Some Doxastic L ukasiewicz Logic

We propose a doxastic L ukasiewicz logic BL that is sound and complete with respect to the class of Kripke-based models in which atomic propositions and accessibility relations are both infinitely valued in the standard MV-algebra [0,1]. We also introduce some extensions of BL corresponding to axioms D, 4, and T of classical epistemic logic. Furthermore, completeness of these extensions are established corresponding to the appropriate classes of models.