JACIII Vol.11 No.1 pp. 105-110
doi: 10.20965/jaciii.2007.p0105


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

April 6, 2006
June 23, 2006
January 20, 2007
three-valued logic, modal logic, Prior, 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.

Cite this article as:
Seiki Akama and Yasunori Nagata, “Prior’s Three-Valued Modal Logic Q and its Possible Applications,” J. Adv. Comput. Intell. Intell. Inform., Vol.11, No.1, pp. 105-110, 2007.
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Last updated on Mar. 05, 2021