Prior’s Three-Valued Modal Logic <I>Q</I> and its Possible Applications

Seiki Akama; Yasunori Nagata

doi:10.20965/jaciii.2007.p0105

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JACIII Vol.11 No.1 pp. 105-110

doi: 10.20965/jaciii.2007.p0105

(2007)

Paper:

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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

Published:

January 20, 2007

Keywords:

three-valued logic, modal logic, Prior, Ǫ, Kripke semantics

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.

Cite this article as:

S. Akama and Y. 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.

Data files:

References

[1] S. Akama, “A proof method for the six-valued logic for incomplete information,” Proc. of ISMVL’97, pp. 223-226, 1997.
[2] S. Akama and Y. Nagata, “On Prior’s three-valued modal logic,” Proc. of ISMVL’2005, pp. 14-19, 2005.
[3] R. A. Bull, “An axiomatization of Prior’s modal calculus Q,” Notre Dame Journal of Formal Logic, 5, pp. 211-214, 1964.
[4] F. Correia, “Adequacy results from some Priorean modal logic,” Notre Dame Journal of Formal Logic, 40, pp. 236-249, 1999.
[5] M. Fitting, “Many-valued modal logics,” Fundamenta Informatica, 15, pp. 235-254, 1992.
[6] O. Garcia and M. Moussavi, “A six-valued logic for representing incomplete information,” Proc. of ISMVL’90, pp. 110-114, 1990.
[7] G. Hughes and M. J. Cresswell, “An Introduction to Modal Logic,” Methuen, London, 1968.
[8] A. N. Prior, “Time and Modality,” Clarendon Press, Oxford, 1957.
[9] A. N. Prior, “Past, Present and Future,” Clarendon Press, Oxford, 1967.
[10] A. N. Prior and K. Fine, “Worlds, Times and Selves,” Duckworth, London, 1977.
[11] K. Segerberg, “Some modal logics based on a three-valued logic,” Theoria, 33, pp. 53-71, 1967.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] S. Akama, “A proof method for the six-valued logic for incomplete information,” Proc. of ISMVL’97, pp. 223-226, 1997.

[2] [2] S. Akama and Y. Nagata, “On Prior’s three-valued modal logic,” Proc. of ISMVL’2005, pp. 14-19, 2005.

[3] [3] R. A. Bull, “An axiomatization of Prior’s modal calculus Q,” Notre Dame Journal of Formal Logic, 5, pp. 211-214, 1964.

[4] [4] F. Correia, “Adequacy results from some Priorean modal logic,” Notre Dame Journal of Formal Logic, 40, pp. 236-249, 1999.

[5] [5] M. Fitting, “Many-valued modal logics,” Fundamenta Informatica, 15, pp. 235-254, 1992.

[6] [6] O. Garcia and M. Moussavi, “A six-valued logic for representing incomplete information,” Proc. of ISMVL’90, pp. 110-114, 1990.

[7] [7] G. Hughes and M. J. Cresswell, “An Introduction to Modal Logic,” Methuen, London, 1968.

[8] [8] A. N. Prior, “Time and Modality,” Clarendon Press, Oxford, 1957.

[9] [9] A. N. Prior, “Past, Present and Future,” Clarendon Press, Oxford, 1967.

[10] [10] A. N. Prior and K. Fine, “Worlds, Times and Selves,” Duckworth, London, 1977.

[11] [11] K. Segerberg, “Some modal logics based on a three-valued logic,” Theoria, 33, pp. 53-71, 1967.

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

Seiki Akama* and Yasunori Nagata**

Seiki Akama^* and Yasunori Nagata^**