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Completeness and decidability of tense logics closely related to logics above K4

Published online by Cambridge University Press:  12 March 2014

Frank Wolter
Frank Wolter*
Affiliation:
School of Information Science, Jaist, Tatsunokuchi, Ishikawa 923-12, Japan, E-mail: wolter@jaist.ac.jp
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Abstract

Tense logics formulated in the bimodal propositional language are investigated with respect to Kripke-completeness (completeness) and decidability. It is proved that all minimal tense extensions of modal logics of finite width (in the sense of K. Kine) as well as all minimal tense extensions of cofinal subframe logics (in the sense of M. Zakharyaschev) are complete. The decidability of all finitely axiomatizable minimal tense extensions of cofinal subframe logics is shown. A number of variations and extensions of these results are also presented.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 1 , March 1997 , pp. 131 - 158
Copyright
Copyright © Association for Symbolic Logic 1997

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References

REFERENCES

[1] Blok, W., Varieties of interior algebras, Ph.D. thesis, University of Amsterdam, 1976.Google Scholar
[2] Bull, R., An algebraic study on tense logics with linear time, this Journal, vol. 33 (1968), pp. 27–38.Google Scholar
[3] Burgess, J., Basic tense logic, Handbook of philosophical logic (Gabbay, D. and Guenthner, F., editors), vol. 2, Dordrecht, 1984.Google Scholar
[4] Doets, H., Completeness and definability, Ph.D. thesis, University of Amsterdam, 1987.Google Scholar
[5] Fine, K., Logics containing K4, Part I, this Journal, vol. 39 (1974), pp. 229–237.Google Scholar
[6] Fine, K., Logics containing K4, Part II, this Journal, vol. 50 (1985), pp. 619–651.Google Scholar
[7] Gabbay, D., Investigations in modal and tense logic with applications to problems in philosophy and linguistics, Dordrecht, 1976.CrossRefGoogle Scholar
[8] Gabbay, D., Hodkinson, I., and Reynolds, M., Temporal logic, Oxford, 1994.Google Scholar
[9] Goldblatt, R., Metamathematics of modal logic, Reports on Mathematical Logic, vol. 6 (1976), pp. 41–77.Google Scholar
[10] Goldblatt, R., Logics of time and computation, CSLI Lecture Notes, Chicago, 1987.Google Scholar
[11] Goranko, V. and Passy, S., Using the universal modality, Journal of Logic and Computation, vol. 2 (1992), pp. 5–30.CrossRefGoogle Scholar
[12] Jónsson, B., A survey of Boolean algebras with operators, manuscript.Google Scholar
[13] Kracht, M. and Wolter, F., Properties of independently axiomatizable bimodal logics, this Journal, vol. 56 (1991), pp. 1469–1485.Google Scholar
[14] Kracht, M. and Wolter, F., Normal modal logics can simulate all others, manuscript, 1994.Google Scholar
[15] Rybakov, V., A modal analog for Glivenko's theorem and its applications, Notre Dame Journal of Formal Logic, vol. 33 (1992), pp. 244–248.CrossRefGoogle Scholar
[16] Segerberg, K., Modal logics with linear alternative relations, Theoria, vol. 36 (1970), pp. 301–322.CrossRefGoogle Scholar
[17] Spaan, E., Complexity of modal logics, Ph.D. thesis, University of Amsterdam, 1993.Google Scholar
[18] van Benthem, J., The logic of time, Dordrecht, 1983.CrossRefGoogle Scholar
[19] Wolter, F., Lattices of modal logics, Ph.D. thesis, Frei Universität Berlin, 1993.Google Scholar
[20] Wolter, F., Solution to a problem of Goranko and Passy, Journal of Logic and Computation, vol. 4 (1994), no. 1, pp. 21–22.CrossRefGoogle Scholar
[21] Wolter, F., Decidability of tense logics, extended abstract, Bulletin of the Section Logic, vol. 24 (1995), pp. 46–51.Google Scholar
[22] Wolter, F., The finite model property in tense logic, this Journal, vol. 60 (1995), pp. 757–774.Google Scholar
[23] Wolter, F., Properties of tense logics, to appear in Mathematical Logic Quarterly, 1995.Google Scholar
[24] Wolter, F., A counterexample in tense logic, to appear in Notre Dame Journal of Formal Logic, 1996.CrossRefGoogle Scholar
[25] Wolter, F., Tense logics without tense operators, Mathematical Logic Quarterly, vol. 42 (1996), pp. 145–171.CrossRefGoogle Scholar
[26] Zakharyaschev, M., Canonical formulas for K4, Part I, this Journal, vol. 57 (1992), pp. 377–402.Google Scholar
[27] Zakharyaschev, M., Canonical formulas for K4, Part II, ITLI Prepublication Series X-93-06, 1993.Google Scholar