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A Computational Glimpse at the Leibniz and Frege Hierarchies

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    0477047 - ÚI 2019 RIV NL eng J - Journal Article
    Moraschini, Tommaso
    A Computational Glimpse at the Leibniz and Frege Hierarchies.
    Annals of Pure and Applied Logic. Roč. 169, č. 1 (2018), s. 1-20. ISSN 0168-0072. E-ISSN 1873-2461
    R&D Projects: GA ČR GA13-14654S
    Institutional support: RVO:67985807
    Keywords : abstract algebraic logic * Leibniz hierarchy * Frege hierarchy Leibniz congruence * decidability * Diophantine equations * relation algebras
    OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
    Impact factor: 0.829, year: 2018

    In 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.
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