Abstract
A certain type of inference rules in (multi-) modal logics, generalizing Gabbay's Irreflexivity rule, is introduced and some general completeness results about modal logics axiomatized with such rules are proved.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
van Benthem, J., Modal Logic and Classical Logic, Bibliopolis, Napoli, 1985.
van Benthem, J., ‘Correspondence theory’, in: D. Gabbay, F. Guenthner (eds.), Handbook on Philosophical Logic, vol. II, Reidel, Dordrecht, 1984, 167–247.
Fine, K., ‘Some connections between modal and elementary logic’, in: S. Kanger (ed.), Proc. Third Scandinavian Logic Symposium, North-Holland, Amsterdam, 1975, 15–31.
Gabbay, D., ‘An Irreflexivity lemma with applications to axiomatizations of conditions on tense frames’, in: U. Monnich (ed.), Aspects of Philosophical Logic, Reidel, Dordrecht, 1981, 67–89.
Gabbay, D., & I. Hodkinson, ‘An axiomatization of the temporal logic with Since and Until over the real numbers’, J. of Logic and Computation 1, 1990, 229–259.
Gargov, G., & V. Goranko, ‘Modal logic with names’, J. of Philosophical Logic 22(6), 1993, 607–636.
Goldblatt, R., ‘Metamathematics of modal logic’, Reports on Mathematical Logic 6, 41–78 (Part I); 7, 21–52 (Part II).
Goldblatt, R. I., Axiomatizing the Logic of Computer Programming, Springer LNCS 130, 1982.
Goranko, V., ‘Applications of quasi-structural rules to axiomatizations in modal logic’, in: Abstracts of the 9th Intern. Congress of Logic, Methodology and Philosophy of Science, Uppsala, 1991, Vol. 1: Logic, p. 119.
Goranko, V., ‘A note on derivation rules in modal logic’, Bull. of the Sect. of Logic, Univ. of Lódź, 24(2), 1995, 98–104.
Goranko, V., ‘Hierarchies of modal and temporal logics with reference pointers’, J. of Logic, Language and Information, 5(1), 1996, 1–24.
Hollenberg, M., ‘Negative definability in modal logic’, manuscript, Department of Philosophy, Utrecht University, 1994, to appear in Studia Logica.
Hughes, G., & M. Cresswell, A New Introduction to Modal Logic, Routledge, London and New York, 1996.
Kracht, M., Internal Definability and Completeness in Modal Logic, Ph. D. Thesis, Free University, Berlin, 1990.
Kracht, M., ‘How completeness and correspondence theory got married’, in: M. de Rijke (ed.), Colloquium on Modal Logic, Dutch Network for Language, Logic and Information, 1991, 161–186.
Passy, S., & T. Tinchev, ‘PDL with data constants’, Information Processing Letters 20, 1985, 35–41.
de Rijke, M., ‘The modal logic of inequality’, J. of Symbolic Logic 57(2), 1992, 566–584.
Sambin, J., & V. Vaccaro, ‘Topology and duality in modal logic’, Annals of Pure and Applied Logic 44, 1988, 173–242.
Thomason, S. K., ‘Semantic analysis of tense logic’, J. of Symbolic Logic 37, 1972, 150–158.
Vakarelov, D., ‘Modal rules for intersection’, Bull. of Symbolic Logic 1(2), 1995, 264–265.
Venema, Y., ‘Expressiveness and completeness of an interval tense logic’, Notre Dame J. of Formal Logic 31, 1990, 529–547.
Venema, Y., ‘A modal logic for chopping intervals’, J. of Logic and Computation 1, 1991, 453–476.
Venema, Y., Many-dimensional Modal Logic, Ph. D. Dissertation, Univ. of Amsterdam, 1991.
Venema, Y., ‘Derivation rules as anti-axioms in modal logic’, J. of Symbolic Logic 58(3), 1993, 1003–1034.
Zanardo, A., ‘A complete deductive system for Since-Until branching-time logic’, J. of Philosophical Logic 20, 1991, 131–148.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Goranko, V. Axiomatizations with Context Rules of Inference in Modal Logic. Studia Logica 61, 179–197 (1998). https://doi.org/10.1023/A:1005021313747
Issue Date:
DOI: https://doi.org/10.1023/A:1005021313747