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The modal logic of inequality

Published online by Cambridge University Press:  12 March 2014

Maarten de Rijke
Maarten de Rijke*
Affiliation:
Department of Mathematics And Computer Science, University of Amsterdam, 1018 TV Amsterdam, The, Netherlands, E-mail: maartenr@fwi.uva.nl
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Abstract

We consider some modal languages with a modal operator D whose semantics is based on the relation of inequality. Basic logical properties such as definability, expressive power and completeness are studied. Also, some connections with a number of other recent proposals to extend the standard modal language are pointed at.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 2 , June 1992 , pp. 566 - 584
Copyright
Copyright © Association for Symbolic Logic 1992

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References

REFERENCES

[1]Ackermann, W., Solvable cases of the decision problem, North-Holland, Amsterdam, 1954.Google Scholar
[2]van Benthem, J. F. A. K., Syntactical aspects of modal incompleteness theorems, Theoria, vol. 45 (1979), pp. 63–77.CrossRefGoogle Scholar
[3]van Benthem, J. F. A. K., The logic of time, Reidel, Dordrecht, 1983.CrossRefGoogle Scholar
[4]van Benthem, J. F. A. K., Modal logic and classical logic, Bibliopolis, Naples, 1985.Google Scholar
[5]van Benthem, J. F. A. K., Notes on modal definability, Notre Dame Journal of Formal Logic, vol. 30 (1989), pp. 20–35.Google Scholar
[6]Blackburn, P., Nominal tense logic and other sorted iniensional frameworks, Dissertation, University of Edinburgh, Edinburgh, 1990.Google Scholar
[7]Chang, C. C. and Keisler, H. J., Model theory, North-Holland, Amsterdam, 1973.Google Scholar
[8]Gabbay, D. M., An irreflexivity lemma with applications to axiomatizations of conditions on linear frames, Aspects of philosophical logic (Mönnich, U., editor), Reidel, Dordrecht, 1981, pp. 67–89.CrossRefGoogle Scholar
[9]Gargov, G. and Goranko, V., Modal logic with names, I, Preprint, Linguistic Modelling Laboratory, CICT, Bulgarian Academy of Science, and Sector of Logic, Faculty of Mathematics and Computer Science, Sofia University, Sofia, 1989.Google Scholar
[10]Gargov, G., Passy, S. and Tinchev, T., Modal environment for Boolean speculations, Mathematical logic and its applications (Skordev, D., editor), Plenum Press, New York, 1987, pp. 253–263.CrossRefGoogle Scholar
[11]Goldblatt, R. and Thomason, S. K., Axiomatic classes in propositional modal logic, Algebra and logic (Crossley, J., editor), Lecture Notes in Mathematics, vol. 450, Springer-Verlag, Berlin, 1974, pp. 163–173.CrossRefGoogle Scholar
[12]Goranko, V., Modal definability in enriched languages, Notre Dame Journal of Formal Logic, vol. 31 (1990), pp. 81–105.Google Scholar
[13]Goranko, V. and Passy, S., Using the universal modality: gains and questions, Preprint, Sector of Logic, Faculty of Mathematics, Sofia University, Sofia, 1990.Google Scholar
[14]Kapron, B. M., Modal sequents and definability, this Journal, vol. 52 (1987), pp. 756–762.Google Scholar
[15]Koymans, R., Specifying message passing and time-critical systems with temporal logic, Dissertation, Eindhoven University of Technology, Eindhoven, 1989.CrossRefGoogle Scholar
[16]Rodenburg, P. H., Intuitionistic correspondence theory, Dissertation, University of Amsterdam, Amsterdam, 1986.Google Scholar
[17]Sahlqvist, H., Completeness and correspondence in the first and second order semantics for modal logic, Proceedings of the Third Scandinavian Logic Symposium (Uppsala, 1973; Kanger, S., editor), North-Holland, Amsterdam, 1975, pp. 110–143.CrossRefGoogle Scholar
[18]Segerberg, K., Modal logics with linear alternative relations, Theoria, vol. 36 (1970), pp. 301–322.CrossRefGoogle Scholar
[19]de Smit, B. and van Emde Boas, P., The complexity of the modal difference operator in propositional logic, Unpublished note, University of Amsterdam, Amsterdam, 1990.Google Scholar
[20]Thomason, S. K., Semantic analysis of tense logics, this Journal, vol. 37 (1972), pp. 150–158.Google Scholar
[21]Venema, Y., The Sahlqvist theorem and modal derivation rules, Manuscript, 02 1991.Google Scholar
[22]Westerståhl, D., Quantifiers in formal and natural languages, Handbook of philosophical logic (Gabbay, D. and Guenthner, F., editors), Vol. IV, Reidel, Dordrecht, 1989, pp. 1–131.Google Scholar