Fleischer po-semigroups and quantum B-algebras
| Authors | |
|---|---|
| Year of publication | 2020 |
| Type | Article in Proceedings |
| Conference | 2020 IEEE 50th International Symposium on Multiple-Valued Logic (ISMVL) |
| MU Faculty or unit | |
| Citation | |
| Web | https://conferences.computer.org/ismvl/pdfs/ISMVL2020-6CeVlZGfQNLgKvukfNXZmZ/540600a285/540600a285.pdf |
| Doi | http://dx.doi.org/10.1109/ISMVL49045.2020.00060 |
| Keywords | Partially ordered semigroup; residuable element; residuated partially ordered semigroup; quantale; quantum B-algebra; Fleischer po-semigroup; (pseudo-) BCK-algebra |
| Description | Following the idea of Fleischer who represented BCK-algebras by means of residuable elements of commutative integral po-monoids, we describe quantum B-algebras as subsets of residuable elements of posemigroups. Moreover, we show that quantum B-algebras correspond one-to-one to what we call Fleischer posemigroups. Such an approach is more economical than using logical quantales introduced by Rump. |
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