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Ambiguous Representations of Semilattices, Imperfect Information, and Predicate Transformers

  • Oleh NykyforchynEmail author
  • Oksana Mykytsey
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Abstract

Crisp and lattice-valued ambiguous representations of one continuous semilattice in another one are introduced and operation of taking pseudo-inverse of the above relations is defined. It is shown that continuous semilattices and their ambiguous representations, for which taking pseudo-inverse is involutive, form categories. Self-dualities and contravariant equivalences for these categories are obtained. Possible interpretations and applications to processing of imperfect information are discussed.

Keywords

Ambiguous representation Continuous semilattice Duality of categories Imperfect information 

Notes

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© The Author(s) 2019

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institute of MathematicsKasimir the Great University in BydgoszczBydgoszczPoland
  2. 2.Department of Mathematics and Computer ScienceVasyl’ Stefanyk Precarpathian National UniversityIvano-FrankivskUkraine

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