On Relationships between Induction and Abduction: A Logical Point of View

Abstract

The concepts of inductive and abductive reasonings have led and still lead to many open discussions. Many works are based on these reasonings, for example in machine learning (e.g. (Kodratoff and Ganascia, 1986; Michalski, 1983a)), inductive logic programming (see (Muggleton and De Raedt, 1994) for a survey), abductive logic programming (e.g. (Poole et al., 1987)), or resolution of diagnosis problems (see (Cox and Pietrzykowski, 1987; de Kleer and Williams, 1987; Poole, 1989b) for various approaches to abduction). However, many of these works deal with only one of these reasonings. When we attempt to relate induction and abduction, the obvious differences between the various approaches make this task difficult. How can we, for example, relate induction characterized by logical conditions of adequacy of the relation “observation O confirms hypothesis H ” (Hempel, 1945) with the ABDUCE procedure in logic programming (Console et al., 1991b)?