Ambiguous Representations of Semilattices, Imperfect Information, and Predicate Transformers

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.

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Correspondence to Oleh Nykyforchyn.

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Nykyforchyn, O., Mykytsey, O. Ambiguous Representations of Semilattices, Imperfect Information, and Predicate Transformers. Order 37, 319–339 (2020). https://doi.org/10.1007/s11083-019-09508-0

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Keywords

  • Ambiguous representation
  • Continuous semilattice
  • Duality of categories
  • Imperfect information