Some Doxastic \L ukasiewicz Logic

TL;DR

This paper introduces a new doxastic ukasziewicz logic BL that is sound and complete with respect to Kripke models with infinitely valued propositions and accessibility, extending classical epistemic logic axioms.

Contribution

It develops a novel doxastic ukasziewicz logic BL and its extensions, establishing soundness and completeness for models with infinitely valued propositions.

Findings

BL is sound and complete for Kripke models with ukasziewicz valuations.

Extensions of BL correspond to classical epistemic axioms D, 4, T.

Completeness results are established for these extended logics.

Abstract

We propose a doxastic \L ukasiewicz logic \textbf{B\L} 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 \textbf{B\L} corresponding to axioms \textbf{D}, \textbf{4}, and \textbf{T} of classical epistemic logic. Furthermore, completeness of these extensions are established corresponding to the appropriate classes of models.