Distinguishing Abduction and Induction under Intensional Complexity

José Hernández-Orallo and Ismael García-Varea

Abstract

This paper presents a theoretical and general differentiation among descriptional induction, explanatory induction and abduction. Descriptional induction is based on the idea of compression (justified by mean- or cross-validation). Explanatory induction is characterised by a 'balanced' compression (exception-free validation). Finally, abduction is a more elusive notion, where the validation comes from a background theory. Since this background theory can also be used in both kinds of induction, we must distinguish between an auxiliary use and a necessary or ‘consilient’ use of the background knowledge. We introduce many new concepts and formalisations for this goal, mainly the idea of ‘intrinsic exception or anomaly’, consilience and an operative measure of reinforcement for logic programs. Finally, the difference between induction and abduction is seen in the context of growth of knowledge and theory revision.

Keywords: Abduction, Induction, Explanation, Compression, Reinforcement, Kolmogorov Complexity, Intensional Complexity, Consilient / Coherent Theories, Philosophy of Science, ALP, ILP, EBL.

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