Paper:

# Prior’s Three-Valued Modal Logic *Q* and its Possible Applications

## Seiki Akama^{*} and Yasunori Nagata^{**}

^{*}Dept. of Information Science, Teikyo Heisei University, 2289 Uruido, Ichihara, Chiba 290-0193, Japan

^{**}Dept. of Elect’l & Electronics Eng., University of the Ryukyus, 1 Senbaru, Nishihara, Okinawa 903-0213, Japan

*Ǫ*, Kripke semantics

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.

*Q*and its Possible Applications,”

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.11, No.1, pp. 105-110, 2007.

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