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On computable formal concepts in computable formal contexts

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Abstract

We introduce and study the notions of computable formal context and computable formal concept. We give some examples of computable formal contexts in which the computable formal concepts fail to form a lattice and study the complexity aspects of formal concepts in computable contexts. In particular, we give some sufficient conditions under which the computability or noncomputability of a formal concept could be recognized from its lattice-theoretic properties. We prove the density theorem showing that in a Cantor-like topology every formal concept can be approximated by computable ones. We also show that not all formal concepts have lattice-theoretic approximations as suprema or infima of families of computable formal concepts.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    A. S. Morozov

  2. Novosibirsk State University, Novosibirsk, Russia

    M. A. L’vova

Authors
  1. A. S. Morozov
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  2. M. A. L’vova
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Corresponding author

Correspondence to A. S. Morozov.

Additional information

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 5, pp. 1083–1092, September–October, 2007.

Original Russian Text Copyright © 2007 Morozov A. S. and L’vova M. A.

The first author was supported by the International DFG-RFBR Grant (RFBR 05-01-04003-NNIOa, DFG 436 RUS 113/829/0-1), the Russian Foundation for Basic Research (Grant 05-01-00819-a), and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-4413.2006.1).

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Morozov, A.S., L’vova, M.A. On computable formal concepts in computable formal contexts. Sib Math J 48, 871–878 (2007). https://doi.org/10.1007/s11202-007-0089-y

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  • DOI: https://doi.org/10.1007/s11202-007-0089-y

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