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Doxastic Lukasiewicz Logic with Public Announcement (2304.08077v1)
Published 17 Apr 2023 in cs.LO and math.LO
Abstract: In this paper, we propose a doxastic extension $BL+$ of Lukasiewicz logic which is sound and complete relative to the introduced corresponding semantics. Also, we equip our doxastic Lukasiewicz logic $BL+$ 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 $BL+$, and prove the soundness and completeness theorems for D L