Catálogo de publicaciones - libros

The general purpose of this chapter is to provide a critical analysis on the controversial enterprise of ‘logics of discovery’. It is naturally divided into six parts. After this introduction, in the second part (section 2) we briefly review the original heuristic methods, namely analysis and synthesis , as conceived in ancient Greece. In the third part (section 3) we tackle the general question of whether there is a logic of discovery. We start by analyzing the twofold division between the contexts of discovery and justification, showing that it may be not only further divided, but also its boundaries may not be so sharply distinguished. We then provide a background history (from antiquity to the XIXth century), divided into three periods in time, each of which is characterized by an epistemological stance (infallibilism or fallibilism) and by the types of logic worked out (generational, justificatory inductive logics, non-generational and self-corrective logics). Finally, we motivate the division of this general question into other three questions, namely one of purpose , one of pursuit and one of achievement , for in general, there is a clear gap between the search and the findings in the question of a logic of discovery. In the fourth part (section 4), we confront two foremost views on the logic of discovery, namely those of Karl Popper and Herbert Simon, and show that despite appearances, their approaches are close together in several respects. They both hold a fallibilist stance in regard to the well-foundedness of knowledge and view science as a dynamic activity of problem solving in which the growth of knowledge is the main aspect to characterize. We claim that both accounts fall under the study of discovery –when a broad view is endorsed– and the convergence of these two approaches is found in that neither Simon’s view really accounts for the epistemics of creativity at large, nor Popper neglects its study entirely. In the fifth part (section 5), we advance the claim that logic should have a place in the methodology of science, on a pair with historical and computational stances, something that naturally gives place to logical approaches to the logic of discovery, to be cherish in a normative account of the methodology of science. However, we claim that the label ‘logics of discovery’ should be replaced by ‘logics of generation and evaluation’, for on the one hand ‘discovery’ turns out to be a misleading term for the processes of generation of new knowledge and on the other hand, a logic of generation can only be conceived together with an account of processes for evaluation and justification. In the final part of this chapter (section 6), we sum up our previous discussion and advance our general conclusions.

The general purpose of this chapter is to give an overview of the field of abduction in order to provide the conceptual framework of our overall study of abductive reasoning and its relation to explanatory reasoning in subsequent chapters. It is naturally divided into seven parts. After this brief introduction, in the second part (section 2) we motivate our study via several examples that show that this type of reasoning pervades common sense reasoning as well as scientific inquiry. Moreover, abduction may be studied from several perspectives; as a product or as a process, the latter in turn leading to either the process of hypotheses construction or of hypotheses selection and finally, abduction makes sense in connection with its sibling induction, but there are several confusions arising from this relation. In the third part (section 3), we turn to the founding father of abduction, the American pragmatist Charles S. Peirce and present very briefly his theory of abduction. In the fourth part (section 4), we review abduction in the philosophy of science, as it is related with the central topic of scientific explanation, existing both in the received view as well as in neglected ones in this field. In the fifth part (section 5), we present abduction in the field of artificial intelligence and show that it holds a place as a logical inference, as a computational process as well as in theories of belief revision. In the sixth part (section 6), we give an overview of two other fields in which abduction is found, namely in linguistics and in mathematics (neither of which is further pursued in this book). Finally, in the seventh part of this chapter (section 7), we tie up our previous overview by proposing a general taxonomy for abduction, one that allows two different abductive triggers (novelty and anomaly), which in turn lead to different abductive procedures; and one that allows for several outcomes: facts, rules, or even whole new theories. On our view, abduction is not a newnotion of inference. It is rather a topic-dependent practice of scientific reasoning, which can be supported by various types of logical inferences or computational processes.

In the preceding overview chapter, we have seen how the notion of abduction arose in the last century out of philosophical reflection on the nature of human reasoning, as it interacts with patterns of explanation and discovery. Our analysis brought out a number of salient aspects to the abductive process, which we shall elaborate in a number of successive chapters. For a start, abduction may be viewed as a kind of logical inference and that is how we will approach it in the analysis to follow here. Evidently, though, as we have already pointed out, it is not standard logical inference, and that for a number of reasons. Intuitively, abduction runs in a backward direction, rather than the forward one of standard inference, and moreover, being subject to revision, it exhibits non-standard nonmonotonic features (abductive conclusions may have to be retracted in the light of further evidence), that are more familiar from the literature on non-standard forms of reasoning in artificial intelligence. Therefore, we will discuss abduction as a broader notion of consequence in the latter sense, using some general methods that have been developed already for non-monotonic and dynamic logics, such as systematic classification in terms of structural rules. This is not a mere technical convenience. Describing abduction in an abstract general way makes it comparable to better-studied styles of inference, thereby increasing our understanding of its contribution to the wider area of what may be called ‘natural reasoning‘. To be sure, in this chapter we propose a logical characterization of what we have called an (abductive) explanatory argument , in order to make explicit that the inference is explanatory (and thus forward chained), while keeping in mind it aims to characterize the conditions for an abductive explanation to be part of this inference (cf. chapter 2).

Our logical analysis of abduction in the previous chapter is in a sense, purely structural. It was possible to state how abductive explanatory logic behaves, but not how abductive explanations are generated. In this chapter we turn to the question of abduction as a computational process. There are several frameworks for computing abductions; two of which are logic programming and semantic tableaux. The former is a popular one, and it has opened a whole field of abductive logic programming [KKT95] and [FK00]. The latter has also been proposed for handling abduction [MP93] and [AN04], and it is our preference here. Semantic tableaux are a well-motivated standard logical framework. But over these structures, different search strategies can compute several versions of abduction with the non-standard behaviour that we observed in the preceding chapter. Moreover, we can naturally compute various kinds of abducibles: atoms, conjunctions or even conditionals. This goes beyond the framework of abductive logic programming, in which abducibles are atoms from a special set of abducibles.

In the philosophy of science, we confront our logical account of chapter 3 with the notion of scientific explanation, as proposed by Hempel in two of his models of scientific inference: deductive-nomological and inductive-statistical [Hem65]. We showthat both can be viewed as forms of (abductive) explanatory arguments, the ultimate products of abductive reasoning. The former with deductive underlying inference, and the latter with statistical inference.

Traditional positivist philosophy of science inherits from logical research not only its language, but also its focus on the truth question , that is to say, the purpose of using its methods as means for testing hypotheses or formulae. As we saw in the previous chapter, Hempelian models of explanation and confirmation seek to establish the conditions under which a theory (composed by scientific laws) together with initial conditions, explains a certain phenomenon or whether certain evidence confirms a theory. As for logical research, it has been characterized by two approaches, namely the syntactic and the semantic. The former account characterizes the notion of derivability and aims to answer the following question: given theory H (a set of formulae) and formula E , is E derivable from H ? The latter characterizes the notion of logical consequence and responds to the following question: is E a logical consequence of H ? (Equivalent to: are the models of H models of E ?) Through the truth question we can only get a “yes–no” answer with regard to the truth or falsity of a given theory. Aiming solely at this question implies a static viewof scientific practice, one in which there is no place for theory evaluation or change. Notions like derivation, logical consequence, confirmation, and refutation are designed for the corroboration –logical or empirical– of theories.

In this chapter, I present the philosophical doctrine known as pragmatism, as proposed by Charles Peirce, namely, as a method of reflexion with the aim at clarifying ideas and guided at all moments by the ends of the ideas it analyzes. Pragmatism puts forward an epistemic aim with an experimental solution, and does so by following the pragmatic maxim , the underlying precept to fix a belief, and accordingly produce its corresponding habits of action.

Notions related to explanation have also emerged in theories of belief change in AI. One does not just want to incorporate new beliefs, but often also, to justify them. The main motivation of these theories is to develop logical and computational mechanisms to incorporate newinformation to a scientific theory, data base or set of beliefs. Different types of change are appropriate in different situations. Indeed, the pioneeringwork of Carlos Alchourrón, PeterGärdenfors and David Makinson (often referred as theAGMapproach) [AGM85], proposes a normative theory of epistemic change characterized by the conditions that a rational belief change operator should satisfy.