Abduction is not Deduction-in-Reverse

This paper is a survey and critical overview of recent work on the extension of Logic Programming to perform Abductive Reasoning (Abductive Logic Programming). It updates the earlier paper \Abductive Logic Programming" 88]. We outline the general framework of Abduction and its applications to Knowledge Assimilation and Default Reasoning; we describe the argumentation-theoretic approach to the use of abduction as an interpretation for Negation as Failure, introduced in the earlier version 88] of this paper; and we present recent work on the generalisation of the argumentation-theoretic approach to provide a framework for default reasoning in general. We also analyse the links between Abduction and Constraint Logic Programming, as well as between Abduction and the extension of Logic Programming obtained by adding a form of explicit negation. Finally we discuss the relation between Abduction and Truth Maintenance.

Publication Name: Synthese (forthcoming; DOI: 10.1007/s11229-014-0496-0)

""A Conditional Logic for Abduction We propose a logic of abduction that (i) provides an appropriate formalization of the explanatory conditional, and that (ii) captures the defeasible nature of abductive inference. For (i), we argue that explanatory conditionals are non-classical, and rely on Brian Chellas’s work on conditional logics for providing an alternative formalization of the explanatory conditional. For (ii), we make use of the adaptive logics framework for modeling defeasible reasoning. We show how our proposal allows for a more natural reading of explanatory relations, and how it overcomes problems faced by other systems in the literature. ""

Logic Journal of IGPL, 2006

This paper presents and illustrates a formal logic for the abduction of singular hypotheses. The logic has a semantics and a dynamic proof theory that is sound and complete with respect to the semantics. The logic presupposes that, with respect to a specific application, the set of explananda and the set of possible explanantia are disjoint (but not necessarily exhaustive). Where an explanandum can be explained by different explanantia, the logic allows only for the abduction of their disjunction.

Journal of Logic and Computation, 1992

This paper is a survey and critical overview of recent w ork on the extension of Logic Programming to perform Abductive Reasoning (Abductive Logic Programming). It updates the earlier paper \Abductive Logic Programming" 88]. We outline the general framework of Abduction and its applications to Knowledge Assimilation and Default Reasoning we describe the argumentation-theoretic approach to the use of abduction as an interpretation for Negation as Failure, introduced in the earlier version 88] of this paper and we present recent w ork on the generalisation of the argumentation-theoretic approach t o provide a framework for default reasoning in general. We also analyse the links between Abduction and Constraint Logic Programming, as well as between Abduction and the extension of Logic Programming obtained by adding a form of explicit negation. Finally we discuss the relation between Abduction and Truth Maintenance.

ACM Computing Surveys …, 1995

Abduction was first introduced by the philosopher C.S. Peirce in the epistemological context of scientific discovery. It was more recently analyzed in Artificial Intelligence, especially with respect to diagnosis analysis or ordinary reasoning. These two fields share a common view of abduction as a general process of hypotheses formation. More precisely, abduction is conceived as a kind of reverse explanation where a hypothesis H can be abduced from facts E if H is a "good explanation" of E. The paper aims at giving a general logical picture of abduction which could be used in both fields.

2007

This article presents the confluence of two general ideas: Defeasible Logic Programming (DeLP, an argumentation based formalism for representing knowledge and reasoning) and Abduction in logic. In first place, we introduce a framework that formally states the problem of doing abduction (obtaining abductive explanations) in the particular case that the abductive theory is a DeLP Program. In the reminder of this work we face that problem, providing a formal characterization of the notion of abductive explanation, in such a way that we could then easily calculate the explanations from this formal characterization. An important advantage of this approach is that by proving the correctness of the characterization, we ensure the correctness of the method for obtaining explanations.

Logic programming, knowledge representation, and nonmonotonic reasoning, 2011

In the context of abduction in Logic Programs, when finding an abductive solution for a query, one may want to check too whether some other literals become true (or false) as a consequence, strictly within the abductive solution found, that is without performing additional abductions, and without having to produce a complete model to do so. That is, such consequence literals may consume, but not produce, the abduced literals of the solution. We show how this type of reasoning requires a new mechanism, not provided by others already available. To achieve it, we present the concept of Inspection Point in Abductive Logic Programs, and show, by means of examples, how one can employ it to investigate side-effects of interest (the inspection points) in order to help choose among abductive solutions. We show how to implement inspection points on top of already existing abduction solving systems -ABDUAL and XSB-XASP -in a way that can be adopted by other systems too.

Logic Programming, 1995

Partial deduction is known as an optimization technique in logic programming. In the context of abductive logic programming, however, we present in this paper that normal partial deduction does not preserve explanations for abductive reasoning. Then we provide an alternative method of partial deduction, called abductive partial deduction, which is shown to preserve the meanings of abductive logic programs. A method of partial abduction is also introduced as an optimization for abductive reasoning in logic programs.