Structural Completeness in Many-Valued Logics with Rational Constants
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F22%3A00559061" target="_blank" >RIV/67985807:_____/22:00559061 - isvavai.cz</a>
Result on the web
<a href="https://dx.doi.org/10.1215/00294527-2022-0021" target="_blank" >https://dx.doi.org/10.1215/00294527-2022-0021</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1215/00294527-2022-0021" target="_blank" >10.1215/00294527-2022-0021</a>
Alternative languages
Result language
angličtina
Original language name
Structural Completeness in Many-Valued Logics with Rational Constants
Original language description
The logics R Ł, RP, and RG have been obtained by expanding Łukasiewicz logic Ł, product logic P, and Gödel–Dummett logic G with rational constants. We study the lattices of extensions and structural completeness of these three expansions, obtaining results that stand in contrast to the known situation in Ł, P, and G. Namely, R Ł is hereditarily structurally complete. RP is algebraized by the variety of rational product algebras that we show to be Q -universal. We provide a base of admissible rules in RP, show their decidability, and characterize passive structural completeness for extensions of RP. Furthermore, structural completeness, hereditary structural completeness, and active structural completeness coincide for extensions of RP , and this is also the case for extensions of RG , where in turn passive structural completeness is characterized by the equivalent algebraic semantics having the joint embedding property. For nontrivial axiomatic extensions of RG , we provide a base of admissible rules. We leave the problem open whether the variety of rational Gödel algebras is Q-universal.
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
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Notre Dame Journal of Formal Logic
ISSN
0029-4527
e-ISSN
1939-0726
Volume of the periodical
63
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
39
Pages from-to
261-299
UT code for WoS article
000933209300001
EID of the result in the Scopus database
2-s2.0-85137050042