On Pre-Hilbert and Positive Implicative Pre-Hilbert Algebras
| dc.contributor.author | Walendziak, Andrzej | |
| dc.date.accessioned | 2024-09-30T13:40:20Z | |
| dc.date.available | 2024-09-30T13:40:20Z | |
| dc.date.issued | 2024-05-20 | |
| dc.identifier.issn | 0138-0680 | |
| dc.identifier.uri | http://hdl.handle.net/11089/53272 | |
| dc.description.abstract | In the paper, pre-Hilbert algebras are defined as a generalization of Hilbert algebras (namely, a Hilbert algebra is just a pre-Hilbert algebra satisfying the property of antisymmetry). Pre-Hilbert algebras have been inspired by Henkin’s Positive Implicative Logic. Their properties and characterizations are investigated. Some important results and examples are given. Moreover, positive implicative pre-Hilbert algebras are introduced and studied, their connections with some algebras of logic are presented. The hierarchies existing between the classes of algebras considered here are shown. | en |
| dc.language.iso | en | |
| dc.publisher | Wydawnictwo Uniwersytetu Łódzkiego | pl |
| dc.relation.ispartofseries | Bulletin of the Section of Logic;3 | en |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0 | |
| dc.subject | Hilbert algebra | en |
| dc.subject | pre-Hilbert algebra | en |
| dc.subject | BCK-algebra | en |
| dc.subject | BCC-algebra | en |
| dc.subject | BE-algebra | en |
| dc.subject | positive implicativity | en |
| dc.title | On Pre-Hilbert and Positive Implicative Pre-Hilbert Algebras | en |
| dc.type | Article | |
| dc.page.number | 345-364 | |
| dc.contributor.authorAffiliation | University of Siedlce, Faculty of Exact and Natural Sciences, Institute of Mathematics | en |
| dc.identifier.eissn | 2449-836X | |
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| dc.contributor.authorEmail | walent@interia.pl | |
| dc.identifier.doi | 10.18778/0138-0680.2024.07 | |
| dc.relation.volume | 53 |
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