@inproceedings { 5666, title = {A fuzzy probability logic for compound conditionals}, booktitle = {XX Spanish Congress on Fuzzy Logic and Technologies (ESTYLF 20/21), Actas CAEPIA 20/21}, pages = {256-261}, year = {2021}, month = {22/09/2021}, abstract = {In this paper we propose a fuzzy modal logic for conditional probability that allows to represent and reason about the probability of not only basic conditional expressions of the form ``$\varphi$ given $\psi$'', written $(\varphi\mid \psi)$, but also compound conditional sentences such as ``$\varphi$ given $\psi$ \{\em and\} $\gamma$ given $\chi$'', written $(\varphi\mid \psi)\wedge(\gamma\mid \chi)$, and more in general, any Boolean combination of basic ones. In order to formalize compound conditional formulas we will adopt the recently defined \{\em Logic for Boolean Conditionals\} (LBC) and hence formalize conditional probability as a simple (unconditional) probability of conditional sentences. In addition to such basic fuzzy modal logic for the probability of compound conditionals, we will also present some extensions and prove that each of them is sound and complete w.r.t. to a suitable class of probabilistic models. Furthermore, we will prove how to recover the usual interpretation of conditional probability, showing that, under minimal requirements, in these logics the probability of a basic conditional $(\varphi\mid \psi)$ can be safely taken as the conditional probability of $\varphi$ given $\psi$, i.e.\ as the ratio $P(\varphi\wedge\psi)/P(\psi)$. }, author = {Tommaso Flaminio and Llu{\'\i}s Godo} }