Operations and structures derived from non-associative MV-algebras
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F19%3A73597865" target="_blank" >RIV/61989592:15310/19:73597865 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/content/pdf/10.1007%2Fs00500-018-3309-4.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007%2Fs00500-018-3309-4.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00500-018-3309-4" target="_blank" >10.1007/s00500-018-3309-4</a>
Alternative languages
Result language
angličtina
Original language name
Operations and structures derived from non-associative MV-algebras
Original language description
The so-called non-associative MV-algebras were introduced recently by the first author and J. Kühr in order to have an appropriate tool for certain logics used in expert systems where associativity of the binary operation is excluded, see, e.g., Botur and Halaš (Arch Math Log 48:243–255, 2009). Since implication is an important logical connective in practically every propositional logic, in the present paper we investigate the implication reducts of non-associative MV-algebras. We also determine their structures based on the underlying posets. The natural question when a poset with the greatest element equipped with sectional switching involutions can be organized into an implication NMV-algebra is solved. Moreover, congruence properties of the variety of implication NMV-algebras with, respectively, without zero are investigated. Analogously to classical propositional logic, we introduce a certain kind of Sheffer operation and we obtain a one-to-one correspondence between NMV-algebras and certain algebras built up by a Sheffer-like operation together with a unary operation.
Czech name
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Czech description
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Classification
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
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SOFT COMPUTING
ISSN
1432-7643
e-ISSN
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Volume of the periodical
23
Issue of the periodical within the volume
12
Country of publishing house
US - UNITED STATES
Number of pages
10
Pages from-to
3935-3944
UT code for WoS article
000466948100004
EID of the result in the Scopus database
2-s2.0-85048593417