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https://open.uns.ac.rs/handle/123456789/10767
Title: | Galois connection for hyperclones | Authors: | Machida H. Pantović, Jovanka Rosenberg I. |
Issue Date: | 12-Aug-2010 | Journal: | Proceedings of The International Symposium on Multiple-Valued Logic | Abstract: | This paper is inspired by the paper of Tarasov [17] in which he investigates maximal partial clones on a two-element set. It happens that the approach of Tarasov can be translated into the language of hyperclone theory. He introduced a notion of quasicomposition which assigns to extended hyperoperations extension of their composition. We introduce a new operation in the set of extended hyperoperationand define a quasiclone as a composition closed set of extended hyperoperations containing all projections which is closed with respect to the new operation. For a Galois connection between sets of extended hyperoperations and power relations, we prove that the set ePolR of all extended hyperoperations e-preserving every relation ρ ∈ R is a quasiclone and that each quasiclone is of the form ePolR for a set R of relations on the power set of A without empty-set. Finally, we re-state results of Tarasov in hyperclone framework. © 2010 IEEE. | URI: | https://open.uns.ac.rs/handle/123456789/10767 | ISBN: | 9780769540245 | ISSN: | 0195623X | DOI: | 10.1109/ISMVL.2010.45 |
Appears in Collections: | FTN Publikacije/Publications |
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