0477047 - ÚI 2019 RIV NL eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR GA13-14654S
Institucionální podpora: RVO:67985807
Klíčová slova: abstract algebraic logic * Leibniz hierarchy * Frege hierarchy Leibniz congruence * decidability * Diophantine equations * relation algebras
Obor OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impakt faktor: 0.829, rok: 2018 ; AIS: 0.747, rok: 2018
DOI: https://doi.org/10.1016/j.apal.2017.07.003

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.
Trvalý link: http://hdl.handle.net/11104/0273441