Traditional abduction imposes as a precondition the restriction that the background information may not derive the goal data. In first-order logic such precondition is, in general, undecidable. To avoid such problem, we present a first-order cut-based abduction method, which has KE-tableaux as its underlying inference system. This inference system allows for the automation of non-analytic proofs in a tableau setting, which permits a generalization of traditional abduction that avoids the undecidable precondition problem. After demonstrating the correctness of the method, we (...) show how this method can be dynamically iterated in a process that leads to the construction of non-analytic first-order proofs and, in some terminating cases, to refutations as well. (shrink)

After a brief comparison of Aliseda’s account with different approaches to abductive reasoning, I try to relate abduction, understood in terms like those of Aliseda, to another concept which also occupies a very important role in scientific change: idealization. In particular, I try to reveal some interesting aspects related to notions like approximation and empirical progress.

In this paper we explore a generalization of traditional abduction which can simultaneously perform two different tasks: given an unprovable sequent Γ ⊢ G, find a sentence H such that Γ, H ⊢ G is provable ; given a provable sequent Γ ⊢ G, find a sentence H such that Γ ⊢ H and the proof of Γ, H ⊢ G is simpler than the proof of Γ ⊢ G . We argue that the two tasks should not be distinguished, (...) and present a general procedure for finding suitable hypotheses or lemmas. When the original sequent is provable, the abduced formula can be seen as a cut formula with respect to Gentzen's sequent calculus, so the abduction method is cut-based. Our method is based on the tableau-like system KE and we argue for its advantages over existing abduction methods based on traditional Smullyan-style Tableaux. (shrink)

The interactions among the components of a biological system can be given a logical representation that is useful for reasoning about them. One of the relevant problems that may be raised in this context is finding what would explain a given behaviour of some component; in other terms, generating hypotheses that, when added to the logical theory modelling the system, imply that behaviour. Temporal aspects have to be taken into account, in order to model the causality relationship that may link (...) the behaviour of a given component to that of another one. This paper presents a hypothesis generation method for linear temporal logic theories whose formulae have a restricted syntactic form, which is however sufficient to model cellular and molecular interactions, as they are often represented by biologists. The method exploits the duality between hypothesis generation and consequence finding, and can therefore be also used to infer the consequences of a given fact. It is based on a resolution system proposed by Cavalli and Fariñas del Cerro in 1984. (shrink)

The present form of mathematical logic originated in the twenties and early thirties from the partial merging of two different traditions, the algebra of logic and the logicist tradition (see [27], [41]). This resulted in a new form of logic in which several features of the two earlier traditions coexist. Clearly neither the algebra of logic nor the logicist’s logic is identical to the present form of mathematical logic, yet some of their basic ideas can be distinctly recognized within it. (...) One of such ideas is Boole’s view that logic is the study of the laws of thought. This is not to be meant in a psychologistic way. Frege himself states that the task of logic can be represented “as the investigation of the mind; [though] of the mind, not of minds” [17, p. 369]. Moreover Frege never charges Boole with being psychologistic and in a letter to Peano even distinguishes between the followers of Boole and “the psychological logicians” [16, p. 108]. In fact for Boole the laws of thought which are the object of logic belong “to the domain of what is termed necessary truth” [2, p. 404]. For him logic does not depend on psychology, on the contrary psychology depends on logic insofar as it is only through an investigation of logical operations that we could obtain “some probable intimations concerning the nature and constitution of the human mind” [2, p. 1]. Logic is normative, not descriptive. For, the laws of thought do not “manifest their presence otherwise than by merely prescribing the conditions of formal inference” [2, p. 419]. They are, “properly speaking, the laws of right reasoning only” [2, p. 408]. So they “form but a part of the system of laws by which the actual processes of reasoning, whether right or wrong, are governed” [2, p. 409]. Boole’s idea that logic is the study of the laws of thought was taken over by Hilbert. According to him logic is “a discipline which expresses the structure of all our thought” [31, p.. (shrink)

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. (shrink)

In this paper I argue for a place for logic inscientific methodology, at the same level asthat of computational and historicalapproaches. While it is well known that a awhole generation of philosophers dismissedLogical Positivism (not just for the logicthough), there are at least two reasons toreconsider logical approaches in the philosophyof science. On the one hand, the presentsituation in logical research has gone farbeyond the formal developments that deductivelogic reached last century, and new researchincludes the formalization of several othertypes of (...) reasoning, like induction andabduction. On the other hand, we call for abalanced Philosophy of Science, one inwhich both methods, the formal and thehistorical may be complementary, togetherproviding a pluralistic view of science, inwhich no method is the predominant one. (shrink)

This papers presents δ-resolution, a dual resolution calculus. It is based on standard resolution, and used appropriate formulae equivalent to disjunctive normal forms, instead of conjunctive normal ones, as it is the case for resolution. This duality is then useful to create a calculus for abductive process, as a way to construct a set of abductive solutions. The proposed calculus is compared to semantic tableaux, an standard logical framework, aslo illuminating when studying abduction.δ-resolution calculus is a contribution to logic programming, (...) and it further suggests new possibilities to explore abduction at a first order level, in the lines of those proposed in [9]. (shrink)

This book examines the philosophical conception of abductive reasoning as developed by Charles S. Peirce, the founder of American pragmatism. It explores the historical and systematic connections of Peirce's original ideas and debates about their interpretations. Abduction is understood in a broad sense which covers the discovery and pursuit of hypotheses and inference to the best explanation. The analysis presents fresh insights into this notion of reasoning, which derives from effects to causes or from surprising observations to explanatory theories. The (...) author outlines some logical and AI approaches to abduction as well as studies various kinds of inverse problems in astronomy, physics, medicine, biology, and human sciences to provide examples of retroductions and abductions. The discussion covers also everyday examples with the implication of this notion in detective stories, one of Peirce’s own favorite themes. The author uses Bayesian probabilities to argue that explanatory abduction is a method of confirmation. He uses his own account of truth approximation to reformulate abduction as inference which leads to the truthlikeness of its conclusion. This allows a powerful abductive defense of scientific realism. This up-to-date survey and defense of the Peircean view of abduction may very well help researchers, students, and philosophers better understand the logic of truth-seeking. (shrink)

The formalization of abductive reasoning has received increasing attention from logicians. However, few work is found beyond abduction in propositional logic, given that in a first order formalism, the undecidability problem naturally appears, and therefore an abductive problem cannot even be appropriately formulated. Still, many applications in artificial intelligence allow finite domains to work with, and this gives an opportunity to apply abduction in first order logic with restricted domains. In this paper, we present an approach to abductive reasoning in (...) C-structures, first order structures with a finite domain in which each of its elements has a corresponding constant representing its interpretation. By using semantic tableaux with bounded depth, that is, C-tableaux (a modification of N-tableaux, introduced by the authors in previous papers) and δ-resolution calculus, we build an effective procedure for the searching of minimal abductive solutions within the proposed semantics. (shrink)

Abductive Reasoning: Logical Investigations into Discovery and Explanation is a much awaited original contribution to the study of abductive reasoning, providing logical foundations and a rich sample of pertinent applications. Divided into three parts on the conceptual framework, the logical foundations, and the applications, this monograph takes the reader for a comprehensive and erudite tour through the taxonomy of abductive reasoning, via the logical workings of abductive inference ending with applications pertinent to scientific explanation, empirical progress, pragmatism and belief revision.

This work proposes an understanding of deductive, default and abductive reasoning as different instances of the same phenomenon: epistemic dynamics. It discusses the main intuitions behind each one of these reasoning processes, and suggest how they can be understood as different epistemic actions that modify an agent’s knowledge and/or beliefs in a different way, making formal the discussion with the use of the dynamic epistemic logic framework. The ideas in this paper put the studied processes under the same umbrella, thus (...) highlighting their relationship and allowing a better understanding of how they interact together. (shrink)

This work proposes an understanding of deductive, default and abductive reasoning as different instances of the same phenomenon: epistemic dynamics. It discusses the main intuitions behind each one of these reasoning processes, and suggest how they can be understood as different epistemic actions that modify an agent’s knowledge and/or beliefs in a different way, making formal the discussion with the use of the dynamic epistemic logic framework. The ideas in this paper put the studied processes under the same umbrella, thus (...) highlighting their relationship and allowing a better understanding of how they interact together. (shrink)

Abductive reasoning involves finding the missing premise of an “unsaturated” deductive inference, thereby selecting a possible _explanans_ for a conclusion based on a set of previously accepted premises. In this paper, we explore abductive reasoning from a structural proof-theory perspective. We present a hybrid sequent calculus for classical propositional logic that uses sequents and antisequents to define a procedure for identifying the set of analytic hypotheses that a rational agent would be expected to select as _explanans_ when presented with an (...) abductive problem. Specifically, we show that this set may not include the deductively minimal hypothesis due to the presence of redundant information. We also establish that the set of all analytic hypotheses exhausts all possible solutions to the given problem. Finally, we propose a deductive criterion for differentiating between the best _explanans_ candidates and other hypotheses. (shrink)

Efforts to formalize qualitative accounts of inference to the best explanation (IBE) confront two obstacles: the imprecise nature of such accounts and the unusual logical properties that explanations exhibit, such as contradiction-intolerance and irreflexivity. This paper aims to surmount these challenges by utilising a new, more precise theory that treats explanations as expressions that codify defeasible inferences. To formalise this account, we provide a sequent calculus in which IBE serves as an elimination rule for a connective that exhibits many of (...) the properties associated with the behaviour of the English expression ‘That... best explains why ... ’. We first construct a calculus that encodes these properties at the level of the turnstile, i.e. as a metalinguistic expression for classes of defeasible consequence relations. We then show how this calculus can be conservatively extended over a language that contains a best-explains-why operator. (shrink)

This paper primarily deals with theconceptual prospects for generalizing the aim ofabduction from the standard one of explainingsurprising or anomalous observations to that ofempirical progress or even truth approximation. Itturns out that the main abduction task then becomesthe instrumentalist task of theory revision aiming atan empirically more successful theory, relative to theavailable data, but not necessarily compatible withthem. The rest, that is, genuine empirical progress aswell as observational, referential and theoreticaltruth approximation, is a matter of evaluation andselection, and possibly new (...) generation tasks forfurther improvement. The paper concludes with a surveyof possible points of departure, in AI and logic, forcomputational treatment of the instrumentalist taskguided by the `comparative evaluation matrix''. (shrink)

Many conditionals seem to convey the existence of a link between their antecedent and consequent. We draw on a recently proposed typology of conditionals to argue for an old philosophical idea according to which the link is inferential in nature. We show that the proposal has explanatory force by presenting empirical results on the evidential meaning of certain English and Dutch modal expressions.

This is an examination of similarities and differences between two recent models of abductive reasoning. The one is developed in Atocha Aliseda’s Abductive Reasoning: Logical Investigations into the Processes of Discovery and Evaluation (2006). The other is advanced by Dov Gabbay and the present author in their The Reach of Abduction: Insight and Trial (2005). A principal difference between the two approaches is that in the Gabbay-Woods model, but not in the Aliseda model, abductive inference is ignorance-preserving. A further differ-ence (...) is that Aliseda reconstructs the abduction relation in a semantic tableaux environment, whereas the Woods-Gabbay model, while less systematic, is more general. Of particular note is the connection between abduction and legal reasoning. (shrink)