Formalization of ⇜natural⇝ classification and ⇜natural⇝ concepts by probabilistic generalization of formal concepts analysis

Evgenii E. Vityaev, Vladislav Degtiarev, Bayar Pak, Yuri Meister

Research output: Contribution to journalConference articlepeer-review

Abstract

In the previous works, a probabilistic generalization of the formal concepts analysis was developed. This generalization is induced by the problem of formal concepts determining under noise conditions, when the lattice of formal concepts exponentially grows. In this paper, probabilistic formal concepts with negation are determined, as well as a statistical method for detecting these probabilistic formal concepts. The purpose of this paper is to show that probabilistic formal concepts have a deeper meaning. It is argued that probabilistic formal concepts formalize the “natural” concepts described in cognitive sciences by “causal models”, which are characterized by a highly correlated structure of attributes. The same structure is specific for the “natural" classification of objects of the external world. The definition of “natural" classification given by J. Stuart Mill is fairly accurately formalized by probabilistic formal concepts.

Original languageEnglish
Pages (from-to)59-73
Number of pages15
JournalCEUR Workshop Proceedings
Volume2648
Publication statusPublished - Oct 2020
Event2020 "Russian Advances in Artificial Intelligence", RAAI 2020 - Moscow, Russian Federation
Duration: 10 Oct 202016 Oct 2020

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