Paper:
Language: English:

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

Received: April 6, 2006

Accepted: June 23, 2006

Keywords: three-valued logic, modal logic, Prior, Q, Kripke semantics

Journal ref: Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.11, No.1 pp. 105-110, 2007

Abstract

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.

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