Implication in pseudocomplemented and Stone lattices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F25%3A73633262" target="_blank" >RIV/61989592:15310/25:73633262 - isvavai.cz</a>
Result on the web
<a href="https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-46-number-1-2025/mvlsc-46-1-p-27-43/" target="_blank" >https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-46-number-1-2025/mvlsc-46-1-p-27-43/</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Implication in pseudocomplemented and Stone lattices
Original language description
Two kinds of the connective implication are introduced as term operations of a pseudocomplemented lattice. It is shown that they share a lot of properties with intuitionistic implication based on Heyting algebras. If the pseudocomplemented lattice in question is a Stone lattice then the considered implications satisfy some kind of quasi-commutativity, of the exchange property, some version of adjointness with the meet-operation and some kind of the derivation rule Modus Ponens and of the contraposition law. Two kinds of deductive systems are defined and their elementary properties are investigated.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF24-14386L" target="_blank" >GF24-14386L: Representations of algebraic semantics for substructural logics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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