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Fuzzy Horn logic I: proof theory

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F06%3A00003269" target="_blank" >RIV/61989592:15310/06:00003269 - isvavai.cz</a>

  • Alternative codes found

    RIV/61989592:15310/06:00002566

  • Result on the web

  • DOI - Digital Object Identifier

Alternative languages

  • Result language

    angličtina

  • Original language name

    Fuzzy Horn logic I: proof theory

  • Original language description

    The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability of formulas from theories. Our basic structure of truth degrees is a complete residuated lattice. We derive a Pavelka-style completeness theorem (degree of provability equals degree of truth) from which we get some particular cases by imposing restrictions on the formulas under consideration. As a particular case, we obtain completeness of fuzzy equational logic.

  • Czech name

    Fuzzy Horn logika I: teorie důkazů

  • Czech description

    Prezentace výsledků zkoumání teorie Fuzzy Horn logiky.

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BD - Information theory

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/KJB1137301" target="_blank" >KJB1137301: Relational systems in presence of vagueness and uncertainty:mathematical foundations for applications</a><br>

  • Continuities

    Z - Vyzkumny zamer (s odkazem do CEZ)

Others

  • Publication year

    2006

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Archive for Mathematical Logic

  • ISSN

    0933-5846

  • e-ISSN

  • Volume of the periodical

    45

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    DE - GERMANY

  • Number of pages

    49

  • Pages from-to

    3-51

  • UT code for WoS article

  • EID of the result in the Scopus database