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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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