Paper:
Language: English:
Prior’s Three-Valued Modal Logic Ǫ 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, Ǫ, 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 Ǫ as a “correct” modal logic from his philosophical motivations. Unfortunately, Prior’s Ǫ 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 Ǫ, which aims to establish Prior’s ideas based on possible worlds. We investigate formal properties of Ǫ and prove the completeness theorem of Ǫ. We also compare our approach with others and suggest possible applications.
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Reference
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