Meta-Level Abduction.

Meta-level abduction (MLA) has been proposed as a method to abduce missing laws in completing proofs and explaining observations at the meta-level. Based on a simple logic of causality, Inoue et al. (2010) firstly proposed meta-level abduction to discover physically unobserved causality in terms of hidden rules to explain given empirical rules with respect to skills for music playing. Meta-level abduction has also been applied to completion of biological networks containing both positive and nega- tive causal effects (Inoue et al. , 2013). In this paper, we define a general framework for meta-level abduction together with a logical system for it, and analyze its potential power in various patterns of abductive reasoning. We will see that meta-level abduction can realize second-order existential abduction by Schurz (2008). Moreover, meta-level abduction can be coordinated with selective, creative and other types of abductions. 1 Abduction and Meta-Reasoning 1. 1 Abductive Reasoning Abduction is one of the three fundamental modes of reasoning characterized by Peirce [58], the others being deduction and induction. Abduction amounts to concluding the minor premise from the major premise and the conclusion, and its original inferential style is given as follows. The (surprising) fact, ψ, is observed; But if ϕ were true, ψ would be a matter of course; Hence, there is reason to suspect that ϕ is true. This corresponds to the rule of the form, called the fallacy of affirming the consequent: ψ ϕ→ψ. (1) ϕ

Authors

• Katsumi Inoue National Institute of Informatics

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