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Implicational (Semilinear) Logics I: A New Hierarchy

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F10%3A00342136" target="_blank" >RIV/67985807:_____/10:00342136 - isvavai.cz</a>

  • Result on the web

  • DOI - Digital Object Identifier

Alternative languages

  • Result language

    angličtina

  • Original language name

    Implicational (Semilinear) Logics I: A New Hierarchy

  • Original language description

    In abstract algebraic logic, the general study of propositional logics is based on the abstraction of the Lindenbaum-Tarski process, one considers the Leibniz relation of indiscernible formulae. It leads to the Leibniz hierarchy; a classification of logics based on generalized equivalences. We perform an analogous abstract study of non-classical logics based on generalized implications. It yields the hierarchy of implicational logics which expands Leibniz hierarchy. The notion of implicational semilinear logic is then naturally introduced as a property of the implication, namely a logic is an implicational semilinear logic iff it has an implication and is complete w.r.t. the matrices where this implication induces a linear order, a property which is satisfied by majority of fuzzy logics. This hierarchy is then restricted to the semilinear case obtaining a classification that encompasses almost all the known examples of fuzzy logics and suggests new directions for research.

  • Czech name

  • Czech description

Classification

  • Type

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

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/GEICC%2F08%2FE018" target="_blank" >GEICC/08/E018: Logical Models of Reasoning with Vague Information</a><br>

  • Continuities

    Z - Vyzkumny zamer (s odkazem do CEZ)

Others

  • Publication year

    2010

  • 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

    1432-0665

  • e-ISSN

  • Volume of the periodical

    49

  • Issue of the periodical within the volume

    4

  • Country of publishing house

    DE - GERMANY

  • Number of pages

    30

  • Pages from-to

  • UT code for WoS article

    000277246000001

  • EID of the result in the Scopus database