On Prior´s three-valued modal logic Q

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.