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Prior proposed a three-valued modal logic  Q  as a “correct” modal logic from his philosophical motivations. Unfortunately, Prior’s  Q  and many-valued modal logic have been neglected in the tradition of many-valued and modal logic. In this paper, we introduce a version of three-valued Kripke semantics for  Q , which aims to establish Prior’s ideas based on possible worlds. We investigate formal properties of  Q  and prove the completeness theorem of  Q . We also compare our approach with others and suggest possible applications.

Prior’s Three-Valued Modal Logic <I>Q</I> and its Possible Applications