On the difference between abduction and induction: a model theoretic perspective
Marc Denecker, Bern Martens, Luc De Raedt · Lirias · 1996
. In this paper, we show how an appropriate possible world semantics exhibits the fundamental differences between various forms of logical reasoning such as deduction, abduction and induction. The ensuing model theoretic formalisation provides a solid foundation for exact further discourse on the issue, such as deciding whether a particular instance of reasoning should be classified as abduction or rather as induction. 1 Introduction In logic and logic programming [17, 13], both inductive and abductive problems are usually phrased as follows: Given a theory T and (an) observation(s) O, find a theory \\Delta such that T [ \\Delta j= O. Many attempts [1, 4, 8, 9] to distinguish between induction and abduction are based on the syntactical conditions \\Delta has to satisfy. In an abductive context, one often (but not always) requires \\Delta to consist of ground atoms. The label induction, on the other hand, is usually (but not exclusively) reserved for applications where \\Delta contains ...