The Role of Abduction in Logic Programming

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.

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.

Lecture Notes in Computer Science, 2001

Abduction, first proposed in the setting of classical logics, has been studied with growing interest in the logic programming area during the last years.

1996

In this paper we present a logic for abduction, namely a language, a semantics and a proof theory where the abductive relation can be expressed. The abductive relation is the relation between a preferred sentence explaining a given observation, in the context of a background theory, and such an observation itself. The proposed logical system, based on a modal approach, captures propositional abduction over a finite language.

Theory and Practice of Logic Programming, 2005

Abduction, first proposed in the setting of classical logics, has been studied with growing interest in the logic programming area during the last years.

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.

2004

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. ""

Journal of Logic and Computation, 1991

Expert Systems with Applications, 1998

In recent years, attention has been devoted to abduction, a hypothetical form of non-monotonic reasoning that tries to fit the best 'explanation' to a given observation. In this paper we present a collection of applications of automated abductive reasoning developed in the Center for Artificial Intelligence of the ITESM (Monterrey, Mexico) in the last five years, covering a range from natural language understanding to software re-use.