Doxastic Lukasiewicz Logic with Public Announcement

04/17/2023

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by   Doratossadat Dastgheib, et al.

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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