Proceedings of the 11th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2019)

Nuclei and conuclei on Girard posets

Authors
David Kruml, Jan Paseka
Corresponding Author
Jan Paseka
Available Online August 2019.
DOI
10.2991/eusflat-19.2019.42How to use a DOI?
Keywords
residuated poset Frobenius poset Girard poset Girard quantale quantic nucleus quantic conucleus ideal conucleus
Abstract

It is well-known that the semantics of a given fuzzy logic can be formally axiomatized by means of a residuated poset. Based on a notion of dualizing (cyclic) element we introduce the notion of a Frobenius (Girard) poset. With this paper we hope to contribute to the theory of Frobenius posets and Girard posets. By means of a dualizing element we establish a one-to-one correspondence between a Frobenius poset and its opposite which is again a Frobenius poset. We also investigate some properties of nuclei and conuclei on Girard posets. Finally, we discuss the relation between quantic nuclei and ideal conuclei on a Girard poset and its opposite. We show that they are in one-to-one correspondence.

Copyright
© 2019, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 11th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2019)
Series
Atlantis Studies in Uncertainty Modelling
Publication Date
August 2019
ISBN
978-94-6252-770-6
ISSN
2589-6644
DOI
10.2991/eusflat-19.2019.42How to use a DOI?
Copyright
© 2019, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - David Kruml
AU  - Jan Paseka
PY  - 2019/08
DA  - 2019/08
TI  - Nuclei and conuclei on Girard  posets
BT  - Proceedings of the 11th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2019)
PB  - Atlantis Press
SP  - 289
EP  - 296
SN  - 2589-6644
UR  - https://doi.org/10.2991/eusflat-19.2019.42
DO  - 10.2991/eusflat-19.2019.42
ID  - Kruml2019/08
ER  -