Abductive Logics in a Belief Revision Framework

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.

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.

IEEE Transactions on Fuzzy Systems, 2013

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.

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. ""

Encyclopedia of Philosophy and the Social Sciences, 2013

The relationship between Peircean abduction and the modern notion of Inference to the Best Explanation (IBE) is a matter of dispute. Some philosophers, such as Harman (1965) and Lipton (1991, p. 58, 2004, p. 56), claim that abduction and IBE are virtually the same. Others, however, hold that they are quite different (Hintikka 1998; Minnameier 2004) and there is no link between them (Campos 2009). In this paper, I argue that neither of these views is correct. I show that abduction and IBE have important similarities as well as differences. Moreover, by bringing a historical perspective to the study of the relationship between abduction and IBE-a perspective that is lacking in the literature-I show that their differences can be well understood in terms of two historic developments in the history of philosophy of science: first, Reichenbach's distinction between the context of discovery and the context of justification-and the consequent jettisoning of the context of discovery from philosophy of science-and second, underdetermination of theory by data.

Studies in Applied Philosophy, Epistemology and Rational Ethics, 2012

The paper starts from the claim that every assertion of belief may be analyzed into an assertion about a counterfactual surprise of the believer in front of a dissonant knowledge. The notion of a counterfactual surprise can be usefully related to the well studied notion of Shackle's potential surprise. In §2 the author stresses the difference between explanation and abduction on one side and interpretation on the other, maintaining that interpretation expresses what the interpreter believes to be the best explanation of the interpreted fact. The analysis which is proposed takes for granted the classical distinction between doxa and episteme, i.e. between a subjective and an objective dimension of the epistemic enterprise. However, in §1 belief is defined by making reference to knowledge, so reversing a relation which has been established by a deeply rooted philosophical tradition. §1. The aim of this note is developing some reflections inspired by a basic intuition about belief statements which may be synthesized as follows : 1) Belief statements have an essentially counterfactual character 2) They presuppose the notion of knowledge and are definable in terms of it 3) They have to do with the notion of surprise To be clearer, the analysis of belief which we want to take as a starting point is provided by the following definition: (Def Be) x believes that A = Df x would be surprised if x were to know that not-A

Logic Journal of the IGPL, 2006

We have described the workings of a dynamic abducer, an abductive reasoning agent that continually fuses information from multiple sources to "maintain situation awareness", that is, to maintain a best estimate of the situation based on incoming data. In particular, we have described a special class of problems of entity tracking and re-identification, and described in some detail how a dynamic abducer for this problem is able, under some circumstances, to appropriately "change its mind". and explicitly revise the conclusion of an earlier reasoning step. This ability results from performing "meta-abductive" reasoning in situations where no plausible hypotheses are available for explaining a new observation report. We have also described ASAS-Smart, an implementation of such a dynamic abducer, and illustrated its capabilities by tracing its reasoning on two example cases. Although the present system is in many ways simple, idealized, and domain-specific, we believe that it illustrates principles of reasoning that have broad applicability.

We study the relationship between some structural rules for abductive reasoning and preference relations for selection preferred explanations. We prove that explanatory relations having good structural properties can always be defined by orders over formulas.

There never was a sounder logical maxim of scientific procedure than Ockham's razor: Entia non sunt multiplicanda praeter necessitatem. That is to say; before you try a complicated hypothesis, you should make quite sure that no simplification of it will explain the facts equally well. No matter if it takes fifty generations of arduous experimentation to explode the simpler hypothesis, and no matter how incredible it may seem that that simpler hypothesis should suffice, still fifty generations are nothing in the life of science, which has all time before it …. But you will mark the limitation of my approval of Ockham's razor. It is a sound maxim of scientific procedure. If the question be what one ought to believe, the logic of the situation must take other factors into account. Charles Sanders Peirce, Harvard Lectures on Pragmatism, Lecture II, 1903. Abstract I will analyse some properties of abduction that are essential from a logical standpoint. When dealing with the so-called 'inferential problem', I will opt for the more general concepts of input and output instead of those of premisses and conclusions, and show that in this framework two consequences can be derived that help clarify basic logical aspects of abductive reasoning: (i) it is more natural to accept the 'multimodal' and 'context-dependent' character of the inferences involved, (ii) inferences are not merely conceived of in the terms of the process leading to the 'generation of an output' or to the proof of it, as in the traditional and standard view of deductive proofs, but rather, from this perspective abductive inferences can be seen as related to logical processes in which input and output fail to hold each other in an expected relation, with the solution involving the modification of inputs, not that of outputs. I will also describe that if we wish to naturalize the logic of the abductive processes and its special consequence relation, we should refer to the following main aspects: 'optimization of situatedness', 'maximization of changeability' of both input and output, and high 'information-sensitiveness'. 1 Abductive Inferences: Input and Output vs. Premisses and Conclusions From the perspective of the EC-Model of abduction, 1 the available logical views concerning abduction have to be reconsidered. By now this fact is acknowledged by some logicians. Estrada-González [10, p. 182], e.g. by referring to the properties called consistency, minimality, etc. stated in the AKM-schema 2 usefully notes: We think that overemphasizing the characteristics of abduction as it occurs in scientific practices and daily life scenarios has led to overlook some features that abduction in those circumstances shares with other phenomena in which some given outputs fail to stand in a certain relation with some given inputs and thus a modification on those inputs is in order. Indeed, abduction in an eco-cognitive perspective is not circumscribed by indicating particular requirements of each particular field of application, such as scientific discovery, diagnosis, machine 1 I have described my eco-cognitive model of abduction (EC-model) in the recent [21, 23]. 2 I have illustrated the classical and so-called AKM-model of abduction in [19].