Paper:

# Concept Finding Proofs

## Norihiro Kamide

Waseda Institute for Advanced Study, Waseda University, 1-6-1 Nishi Waseda, Shinjuku-ku, Tokyo 169-8050, Japan

We propose a proof-theoretical way of obtaining detailed and precise information on conceptual hierarchies. The notion of concept finding proof, which represents a hierarchy of concepts, is introduced based on a substructural logic with mingle and strong negation. Mingle, which is a structural inference rule, is used to represent a process for finding a more general (or specific) concept than some given concepts. Strong negation, which is a negation connective, is used to represent a concept inverse operator. The problem for constructing a concept finding proof is shown to be decidable in PTIME.^{1} 1. This paper is an extended version of [1].

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.15, No.7, pp. 777-784, 2011.

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