Translating Classical Probability Logics into Modal Fuzzy Logics

DOI

10.2991/eusflat-19.2019.49How to use a DOI?

Keywords

Mathematical Fuzzy Logic Logics of uncertainty Lukasiewicz logic Probability logics Two-layered modal logics

Abstract

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

Copyright

© 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/).

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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  -