use these semantics for their underlying LP framework. SLDNFA and ID-logic. SLDNFA [17,20] is an abductive extension of SLDNFr... |

1452 | A logic for default reasoning - Reiter - 1980 |

973 |
Negation as failure
- Clark
- 1978
(Show Context)
Citation Context ...is that of [10]. The syntax in this framework is that of hierarchical logic programs 7 with a predefined set of abducible predicates. The formal syntax is an extension of Clark’s completion semantics =-=[9]-=- in which onlythe non-abducible predicates are completed. The main aim of this work was to studythe relationship between abduction and deduction in the setting of non-monotonic reasoning. In particula... |

868 | Classical negation in logic programs and disjunctive databases
- Gelfond, Lifschitz
- 1991
(Show Context)
Citation Context ...eworks and systems for ALP it has become clear that there exist strong links between some ALP frameworks and other extensions of Logic Programming. ALP has tight connections to Answer Set Programming =-=[32]-=-. Recall that the ABDUAL framework [1] is an extension of Answer Set Programming with abduction. Standard ALP (with one negation) is stronglyrelated Stable Logic Programming [69,75], the restriction o... |

858 | The Well-Founded Semantics for General Logic Programs
- Gelder, Ross, et al.
- 1991
(Show Context)
Citation Context ...ounded Semantics In Logic Programming other semantics have been proposed as refinements of the completion semantics. These include the stable model semantics [38] and the well-founded model semantics =-=[116]-=-. The following ALP frameworks use these semantics for their underlying LP framework. SLDNFA and ID-logic. SLDNFA [17,20] is an abductive extension of SLDNFresolution [68], suitable for abductive reas... |

805 | On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games
- Dung
- 1995
(Show Context)
Citation Context ...ogic can be understood in such terms and proposed a default reasoning framework based on the argumentation-theoretic acceptability semantics (see section 4.3) as an alternative to default logic. Dung =-=[44]-=- proposed an abstraction of the argumentation-theoretic interpretation of NAF introduced in [88], where arguments and the notion of one argument attacking another are treated as primitive concepts whi... |

636 |
Sergot M.: A logic-based calculus of events
- Kowalski
- 1986
(Show Context)
Citation Context ...se problems, different researchers proposed to extend logic programming with abduction. Eshghi [28] introduced abduction in logic programming in order to solve planning problems in the Event Calculus =-=[65]-=-. In this approach, abduction solves a planning goal by explaining it byan ordered sets of events -a plan- that entails the planning goal. This approach was further explored byShanahan [110], Missiaen... |

634 |
A Truth Maintenance System
- DOYLE
- 1979
(Show Context)
Citation Context ...70] present a method for computing generalised stable models for logic programs with integrity constraints represented as denials. The method is a bottomup computation based upon the TMS procedure of =-=[36]-=-. Although the computation is not goal-directed, goals (or queries) can be represented as denials and be treated as integrity constraints. Compared with other bottom-up procedures for computing genera... |

626 | Knowledge in Flux. Modeling the Dynamics of Epistemic States - Gärdenfors - 1988 |

594 | Interpretation as abduction - Hobbs, Stickel, et al. - 1988 |

454 | An assumption-based TMS - Kleer - 1986 |

452 | Concurrent constraint programming - Saraswat, Rinard - 1990 |

379 |
A logical framework for default reasoning
- POOLE
- 1988
(Show Context)
Citation Context ... of abduction has been demonstrated in a varietyof applications. It has been proposed as a reasoning paradigm in AI for diagnosis [8,90], natural language understanding [8,39,4,93], default reasoning =-=[81,29,25,50]-=-, planning [28,110,71,59], knowledge assimilation and belief revision [54,76], multiagent systems [7,64,102] and other problems. In the context of logic programming, the studyof abductive inference st... |

371 | Logic for Problem Solving - Kowalski - 1979 |

340 | Logic programs with classical negation - Gelfond, Lifschitz - 1990 |

330 | Logic programs with stable model semantics as a constraint programming paradigm
- Niemelä
- 1999
(Show Context)
Citation Context ...nswer Set Programming [32]. Recall that the ABDUAL framework [1] is an extension of Answer Set Programming with abduction. Standard ALP (with one negation) is stronglyrelated Stable Logic Programming =-=[69,75]-=-, the restriction of Answer Set Programming [32] to pure logic programs. As mentioned in section 4, an abductive logic framework under the generalized stable semantics can be translated in an equivale... |

302 | An assumption-based truth maintenance system - Kleer - 1986 |

299 | Probabilistic Horn abduction and Bayesian networks
- Poole
- 1993
(Show Context)
Citation Context ...at might cause the diagnosis system to come up with a wrong diagnosis violating the specification constraints. Probabilistic Horn Abduction and Independence Choice Logic. Probabilistic Horn abduction =-=[84]-=-, later extended into the independent choice logic [86], is a wayto combine logical reasoning and belief networks into a simpleAbduction in Logic Programming 417 and coherent framework. Its developme... |

275 | On closed world data bases - Reiter - 1987 |

263 | Smodels – an implementation of the stable model and well-founded semantics for normal logic programs
- Niemelä, Simons
- 1997
(Show Context)
Citation Context ... order aggregates and is described in detail in section 5.1. Recently, [78] compared SLDNFAC with different other approaches for solving constraint problems including CLP, ACLP and the Smodels system =-=[74]-=- and shows that in manyproblems the system is competitive. Bottom up Abduction. This approach was proposed originallyin [107] and aims to develop efficient techniques for computing abductive solutions... |

258 | Inroduction to Artificial Intelligence - Charniak, McDermott - 1987 |

252 | Nonmonotonic logic and temporal projection - Hanks, McDermott - 1987 |

250 | Stable models and an alternative logic programming paradigm, in: The Logic Programming Paradigm: a 25-Year Perspective (Springer
- Marek, Truszczyński
- 1999
(Show Context)
Citation Context ...nswer Set Programming [32]. Recall that the ABDUAL framework [1] is an extension of Answer Set Programming with abduction. Standard ALP (with one negation) is stronglyrelated Stable Logic Programming =-=[69,75]-=-, the restriction of Answer Set Programming [32] to pure logic programs. As mentioned in section 4, an abductive logic framework under the generalized stable semantics can be translated in an equivale... |

228 | Logic programming and knowledge representation
- Baral, Gelfond
- 1994
(Show Context)
Citation Context ...e need to decide whether information should be represented as part of the program, as an integrity constraint, or as an observation to be explained, as illustrated by the following example taken from =-=[9]-=-. Example 5.4 fly(X) bird(X)� abnormal bird(X) abnormal bird(X) penguin(X) has beak(X) bird(X): Suppose that bird is abducible and consider the three cases in which fly(tweety) is either added to the ... |

220 | Unfounded sets and wellfounded semantics for general logic programs - Gelder, Ross, et al. - 1988 |

209 |
Situations and Actions and Causal Laws
- McCarthy
- 1963
(Show Context)
Citation Context ...stems to solve computational tasks arising in this domain. Although in the earlydays of logicbased AI, deduction was considered as the unique fundamental problem solving paradigm of declarative logic =-=[70]-=- in the current state of the art deduction has lost this unique place as the central inferential paradigm of logic in AI. Indeed, we argue that a declarative problem solving methodologywill often lead... |

204 |
Abduction compared with negation by failure
- Eshghi, Kowalski
- 1989
(Show Context)
Citation Context ... of abduction has been demonstrated in a varietyof applications. It has been proposed as a reasoning paradigm in AI for diagnosis [8,90], natural language understanding [8,39,4,93], default reasoning =-=[81,29,25,50]-=-, planning [28,110,71,59], knowledge assimilation and belief revision [54,76], multiagent systems [7,64,102] and other problems. In the context of logic programming, the studyof abductive inference st... |

203 | Preferred subtheories: An extended logical framework for default reasoning
- Brewka
- 1989
(Show Context)
Citation Context ...f query evaluation. Moreover various (domain speci c) criteria of preference can be speci ed. They impose a (partial) order on the sets of hypotheses which leads to the discrimination of explanations =-=[13, 22, 61, 77, 143, 148, 180]-=-. Cox and Pietrzykowski [29] identify other desirable properties of abductive explanations. For instance, an explanation should be basic, i.e. should not be explainable in terms of 4other explanation... |

178 | A Mathematical Treatment of Defeasible Reasoning and its Implementation - Simari, Loui - 1992 |

173 |
Acyclic programs
- APT, BEZEM
- 1991
(Show Context)
Citation Context ...on-minimal explanation fq� rg are computed for the observation p. The abductive task for the logic-based approach has been proved to be highly intractable: it is NP-hard even if T is a set of acyclic =-=[7]-=- propositional de nite clauses [174, 48], and is even harder if T is a set of any propositional clauses [48]. These complexity results hold even if explanations are not required to be minimal. However... |

168 | On the Relationship Between Abduction and Deduction
- Console, Dupr, et al.
- 1991
(Show Context)
Citation Context ...d Mancarella showed the application of abduction in logic programming for deductive database updating and knowledge assimilation [53,55]. The application of abduction to diagnosis has been studied in =-=[10,11]-=- A.C. Kakas, F. Sadri (Eds.): Computat. Logic (Kowalski Festschrift), LNAI 2407, pp. 402–436, 2002. c○ Springer-Verlag Berlin Heidelberg 2002Abduction in Logic Programming 403 within an abductive log... |

152 | The independent choice logic for modelling multiple agents under uncertainty
- Poole
- 1997
(Show Context)
Citation Context ...rong diagnosis violating the specification constraints. Probabilistic Horn Abduction and Independence Choice Logic. Probabilistic Horn abduction [84], later extended into the independent choice logic =-=[86]-=-, is a wayto combine logical reasoning and belief networks into a simpleAbduction in Logic Programming 417 and coherent framework. Its development has been motivated bythe Theorist system [88] but it... |

144 | Prediction is deduction but explanation is abduction
- Shanahan
- 1989
(Show Context)
Citation Context ...emonstrated in a varietyof applications. It has been proposed as a reasoning paradigm in AI for diagnosis [8,90], natural language understanding [8,39,4,93], default reasoning [81,29,25,50], planning =-=[28,110,71,59]-=-, knowledge assimilation and belief revision [54,76], multiagent systems [7,64,102] and other problems. In the context of logic programming, the studyof abductive inference started at the end of the e... |

140 | Default Reasoning, Non-monotonic Logics, and the Frame Problem - Hanks, McDermott - 1986 |

137 | On Indefinite Databases and the Closed World Assumption - Minker |

136 | Database Updates Through Abduction - Kakas, Mancarella - 1990 |

131 | Constructive negation based on the completed database - Chan - 1988 |

131 | Stable models and non-determinism in logic programs with negation
- Saccá, Zaniolo
- 1990
(Show Context)
Citation Context ...ctive solutions, [107] also proposed a procedure for bottom-up stable model computation based on truth maintenance techniques. It is an extension of the procedure for computing well-founded models of =-=[33,94]-=- and dynamicallychecks integrityconstraints during the computation of stable models and uses them to derive facts. Later this bottom up procedure was integrated with a procedure for top-down expectati... |

130 |
Theorist: a logical reasoning system for defaults and diagnosis
- Poole, Goebel, et al.
- 1987
(Show Context)
Citation Context ... logic [86], is a wayto combine logical reasoning and belief networks into a simpleAbduction in Logic Programming 417 and coherent framework. Its development has been motivated bythe Theorist system =-=[88]-=- but it has been extended into a framework for decision and game-theoretic agents that includes logic programs, belief networks, Markov decision processes and the strategic form of a game as special c... |

128 |
Memoing for logic programs
- Warren
- 1992
(Show Context)
Citation Context ...�:::�Ln is called the body of the clause. A logic program where each literal Li in the body of every clause is atomic is said to be de nite. Abduction can be computed in LP by extending SLD and SLDNF =-=[23, 53, 54, 91, 94, 34, 181]-=-. Instead of failing in a proof when a selected subgoal fails to unify with the head of any rule, the subgoal can be viewed as a hypothesis. This is similar to viewing abducibles as \askable" conditio... |

117 | Rationality and Reasoning - Evans, Over - 1996 |

117 | General Theory of Cumulative Inference - Makinson - 1989 |

116 |
Abductive planning with event calculus
- Eshghi
- 1988
(Show Context)
Citation Context ...emonstrated in a varietyof applications. It has been proposed as a reasoning paradigm in AI for diagnosis [8,90], natural language understanding [8,39,4,93], default reasoning [81,29,25,50], planning =-=[28,110,71,59]-=-, knowledge assimilation and belief revision [54,76], multiagent systems [7,64,102] and other problems. In the context of logic programming, the studyof abductive inference started at the end of the e... |

112 | Belief revision and default reasoning: Syntax-based approaches - Nebel - 1991 |

109 | Generalized stable models: a semantics for abduction - Kakas, Mancarella - 1990 |

104 | On the Comparison of Theories: Preferring the Most Speci¯c Explanation - Poole - 1985 |

99 | On the mechanization of abductive logic - Pople - 1973 |

96 | Extended stable semantics for normal and disjunctive programs - Przymusinski - 1990 |