Fleischer po-semigroups and quantum B-algebras

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Authors	KÜHR Jan PASEKA Jan
Year of publication	2020
Type	Article in Proceedings
Conference	2020 IEEE 50th International Symposium on Multiple-Valued Logic (ISMVL)
MU Faculty or unit	Faculty of Science
Citation
web	https://conferences.computer.org/ismvl/pdfs/ISMVL2020-6CeVlZGfQNLgKvukfNXZmZ/540600a285/540600a285.pdf
Doi	https://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.
Related projects:	Grupové techniky a kvantová informace