Abduction in Non-Axiomatic Logic

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].

International Journal of Approximate Reasoning, 1994

A nonaxiomatic reasoning system is an adaptive system that works with insufficient knowledge and resources. At the beginning of the paper, three binary term logics are defined. The first is based only on an inheritance relation. The second and the third suggest a novel way to process extension and intension, and they also have interesting relations with Aristotle's syllogistic logic. Based on the three simple systems, a nonaxiomatic logic is defined. It has a term-oriented language and an experience-grounded semantics. It can uniformly represent and process randomness, fuzziness, and ignorance. It can also uniformly carry out deduction, abduction, induction, and revision.

International Journal of Approximate Reasoning, 1994

A nonaxiomatic reasoning system is an adaptive system that works with insufficient knowledge and resources. At the beginning of the paper, three binary term logics are defined. The first is based only on an inheritance relation. The second and the third suggest a novel way to process extension and intension, and they also have interesting relations with Aristotle's syllogistic logic. Based on the three simple systems, a nonaxiomatic logic is defined. It has a term-oriented language and an experience-grounded semantics. It can uniformly represent and process randomness, fuzziness, and ignorance. It can also uniformly carry out deduction, abduction, induction, and revision.

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. ""

Handbook of Logic in Artificial Intelligence and Logic Programming: Volume 5: Logic Programming, 1998

This paper extends and updates our earlier survey and analysis of work on the extension of logic programming to perform abductive reasoning [Kakas et al., 1993]. The purpose of the paper is to provide a critical overview of some of the main research results, in order to develop a common framework for evaluating these results, to identify the main unresolved problems, and to indicate directions for future work. The emphasis is not on technical details but on relationships and common features of different approaches. Some of the main issues we will consider are the contributions that abduction can make to the problems of reasoning with incomplete or negative information, the evolution of knowledge, and the semantics of logic programming and its extensions. We also discuss recent work on the argumentation-theoretic interpretation of abduction, which was introduced in the earlier version of this paper. The philosopher Peirce first introduced the notion of abduction. In [Peirce, 1931-58]...

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.

Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia, 2008

ABSTRACT: In her book Abductive Reasoning Atocha Aliseda (2006) stresses the attention to the logical models of abduction, centering on the semantic tableaux as a method for extending and improving both the whole cognitive/philosophical view on it and on other more restricted logical approaches. I will provide further insight on two aspects. The first is related to the importance of increasing logical knowledge on abduction: Aliseda clearly shows how the logical study on abduction in turn helps us to extend and modernize the ...

Applied Logic Series, 2000

Abduction and induction in philosophy and logic 2 1.3 Abduction and induction in logic programming and artificial intelligence 11 1.4 Integration of abduction and induction 1.5 Conclusions Part I The philosophy of abduction and induction 2 Smart inductive generalizations are abductions John R. Josephson 2.1 A distinctive pattern of inference 2.2 What is an explanation? 2.3 Smart inductive generalizations are abductions 2.4 Conclusion 3

Theoretical Computer Science, 1997

Abduction{ from observations and a theory, nd using hypotheses an explanation for the observations { gained increasing interest during the last years. This form of reasoning has wide applicability in di erent areas of computer science; in particular, it has been recognized as an important principle of common-sense reasoning.