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Abstract

Formal concept analysis, originally proposed by Wille, is a mathematical tool to analyse and represent data in the form of complete formal context. However, in situations with incomplete information, one only has partial knowledge about a concept, recently, a common conceptual framework of the notions of interval sets and incomplete formal contexts for representing partially-known concepts were presented. In this study, we examine and reinterpret the existing studies on partially known concepts by means of three-valued logics. By treating an incomplete formal context as a three-valued formal context and considering the one-to-one correspondence between interval sets and three-valued mappings, we investigate the condition under which the four types of partially known concepts can be generated by using three-valued implication operators. Moreover, we also evaluate the role of three-valued logic in characterizing attribute implications. A sufficient and necessary condition for computing the true value of an implication correctly in the sense of Kriple semantics is provided.

Keywords

Formal context partially-known concept three-valued logic attribute implication

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A three-valued logic approach to partially known formal concepts 1

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