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A Computational Glimpse at the Leibniz and Frege Hierarchies

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    SYSNO ASEP0477047
    Document TypeJ - Journal Article
    R&D Document TypeJournal Article
    Subsidiary JČlánek ve WOS
    TitleA Computational Glimpse at the Leibniz and Frege Hierarchies
    Author(s) Moraschini, Tommaso (UIVT-O) SAI, RID
    Source TitleAnnals of Pure and Applied Logic. - : Elsevier - ISSN 0168-0072
    Roč. 169, č. 1 (2018), s. 1-20
    Number of pages20 s.
    Languageeng - English
    CountryNL - Netherlands
    Keywordsabstract algebraic logic ; Leibniz hierarchy ; Frege hierarchy Leibniz congruence ; decidability ; Diophantine equations ; relation algebras
    Subject RIVBA - General Mathematics
    OECD categoryComputer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
    R&D ProjectsGA13-14654S GA ČR - Czech Science Foundation (CSF)
    Institutional supportUIVT-O - RVO:67985807
    UT WOS000416196700001
    EID SCOPUS85026378538
    DOI10.1016/j.apal.2017.07.003
    AnnotationIn this paper we consider, from a computational point of view, the problem of classifying logics within the Leibniz and Frege hierarchies typical of abstract algebraic logic. The main result states that, for logics presented syntactically, this problem is in general undecidable. More precisely, we show that there is no algorithm that classifies the logic of a finite consistent Hilbert calculus in the Leibniz and in the Frege hierarchies.
    WorkplaceInstitute of Computer Science
    ContactTereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800
    Year of Publishing2019
Number of the records: 1  

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