Doxastic Extensions of Łukasiewicz Logic
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We propose two new doxastic extensions of fuzzy Łukasiewicz logic in which their semantics are Kripke-based with both fuzzy atomic propositions and fuzzy accessibility relations. A class of these extensions is equipped with uninformed belief operator, and the other class is based on a new notion of skeptical belief. We model a fuzzy version of muddy children problem and a CPA-security experiment using uniformed belief and skeptical belief, respectively. Moreover, we prove soundness and completeness for both of these belief extensions.
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