Translating Classical Probability Logics into Modal Fuzzy Logics
- 10.2991/eusflat-19.2019.49How to use a DOI?
- Mathematical Fuzzy Logic Logics of uncertainty Lukasiewicz logic Probability logics Two-layered modal logics
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
- © 2019, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - CONF AU - Paolo Baldi AU - Petr Cintula AU - Carles Noguera PY - 2019/08 DA - 2019/08 TI - Translating Classical Probability Logics into Modal Fuzzy Logics BT - Proceedings of the 11th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2019) PB - Atlantis Press SP - 342 EP - 349 SN - 2589-6644 UR - https://doi.org/10.2991/eusflat-19.2019.49 DO - 10.2991/eusflat-19.2019.49 ID - Baldi2019/08 ER -