Atocha Aliseda

In this dissertation I study abduction, that is, reasoning from an observation to its possible explanations, from a logical point of view. This approach naturally leads to connections with theories of explanation in the philosophy of science, and to computationally oriented theories of belief change in Artificial Intelligence.

Many different approaches to abduction can be found in the literature, as well as a bewildering variety of instances of explanatory reasoning. To delineate our subject more precisely, and create some order, a general taxonomy for abductive reasoning is proposed in chapter 1. Several forms of abduction are obtained by instantiating three parameters: the kind of reasoning involved (e.g., deductive, statistical), the kind of observation triggering the abduction (novelty, or anomaly w.r.t. some background theory), and the kind of explanations produced (facts, rules, or theories). In chapter 2, I choose a number of major variants of abduction, thus conceived, and investigate their logical properties. A convenient measure for this purpose are so-called `structural rules' of inference. Abduction deviates from classical consequence in this respect, much like many current non-monotonic consequence relations and dynamic styles of inference. As a result we can classify forms of abduction by different structural rules. A more computational analysis of processes producing abductive inferences is then presented in chapter 3, using the framework of semantic tableaux. I show how to implement various search strategies to generate various forms of abductive explanations.

Our eventual conclusion is that abductive processes should be our primary concern, with abductive inferences their secondary 'products'. Finally, chapter 4 is a confrontation of the previous analysis with existing themes in the philosophy of science and artificial intelligence. In particular, I analyse two well-known models for scientific explanation (the deductive-nomological one, and the inductive-statistical one) as forms of abduction. This then provides them with a structural logical analysis in the style of chapter 2. Moreover, I argue that abduction can model dynamics of belief revision in artificial intelligence. For this purpose, an extended version of the semantic tableaux of chapter 3 provides a new representation of the operations of expansion, and contraction.