Doxastic Extensions of Łukasiewicz Logic

We propose two classes of doxastic extensions of fuzzy \L ukasiewicz logic that are sound and complete with respect to some appropriate classes of Kripke-based models in which both atomic propositions and accessibility relations are fuzzy. One class of these extensions is equipped with pseudo-classical belief that has properties similar to the classical belief, and the other class is based on a new notion of belief that we call it \textit{skeptical} belief. We model a fuzzy version of the muddy children problem using pseudo-classical belief and a CPA-security experiment using skeptical belief, then by showing that the pseudo-classical belief is not appropriate for modeling the belief of an adversary in a CPA-experiment we justify proposing the notion of skeptical belief. Furthermore, we prove the soundness and completeness theorems for some of the proposed doxastic extensions.