Some Doxastic Łukasiewicz Logic
This work provides a formal logic framework for reasoning about belief under uncertainty, which is incremental as it adapts classical epistemic logic axioms to a fuzzy logic setting.
The authors tackled the problem of developing a doxastic logic based on Łukasiewicz logic by proposing BŁ, which is sound and complete with respect to Kripke-based models with infinitely valued atomic propositions and accessibility relations in the standard MV-algebra [0,1], and they extended it with axioms D, 4, and T, establishing completeness for these extensions.
We propose a doxastic Łukasiewicz logic \textbf{BŁ} 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{BŁ} 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.