0508606 20241106135746.720190919235959.9 85089600355 000558710000049 10.2991/eusflat-19.2019.49 Translating Classical Probability Logics into Modal Fuzzy Logics 8 s. E cav_un_epca*0508605978-94-6252-770-62589-6644Proceedings of the 11th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2019)Atlantis Studies in Uncertainty Modelling342-349AmsterdamAtlantis Press2019ŠtěpničkaM. Mathematical Fuzzy Logic Logics of uncertainty Lukasiewicz logic Probability logics Two-layered modal logics cav_un_auth*0312526 Baldi Paolo UIVT-O Oddělení teoretické informatiky Department of Theoretical Computer Science Department of Theoretical Computer Science AT Ústav informatiky AV ČR, v. v. i. 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. https://download.atlantis-press.com/article/125914819.pdf GA17-04630S GA ČR cav_un_auth*0349495 This paper is a contribution to the study of two distinct kinds of modal logics for modeling uncertainty. Both approaches use logics with a two-layered syntax, but while one employs classical logic on both levels, the other involves a suitable system of fuzzy logic in the upper layer. We take two prominent examples of the former approach, probability logics Pr_lin and Pr_pol, and build explicit faithful translations into, respectively, the two-layered modal fuzzy logics given by Lukasiewicz logic with 4 and its expansion with the product connective. We first prove the faithfulness of both translations using semantics of all four involved logics. Then, we use the axiomatization of Pr_lin and a hypersequent presentation of the two-layered system over Lukasiewicz logic to obtain an alternative syntactical proof. cav_un_auth*0379993 EUSFLAT 2019. Conference of the European Society for Fuzzy Logic and Technology /11./ 20190909 20190913 Praha CZ IN 10000 10200 10201 2020 UTIA-B 10000 10100 10101 4 O 4o 20241106135746.7 UTIA-B BA RVO:67985807 RVO:67985556 http://hdl.handle.net/11104/0299464 S RIV/67985807:_____/19:00508606!RIV20-AV0-67985807 192162512 Doplněn WOS a SCOPUS kód RIV/67985807:_____/19:00508606!RIV20-GA0-67985807 192182641 Doplněn WOS a SCOPUS kód RIV/67985556:_____/19:00508606!RIV20-AV0-67985556 192162349 Doplněn WOS a SCOPUS kód UTIA-B RIV/67985556:_____/19:00508606!RIV20-GA0-67985556 192182558 Doplněn WOS a SCOPUS kód UTIA-B 2 Article Materials Science Ceramics 2019 Soubory v repozitáři: 0508606-aoa.pdf 85089600355 SCOPUS PUBMED 000558710000049 WOS cav_un_epca*0508605 Proceedings of the 11th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2019) 978-94-6252-770-6 2589-6644 342 349 Amsterdam Atlantis Press 2019 Atlantis Studies in Uncertainty Modelling 340 Štěpnička M.