The propositional logic induced by means of basic algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F15%3A33155644" target="_blank" >RIV/61989592:15310/15:33155644 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/article/10.1007%2Fs10773-014-2500-3" target="_blank" >http://link.springer.com/article/10.1007%2Fs10773-014-2500-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10773-014-2500-3" target="_blank" >10.1007/s10773-014-2500-3</a>

Result language
angličtina
Original language name
The propositional logic induced by means of basic algebras
Original language description
A propositional logic induced by means of commutative basic algebras was already described by M. Botur and R. Hala. It turns out that this is a kind of non-associative fuzzy logic which can be used e.g. in expert systems. Unfortunately, there are other important classes of basic algebras which are not commutative, e.g. orthomodular lattices which are used as an axiomatization of the logic of quantum mechanics. This motivated us to develop another axioms and derivation rules which form a propositional logic induced by basic algebras in general. We show that this logic is algebraizable in the sense of W. J. Blok and D. Pigozzi.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/EE2.3.20.0051" target="_blank" >EE2.3.20.0051: Algebraic methods in Quantum Logic</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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