Publication details

Nuclei and conuclei on Girard posets



Year of publication 2019
Type Article in Proceedings
Conference Atlantis Studies in Uncertainty Modelling, volume 1
MU Faculty or unit

Faculty of Science

Keywords Residuated poset; Frobenius poset; Girard poset; Girard quantale; quantic nucleus; quantic conucleus; ideal conucleus
Description 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.
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