0531341 20240103224301.020200731235959.9 85089596847 000565532900046 10.2991/ijcis.d.200703.001 14 s. cav_un_epca*03444981875-6891131 (2020)988-1001Springer Mathematical fuzzy logic Logics of uncertainty Łukasiewicz logic Probability logics Two-layered modal logics Hypersequent calculi cav_un_auth*0378830 Baldi P. IT K cav_un_auth*0100737 Cintula Petr UIVT-O Oddělení teoretické informatiky Department of Theoretical Computer Science Department of Theoretical Computer Science Ústav informatiky AV ČR, v. v. i. cav_un_auth*0293476 Noguera Carles UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. http://hdl.handle.net/11104/0310016 GA17-04630S GA ČR cav_un_auth*0349495 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 10000 10200 10201 2021 UTIA-B 10000 10100 10102 4 O 4o 20231122145035.8 UTIA-B BA RVO:67985807 RVO:67985556 http://hdl.handle.net/11104/0310016 S 2 Article Computer Science Artificial Intelligence|Computer Science Interdisciplinary Applications A COMPUTERSCIENCE.ARTIFICIALINTELLIGENCE|COMPUTERSCIENCE.INTERDISCIPLINARYAPPLICATIONS 2.181 0.286 5.1 0.00197 0.375 1771 59 0.385 38.22 2.12 765 Q2 1.589 140 Q3 11.698 25.2 Q4 Q3 0.46 Q3 28.417 2020 Soubory v repozitáři: 0531341-aoa.pdf 85089596847 SCOPUS PUBMED 000565532900046 WOS cav_un_epca*0344498 International Journal of Computational Intelligence Systems 1875-6891 1875-6883 Roč. 13 č. 1 2020 988 1001 Springer