Classical and Fuzzy Two-Layered Modal Logics for Uncertainty: Translations and Proof-Theory

0531341 - ÚI 2021 RIV FR eng J - Článek v odborném periodiku
Baldi, P. - Cintula, Petr - Noguera, Carles
Classical and Fuzzy Two-Layered Modal Logics for Uncertainty: Translations and Proof-Theory.
International Journal of Computational Intelligence Systems. Roč. 13, č. 1 (2020), s. 988-1001. ISSN 1875-6891. E-ISSN 1875-6883
Grant CEP: GA ČR GA17-04630S
Institucionální podpora: RVO:67985807 ; RVO:67985556
Klíčová slova: Mathematical fuzzy logic * Logics of uncertainty * Łukasiewicz logic * Probability logics * Two-layered modal logics * Hypersequent calculi
Obor OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8); Applied mathematics (UTIA-B)
Impakt faktor: 1.736, rok: 2020
Způsob publikování: Open access

This paper is a contribution to the study of two distinct kinds of logics for modelling uncertainty. Both approaches use logics with a two-layered modal syntax, but while one employs classical logic on both levels and infinitely-many multimodal operators, the other involves a suitable system of fuzzy logic in the upper layer and only one monadic modality. We take two prominent examples of the former approach, the probability logics Pr_lin and Pr_pol (whose modal operators correspond to all possible linear/polynomial inequalities with integer coefficients), and three prominent logics of the latter approach: Pr^L, Pr^L_triangle and Pr^PL_triangle (given by the Lukasiewicz logic and its expansions by the Baaz-Monteiro projection connective triangle and also by the product conjunction). We describe the relation between the two approaches by giving faithful translations of Pr_lin and Pr_pol into, respectively, Pr^L_triangle and Pr^PL_triangle, and vice versa. We also contribute to the proof theory of two-layered modal logics of uncertainty by introducing a hypersequent calculus for the logic Pr^L. Using this formalism, we obtain a translation of Pr_lin into the logic Pr^L, seen as a logic on hypersequents of relations, and give an alternative proof of the axiomatization of Pr_lin.
Trvalý link: http://hdl.handle.net/11104/0310016