Abstract
Predicate modal logics based on Kwith non-compact extra axioms are discussed and a sufficient condition for the model existence theorem is presented. We deal with various axioms in a general way by an algebraic method, instead of discussing concrete non-compact axioms one by one.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chagrov, A.V., and M.V. Zakharyaschev, Modal Logic, Oxford University Press, 1997.
Dickmann, M. A., Large Infinitary Languages, North-Holland, 1975.
Dickmann, M.A., 'Larger infinitary languages', in J. Barwise and S. Feferman, editors, Model-Theoretic Logic, pages 317-364, Springer-Verlag, 1985.
Fagin, R., J. Y. Halpern, Y. Moses, and M. Y. Vardi, Reasoning About Knowledge, The MIT Press, 1995.
Goldblatt, R., Mathematics of Modality, volume 43 of CSLI Lecture Notes, CSLI Publications, 1993.
GÓrnemann, S., 'A logic stronger than intuitionism', Journal of Symbolic Logic 36:249-261, 1971.
Halpern, J.H., and Y. Moses, 'A guide to completeness and complexity for modal logics of knowledge and beliefs', Artificial Intelligence 54:319-379, 1992.
JÓnsson, B., and A. Tarski, 'Boolean algebras with operators I', American Journal of Mathematics 73:891-931, 1951.
JÓnsson, B., and A. Tarski, 'Boolean algebras with operators II', American Journal of Mathematics 74:127-162, 1952.
Kaneko, M., and T. Nagashima, 'Game logic and its applications I', Studia Logica 57:325-354, 1996.
Kaneko, M., and T. Nagashima, 'Game logic and its applications II', Studia Logica 58:273-303, 1997.
Karp, C., Languages with Expressions of Infinite Length, North-Holland, 1964.
LÓpez-Escobar, E.G.K., 'An interpolation theorem for denumerably long formulas', Fundamenta Mathematicæ 57:253-272, 1965.
Nadel, M.E., 'Infinitary intuitionistic logic from a classical point of view', Annals of Mathematical Logic 14:159-191, 1978.
Rasiowa, H., and R. Sikorski, 'A proof of the completeness theorem of Gödel', Fundamenta Mathematicæ 37:193-200, 1950.
Rasiowa, H., and R. Sikorski, The Mathematics of Metamathematics, PWN-Polish Scientific Publishers, 1963.
Rauszer, C., and B. Sabalski, 'Remarks on distributive pseudo-Boolean algebra', Bulletin De L'academie Polonaise des Sciences Serie des sciences math., astr., et phys. 23 (2), 1975.
Segerberg, K., 'A model existence theorem in infinitary propositional modal logic', Journal of Philosophical Logic 23:337-367, 1994.
Tanaka, Y., Representations of Algebras and Kripke Completeness of Infinitary and Predicate Logics, PhD thesis, Japan Advanced Institute of Science and Technology, 1999.
Tanaka, Y., 'Kripke completeness of infinitary predicate multi-modal logics', to appear in Notre Dame Journal of Formal Logic (accepted in 2000).
Tanaka Y., and H. Oon, 'The Rasiowa-Sikorski lemma and Kripke completeness of predicate and infinitary modal logics', in M. Zakharyaschev, K. Segerberg, M. de Rijke (eds), Advances in Modal Logic, volume 2, pages 419-437, CSLI Publication, 2000.
Wolter, F., 'First order common knowledge logics', Studia Logica 65 (2000), 249-271.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tanaka, Y. Model Existence in Non-Compact Modal Logic. Studia Logica 67, 61–73 (2001). https://doi.org/10.1023/A:1010573427578
Issue Date:
DOI: https://doi.org/10.1023/A:1010573427578