Doxastic Lukasiewicz Logic with Public Announcement

Abstract

In this paper, we propose a doxastic extension $B{L}^{+}$ of Lukasiewicz logic which is sound and complete relative to the introduced corresponding semantics. Also, we equip our doxastic Lukasiewicz logic $B{L}^{+}$ with public announcement and propose the logic $DL$. As an application, we model a fuzzy version of muddy children puzzle with public announcement using $DL$. Finally, we define a translation between $DL$ and $B{L}^{+}$, and prove the soundness and completeness theorems for D L