Quasiorders, Tolerance Relations and Corresponding “Partitions”
Bulletin of the Section of Logic (2016)
- Volume: 45, Issue: 2
- ISSN: 0138-0680
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topMarek Nowak. "Quasiorders, Tolerance Relations and Corresponding “Partitions”." Bulletin of the Section of Logic 45.2 (2016): null. <http://eudml.org/doc/295565>.
@article{MarekNowak2016,
abstract = {The paper deals with a generalization of the notion of partition for wider classes of binary relations than equivalences: for quasiorders and tolerance relations. The counterpart of partition for the quasiorders is based on a generalization of the notion of equivalence class while it is shown that such a generalization does not work in case of tolerances. Some results from [5] are proved in a much more simple way. The third kind of “partition” corresponding to tolerances, not occurring in [5], is introduced.},
author = {Marek Nowak},
journal = {Bulletin of the Section of Logic},
keywords = {partition; quasiorder; tolerance relation},
language = {eng},
number = {2},
pages = {null},
title = {Quasiorders, Tolerance Relations and Corresponding “Partitions”},
url = {http://eudml.org/doc/295565},
volume = {45},
year = {2016},
}
TY - JOUR
AU - Marek Nowak
TI - Quasiorders, Tolerance Relations and Corresponding “Partitions”
JO - Bulletin of the Section of Logic
PY - 2016
VL - 45
IS - 2
SP - null
AB - The paper deals with a generalization of the notion of partition for wider classes of binary relations than equivalences: for quasiorders and tolerance relations. The counterpart of partition for the quasiorders is based on a generalization of the notion of equivalence class while it is shown that such a generalization does not work in case of tolerances. Some results from [5] are proved in a much more simple way. The third kind of “partition” corresponding to tolerances, not occurring in [5], is introduced.
LA - eng
KW - partition; quasiorder; tolerance relation
UR - http://eudml.org/doc/295565
ER -
References
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- [3] S. N. Gerasin, V. V. Shlyakhov, S. V. Yakovlev, Set coverings and tolerance relations, Cybernetics and System Analysis 44 (2008), pp. 333–340.
- [4] A. I. Krivoruchko, Tolerance classes, Cybernetics and System Analysis 20 (1984), pp. 6–11.
- [5] M. Nowak, On some generalization of the concept of partition, Studia Logica 102 (2014), pp. 93–116.
- [6] J. Pogonowski, Tolerance spaces with application to linguistics, Adam Mickiewicz University Press, Poznań, 1981.
- [7] E. C. Zeeman, The Topology of the Brain and Visual Perception, [in:] M. K. Fort (ed.), The Topology of 3-Manifolds and Related Topics, 1962, pp. 240–256.
- [8] B. Zelinka, A remark on systems of maximal cliques of a graph, Czechoslovak Math. J. 27 (1977), pp. 617–618.
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