Nuclei and conuclei on Girard posets

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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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  -