A Practical Logic of Cognitive Systems

The Reach of Abduction: Insight and Trial

Dov M. Gabbay, John Woods

• Publisher: Elsevier Science
• Year: 2005
• Print ISBN: 9780444517913
• eBook ISBN: 9780080460925
• Topic: Psychology
• Subtopic: Logic in Mathematics
• Index: Psychology

The present work is a continuation of the authors' acclaimed multi-volume APractical Logic of Cognitive Systems. After having investigated the notion ofrelevance in their previous volume, Gabbay and Woods now turn to abduction. Inthis highly original approach, abduction is construed as ignorance-preservinginference, in which conjecture plays a pivotal role. Abduction is a response to acognitive target that cannot be hit on the basis of what the agent currently knows.The abducer selects a hypothesis which were it true would enable the reasoner to attain his target. He concludes from this fact that the hypothesis may be conjectured. In allowing conjecture to stand in for the knowledge he fails to have, the abducer reveals himself to be a satisficer, since an abductive solution is not a solution from knowledge. Key to the authors' analysis is the requirement that a conjectured proposition is not just what a reasoner might allow himself to assume, but a proposition he must defeasibly release as a premiss for further inferences in the domain of enquiry in which the original abduction problem has arisen.The coverage of the book is extensive, from the philosophy of science tocomputer science and AI, from diagnostics to the law, from historical explanation to linguistic interpretation. One of the volume's strongest contributions is its exploration of the abductive character of criminal trials, with special attention given to the standard of proof beyond a reasonable doubt.Underlying their analysis of abductive reasoning is the authors' conception ofpractical agency. In this approach, practical agency is dominantly a matter of thecomparative modesty of an agent's cognitive agendas, together with comparatively scant resources available for their advancement. Seen in these ways, abduction has a significantly practical character, precisely because it is a form of inference that satisfices rather than maximizes its response to the agent's cognitive target.The Reach of Abduction will be necessary reading for researchers, graduatestudents and senior undergraduates in logic, computer science, AI, belief dynamics, argumentation theory, cognitive psychology and neuroscience, linguistics, forensic science, legal reasoning and related areas.Key features: - Reach of Abduction is fully integrated with a background logic of cognitive systems.- The most extensive coverage compared to competitive works.- Demonstrates not only that abduction is a form of ignorance preservinginference but that it is a mode of inference that is wholly rational.- Demonstrates the satisficing rather than maximizing character ofabduction.- The development of formal models of abduction is considerably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticatedconceptual analysis and extensive logical modelling.· Reach of Abduction is fully integrated with a background logic of cognitive systems.· The most extensive coverage compared to competitive works· Demonstrates not only that abduction is a form of ignorance preservinginference but that it is a mode of inference that is wholly rational.· Demonstrates the satisficing rather than maximizing character ofabduction.· The development of formal models of abduction is considerably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticatedconceptual analysis and extensive logical modelling.

Part I

A Practical Logic of Cognitive Systems

Chapter 1

Introduction

Dav M. Gabbay Department of Computer Science King's College London Strand, London, WC2R 2LS, U.K.

John Woods Philosophy Department University of British Columbia, Vancouver, BC Canada, V6T 1Z1
Department of Computer Science King's College London Strand, London, WC2R 2LS, U.K.

It is sometimes said that the highest philosophical gift is to invent important new philosophical problems. If so, Peirce is a major star on the firmament of philosophy. By thrusting the notion of abduction to the forefront of philosophers’ consciousness he created a problem which — I will argue — is the central one in contemporary epistemology.

Jaakko Hintikka,

The surprising fact C is observed. But if A were true, C would be a matter of course. Hence there is reason to suspect that A is true.

Charles S. Peirce

Abduction is our subject here. We meet it in a state of heightened theoretical activity. It is part of the contemporary research programmes of logic, cognitive science, AI, logic programming, and the philosophy of science. This is a welcome development. It gives us multiple places to look for instruction and guidance.

The approach that we take in this book is broadly logical. Any fears, even so, that this will be an over-narrow orientation may be allayed by our decision to define logic as the disciplined description of the behaviour of real-life logical agents. In this we command a theme that has played since antiquity: that logic is an account of how thinking agents reason and argue. Because we wish to give due attention to the process side of the process-product distinction, we propose a rapprochement between logic and psychology, with a special emphasis on developments in cognitive science. It would be foolish to suggest that the hugely profitable theoretical attainments of modem mathematical logic have no place in an agent-based, psychologically realistic account of abduction. The rich yield in the four pillars of post-Fregean logic — proof theory, set theory, model theory and recursion theory — are bench marks of intellectual achievement. But because these results bear on properties of linguistic structures independently of the involvement of an agent, or (as in proof theory) in ways involving only highly abstract intimations of agency, the theorems of standard mathematical logic tend not to have much in the way of direct application to what thinking agents do when they reason. Indirect relevance is another matter. Part of the story of an agent’s discharge of his cognitive agenda will involve his taking into account (perhaps only tacitly at times) properties of linguistic structures, such as consistency and consequence. Accordingly, we propose to absorb the logic of linguistic structures into a more comprehensive logic of agency. In so doing, we are mindful of various ways in which to ‘agentify’ logics of linguistic structures, whether by way of natural deduction protocols, relevance constraints, Prolog with restart and diminishing resources, N-Prolog with bounded restart for intuitionistic logic, action and time modalities, labelled instructions to presumed agents in proof theoretic environments (e.g., labelled deductive systems), “soft” consequence (as in non-monotonic, default and defeasible logics), enriching semantic models (e.g., as in fibred semantics), and applications to fallacious reasoning (e.g., the analysis of petito principii by way of intuitionistic modal logic). Also important in this regard is the structuralist approach to logic ensuing from [Gentzen, 1935, pp. 176–210, 149–167], and given new impetus by [Scott, 1972]. Such logics have been imaginatively exploited by AI researchers in developing approaches to plausible reasoning [Kraus et al., 1990], as well as more general frameworks for non-monotonic consequence relations [Gabbay, 1985b]. Structural logics have also been appropriated to advantage by the research community in dynamic semantics, where a variety of consequence relations have been analyzed non-monotonically [van Benthem, 1996; Port and van Gelder, 1995] and [Gochet, 2002]. It is these developments collectively to which the name of the new logic has been applied [Gabbay and Woods, 2001a]. It is a conception of logic especially suited to our purposes here.

In seeking a reconciliation with psychology, we risk the opprobrium of those who, like Frege, abjure psychologism in logic. It may surprise the reader to learn that in this we are entirely at one with Frege. If logic is confined to an examination of propositional structures independently of considerations of agency and contexts of use, then psychology has no place in logic. If, moreover, psychologism were to require that logic be thought of as just another experimental science, then, with Frege, we would part company with psychologism. If, however, it is legitimate to regard a logic as furnishing formal models of certain aspects of the cognitive behaviour of logical agents, then not only do psychological considerations have a defensible place, they cannot reasonably be excluded.¹

If, as we think, the distinction between logic and psychology is neither sharp nor exhaustive, it is necessary to say what a logic, as opposed to a psychology, of abduction, or of any inferential practice of a logical agent, would be. In this regard, we see ourselves in the historical mainstream of logic. From its inception, logic has been an account of target properties of linguistic structures, or of relations between linguistic and set theoretic structures, which are then adapted for use in the larger precincts of reasoning and arguing. Aristotle invented syllogistic logic to serve as the theoretical core of a wholly general and psychologically real theory of argument and inference. Doing so led him to ‘agentify’ the defining conditions on the syllogistic logic of linguistic structures in ways that made it, in effect, the first ever intuitionistic, non-monotonic, relevant (hence paraconsistent) logic [Woods, 2001].Aristotle developed the syllogistic constraints in ways that took explicit recognition of agency, action and interaction. The father of logic, therefore, ran the subject’s broad programme by adapting the logic of linguistic structures to the more comprehensive logic of inference and argument. What made it appropriate to consider the larger project as logic was that it was a principled extension and adaptation of the theory of those core structures. It is something in this same sense that ours too is a work of logic. We seek an account of what abductive agents do, in part by extension and adaptation of accounts of properties of linguistic structures, which themselves have been set up in ways that facilitate the adaptation and anticipate the approximate psychological reality of the requisite formal models. Oddly, then, what we are calling the new logic is in its general methodological outlines not only the old logic, but logic as it has been with few exceptions throughout all of its long history.

For us there is a point of departure. Although we concede that key logical properties of propositional structures play a central role in the broader logic of argument and inference, it is also our view that this broader logic must also take into account the fact, attested to by science and intuition alike, that real-life reasoning in real time is not always a matter of conscious symbol-processing.

Cognitive science engages our logical interests in its two main branches. Like cognitive neuropsychology, the new logic has an interest in modelling natural cognition. Like artificial intelligence, the new logic seeks an understanding of model of artificial intelligence with extensions to robotics and artificial life. In both domains it remains a characteristic contribution of cognitive science to conceive of cognition as computational; so its emphasis is on computer modelling of cognition, whether artificial or biological.

Much of the impetus for theoretical work on abduction comes from the philosophy of science. Philosophy of science was, in effect, invented by the Vienna Circle and the Berlin Group in the first third of the century just past. For the thirty or forty years after the mid-thirties, philosophy of science was a foundational enterprise. It proposed a logic of science as giving the logical syntax of the language of (all) science. It was an approach that disclaimed as excessively psychological the context of discovery (as Reichenbach called it), and concentrated on the context of justification (also Reichenbach). It was an imperious rather than case-based orientation, in which the flow of enquiry is top-down, from logic to the philosophy of science, and thence to science itself. And its analytical method was that of the explication of concepts.

In the past decades, philosophy of science has evolved from its original stance to its present non-foundational or neoclassical [Kuipers, 2000]. In it a place is provided for the contest of discovery, and there is much less attention paid to the (presumed) logical syntax of science and more on the construction of mathematical models of the conceptual products of natural scientific theorizing. Accordingly, the flow of enquiry is bottom-up, from science, to the philosophy of science, to the logic of science.

As conceived of in the neoclassical orientation, the logic of science provides formal idealized models of the most general an...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright page
• Dedication
• Acknowledgements
• Preface
• Part I: A Practical Logic of Cognitive Systems
• Part II: Conceptual models of abduction
• Part III: Formal Models of Abduction
• Bibliography
• Index