Translating Classical Probability Logics into Modal Fuzzy Logics

0508606 - ÚI 2020 RIV NL eng C - Konferenční příspěvek (zahraniční konf.)
Baldi, Paolo - Cintula, Petr - Noguera, Carles
Translating Classical Probability Logics into Modal Fuzzy Logics.
Proceedings of the 11th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2019). Amsterdam: Atlantis Press, 2019 - (Štěpnička, M.), s. 342-349. Atlantis Studies in Uncertainty Modelling. ISBN 978-94-6252-770-6. ISSN 2589-6644.
[EUSFLAT 2019. Conference of the European Society for Fuzzy Logic and Technology /11./. Praha (CZ), 09.09.2019-13.09.2019]
Grant CEP: GA ČR GA17-04630S
Institucionální podpora: RVO:67985807 ; RVO:67985556
Klíčová slova: Mathematical Fuzzy Logic * Logics of uncertainty * Lukasiewicz logic * Probability logics * Two-layered modal logics
Obor OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8); Pure mathematics (UTIA-B)
https://download.atlantis-press.com/article/125914819.pdf

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.
Trvalý link: http://hdl.handle.net/11104/0299464