Abductive Logics in a Belief Revision Framework (original) (raw)

Abduction as belief revision

Artificial intelligence, 1995

We propose a model of abduction based on the revision of the epistemic state of an agent. Explanations must be sufficient to induce belief in the sentence to be explained (for instance, some observation), or ensure its consistency with other beliefs, in a manner that adequately accounts for factual and hypothetical sentences. Our model will generate explanations that nonmonotonically predict an observation, thus generalizing most current accounts, which require some deductive relationship between explanation and observation. It also provides a natural preference ordering on explanations, defined in terms of normality or plausibility. To illustrate the generality of our approach, we reconstruct two of the key paradigms for model-based diagnosis, abductive and consistency-based diagnosis, within our framework. This reconstruction provides an alternative semantics for both and extends these systems to accommodate our predictive explanations and semantic preferences on explanations. It also illustrates how more general information can be incorporated in a principled manner.

A study on the logic of abduction

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.

A Formal Logic for Abductive Reasoning

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.

To appear, Artificial Intelligence, 1995 Abduction as Belief Revision

2010

We propose a model of abduction based on the revision of the epistemic state of an agent. Explanations must be sufficient to induce belief in the sentence to be explained (for instance, some observation), or ensure its consistency with other beliefs, in a manner that adequately accounts for factual and hypothetical sentences. Our model will generate explanations that nonmonotonically predict an observation, thus generalizing most current accounts, which require some deductive relationship between explanation and observation. It also provides a natural preference ordering on explanations, defined in terms of normality or plausibility. To illustrate the generality of our approach, we reconstruct two of the key paradigms for model-based diagnosis, abductive and consistency-based diagnosis, within our framework. This reconstruction provides an alternative semantics for both and extends these systems to accommodate our predictive explanations and semantic preferences on explanations. It ...

Abduction is not Deduction-in-Reverse

Logic Journal of IGPL, 1996

Abduction is a topic that attracts much interest in AI and automated reasoning research. Di erent approaches have been devised, that give a formalized account of explanatory reasoning, propose methods to compute explanations, frame abduction in the context of logic programming. However, the logical nature of abduction is still far from being clear and di erent speci cations of the key underlying concepts have been given, that make it di cult to speak of abduction as a single wellde ned form of reasoning. This work is a preliminary discussion on the logical nature of abductive reasoning, emphasizing the fundamental di erence between abductive and deductive inference. Some logical properties of the inference to the \best explanation" are put forward and analyzed when the underlying logic is any extension of classical propositional logic (rst order logic, modal logic) or a non monotonic system.

Abduction As Belief Revision: A Model of Preferred Explanations

1993

We propose a natural model of abduction based on the revision of the epistemic state of an agent. We require that explanations be sufficient to induce belief in an observation in a manner that adequately accounts for factual and hypothetical observations. Our model will generate explanations that nonmonotonically predict an observation, thus generalizing most current accounts, which require some deductive relationship between explanation and observation. It also provides a natural preference ordering on explanations, defined in terms of normality or plausibility. We reconstruct the Theorist system in our framework, and show how it can be extended to accommodate our predictive explanations and semantic preferences on explanations.

Structural rules for Abduction

Theoria an International Journal For Theory History and Foundations of Science, 2007

Atocha Aliseda's Abductive Reasoning (2006) gives a structural characterization of the "forward" explanatory reasoning from a theory to observational data. This paper asks whether there are any interesting structural rules for the "backward" abductive reasoning from observations to explanatory theories. Ignoring statistical cases, a partial explication of abduction is converse deductive explanation: h is abducible from e iff h deductively explains e. This relation of abducibility trivially satisfies Converse Entailment (if h entails e, then h is abducible from e), but it does not generally satisfy Converse Consequence (if h is abducible from e and g entails h, then g is abducible from e), since deductive explanation is not always transitive.

A Conditional Logic of Abduction

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. ""