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Bibliografie

Journal Article

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

Baldi P., Cintula Petr, Noguera Carles

: International Journal of Computational Intelligence Systems vol.13, 1 (2020), p. 988-1001

: GA17-04630S, GA ČR

: Mathematical fuzzy logic, Logics of uncertainty, Łukasiewicz logic, Probability logics, Two-layered modal logics, Hypersequent calculi

: 10.2991/ijcis.d.200703.001

: http://hdl.handle.net/11104/0310016

(eng): 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.

: IN

: 10201

07.01.2019 - 08:39