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A Computational Glimpse at the Leibniz and Frege Hierarchies
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SYSNO ASEP 0477047 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A Computational Glimpse at the Leibniz and Frege Hierarchies Author(s) Moraschini, Tommaso (UIVT-O) SAI, RID Source Title Annals of Pure and Applied Logic. - : Elsevier - ISSN 0168-0072
Roč. 169, č. 1 (2018), s. 1-20Number of pages 20 s. Language eng - English Country NL - Netherlands Keywords abstract algebraic logic ; Leibniz hierarchy ; Frege hierarchy Leibniz congruence ; decidability ; Diophantine equations ; relation algebras Subject RIV BA - General Mathematics OECD category Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) R&D Projects GA13-14654S GA ČR - Czech Science Foundation (CSF) Institutional support UIVT-O - RVO:67985807 UT WOS 000416196700001 EID SCOPUS 85026378538 DOI 10.1016/j.apal.2017.07.003 Annotation 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. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2019
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