1 Abduction : between Conceptual Richness and Computational Complexity

The aim of this chapter is two-fold: first, to explore the relationship between abduction and induction from a philosophical point of view; and second, to examine critically some recent attempts to provide computational models of abduction. Induction is typically conceived as the mode of reasoning which produces generalisations over domains of individuals based on samples. Abduction, on the other hand, is typically seen as the mode of reasoning which produces hypotheses such that, if true, they would explain certain phenomena or evidence. Recently there has been some increasing interest in the issue of how exactly, if at all, they are related. Two seem to be the main problems: first, whether or not induction and abduction are conceptually distinct modes of reasoning; second, whether or not they can be modelled computationally in the same, or similar, ways. The second issue is explored in some detail by several chapters in this collection (e.g. the contributions by Aliseda, Mooney and Poole). The first issue is what the present chapter will concentrate on. My suggestion will be that abduction is the basic type of ampliative reasoning. It comprises as special case both Induction and what the American philosopher Charles Peirce called “the Method of Hypothesis”. In order to motivate and defend my thesis, I proceed as follows. Section 1.2 describes the basic logical features of ampliative reasoning. Section 1.3 takes its cue from Peirce’s distinction between Induction and Hypothesis and raises the following question: should the fact that Induction and Hypothesis admit different logical forms