Nuclei and conuclei on Girard posets
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Proceedings |
| Conference | Atlantis Studies in Uncertainty Modelling, volume 1 |
| MU Faculty or unit | |
| Citation | |
| Web | https://download.atlantis-press.com/article/125914812.pdf |
| Doi | http://dx.doi.org/10.2991/eusflat-19.2019.42 |
| 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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