In this paper, adaptive logics are studied from the viewpoint of universal logic (in the sense of the study of common structures of logics). The common structure of a large set of adaptive logics is described. It is shown that this structure determines the proof theory as well as the semantics of the adaptive logics, and moreover that most properties of the logics can be proved by relying solely on the structure, viz. without invoking any specific properties of the logics themselves.

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A Universal Logic Approach to Adaptive Logics

ENTAILMENT: The Logic of Relevance and Necessity (Volume I)

This paper contains a unified characterization of adaptive logics. The general structure is presented in the simplest possible guise, both for flat and prioritized adaptive logics. The latter are presented as a special case of combined adaptive logics. The aim of the paper is to provide the general framework underlying several other papers in this volume and to prepare the unified metatheory of adaptive logics.

A General Characterization of Adaptive Logics

Charles Sanders Peirce, far more than any scholar in recent centuries in the West, devoted much of his productive life to probing the idea of and behavior of “habit”. In order to do so, he both narrowed and widened his focus on the notion. Otherwise an ordinary term in quotidian use in English, habit suggests regularity, usually pertaining to individual human behavior—but Peirce also focused on habit’s utility for understanding behavior beyond the human, and even processes beyond the organic world. In pursuit of refining and operationalizing habit, Peirce drew on any number of disciplines, close to and far from his expertise—these spanning from logic/philosophy, biology and psychology to theology and cosmology. Peirce’s foundational work on habit continues to be irresistible for contemporary humanities scholars, social scientists, scientists, and for practitioners beyond the academy diagnosing the ills of self and society, as Peirce’s oeuvre in its infra-dialectical form (frequently in fragmentary paragraphs), cannot be satisfactorily appreciated through any rear-view mirror. Rather, one might say that, in recognizing the habits behind habits and habit-change—whether confirming them through belief or challenging them through doubt—Peirce still invites us to permute, expand, contest, and refine his explorations of a century ago.

Consensus on Peirce’s Concept of Habit

The purpose of this study was to analyze and develop various forms of abduction as a means of conceptualizing processes of discovery. Abduction was originally presented by Charles S. Peirce (1839-1914) as a “weak”, third main mode of inference -besides deduction and induction -one which, he proposed, is closely related to many kinds of cognitive processes, such as instincts, perception, practices and mediated activity in general. Both abduction and discovery are controversial issues in philosophy of science. It is often claimed that discovery cannot be a proper subject area for conceptual analysis and, accordingly, abduction cannot serve as a “logic of discovery”. I argue, however, that abduction gives essential means for understanding processes of discovery although it cannot give rise to a manual or algorithm for making discoveries. In the first part of the study, I briefly present how the main trend in philosophy of science has, for a long time, been critical towards a systematic account of discovery. Various models have been suggested. I outline a short history of abduction; first Peirce's evolving forms of his theory, and then later developments. Although abduction has not been a major area of research until quite recently, I review some critiques of it and look at the ways it has been analyzed, developed and used in various fields of research. Peirce’s own writings and later developments, I argue, leave room for various subsequent interpretations of abduction. The second part of the study consists of six research articles. First I treat “classical” arguments against abduction as a logic of discovery. I show that by developing strategic aspects of abductive inference these arguments can be countered. Nowadays the term ‘abduction’ is often used as a synonym for the Inference to the Best Explanation (IBE) model. I argue, however, that it is useful to distinguish between IBE (“Harmanian abduction”) and “Hansonian abduction”; the latter concentrating on analyzing processes of discovery. The distinctions between loveliness and likeliness, and between potential and actual explanations are more fruitful within Hansonian abduction. I clarify the nature of abduction by using Peirce’s distinction between three areas of “semeiotic”: grammar, critic, and methodeutic. Grammar (emphasizing “Firstnesses” and iconicity) and methodeutic (i.e., a processual approach) especially, give new means for understanding abduction. Peirce himself held a controversial view that new abductive ideas are products of an instinct and an inference at the same time. I maintain that it is beneficial to make a clear distinction between abductive inference and abductive instinct, on the basis of which both can be developed further. Besides these, I analyze abduction as a part of distributed cognition which emphasizes a long-term interaction with the material, social and cultural environment as a source for abductive ideas. This approach suggests a “trialogical” model in which inquirers are fundamentally connected both to other inquirers and to the objects of inquiry. As for the classical Meno paradox about discovery, I show that abduction provides more than one answer. As my main example of abductive methodology, I analyze the process of Ignaz Semmelweis’ research on childbed fever. A central basis for abduction is the claim that discovery is not a sequence of events governed only by processes of chance. Abduction treats those processes which both constrain and instigate the search for new ideas; starting from the use of clues as a starting point for discovery, but continuing in considerations like elegance and 'loveliness'. The study then continues a PeirceanHansonian research programme by developing abduction as a way of analyzing processes of discovery.

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On the Origin of Ideas: An Abductivist Approach to Discovery

In this paper, we propose a reconstruction of logic-based approaches to abductive reasoning in terms of ampliative adaptive logics. A main advantage of this reconstruction is that the resulting logics have a proof theory. As abductive reasoning is non-monotonic, the latter is necessarily dynamic (conclusions derived at some stage may at a later stage be rejected). The proof theory warrants, however, that the conclusions derived at a given stage are justified in view of the insight in the premises at that stage. Thus, it even leads to justified conclusions for undecidable fragments. Another advantage of the proposed logics is that they are much closer to natural reasoning than the existing systems. Usually, abduction is viewed as a form of “backward reasoning”. The search procedure by which this is realized (for instance, some form of linear linear resolution) is very different from the search procedures of human reasoners. The proposed logics treat abduction as a form of “forward reasoning” (Modus Ponens in the “wrong direction”). As a result, abductive steps are very natural, and are moreover nicely integrated with deductive steps. We present two new adaptive logics for abduction, and illustrate both with some examples from the history of the sciences (the discovery of Uranus and of Neptune). We also present some alternative systems that are better suited for non-creative forms of abductive reasoning.

Ampliative Adaptive Logics and the Foundation of Logic-Based Approaches to Abduction

Introducing techniques deriving from dynamic proofs in proofs for propositional classical logic is shown to lead to a proof format that enables one to push search paths into the proofs themselves. The resulting goal directed proof format is shown to provide a decision method for A1, . . . An ` B and a positive test for Γ ` A.

Pushing the Search Paths in the Proofs. A Study in Proof Heuristics

A logic of diagnosis proceeds in terms of a set of data and one or more (prioritized) sets of expectancies. In this paper we generalize the logics of diagnosis from [27] and present some alternatives. The former operate on the premises and expectancies themselves, the latter on their consequences.

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Some Adaptive Logics for Diagnosis

In this paper we characterize the six (basic) signed systems from [18] in terms of adaptive logics. We prove the characterization correct and show that it has a number of advantages.

https://biblio.ugent.be/publication/505754/file/505756.pdf

An Adaptive Characterization of Signed Systems for Paraconsistent Reasoning

In this paper, we present a goal-directed proof procedure for abductive reasoning. This procedure will be compared with Aliseda's approach based on semantic tableaux. We begin with some comments on Alis- eda's algorithms for computing conjunctive abductions and show that they do not entirely live up to their aims. Next we give a concise account of goal-directed proofs and we show that abductive explanations are a natural spin-off of these proofs. Finally, we show that the goal-directed procedure solves the problems we encountered in Aliseda's algorithms.

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Dagmar Provijn

Papers

Ampliative Adaptive Logics and the Foundation of Logic-Based Approaches to Abduction

Pushing the Search Paths in the Proofs. A Study in Proof Heuristics

Some Adaptive Logics for Diagnosis

An Adaptive Characterization of Signed Systems for Paraconsistent Reasoning

Abduction through Semantic Tableaux versus Abduction through Goal-Directed Proofs