Abstract
We prove that every normal extension of the bi-modal system S52 is finitely axiomatizable and that every proper normal extension has NP-complete satisfiability problem.
Similar content being viewed by others
References
Bezhanishvili, N., ‘Varieties of two-dimensional cylindric algebras. Part I: Diagonal-free case’, Algebra Universalis 48 (2002), 11–42.
Bezhanishvili, N., ‘Varieties of two-dimensional cylindric algebras. Part II’, Algebra Universalis 51 (2004) 177–206.
Bezhanishvili, N., and M. Marx, ‘All proper normal extensions of S5-square have the polynomial size model property’, Studia Logica 73 (2003), 367–382.
Blackburn, P., M. de Rijke, and Y. Venema, Modal Logic, Cambridge University Press, 2001.
Gabbay, D., A. Kurucz, F. Wolter, and M. Zakharyaschev, Many-Dimensional Modal Logics: Theory and Applications, Studies in Logic, vol. 148, North-Holland, 2003.
Grädel, E., P. Kolaitis, and M. Vardi, ‘On the decision problem for two-variable first order logic’, Bulletin of Symbolic Logic 3 (1997), 53–69.
Higman, G., ‘Ordering by divisibility in abstract algebras’, Proc. London Math. Soc. 2 (1952), 326–336.
Kracht, M., ‘Prefinitely axiomatizable modal and intermediate logics’, Mathematical Logic Quarterly 39 (1993), 301–322.
Laver, R., Better-quasi-orderings and a class of trees, in: Studies in Foundations and Combinatorics, Gian-Carlo Rota, ed., vol. 1 of Advances in Mathematics Supplementary Studies, Academic Press, 1978, pp. 31–48.
Rado, R., ‘Partial well ordering of sets of vectors’, Mathematica 1 (1954), 89–95.
Segerberg, K., ‘Two-dimensional modal logic’, Journal of Philosophical logic 2 (1973), 77–96.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bezhanishvili, N., Hodkinson, I. All Normal Extensions of S5-squared Are Finitely Axiomatizable. Stud Logica 78, 443–457 (2004). https://doi.org/10.1007/s11225-004-6044-z
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11225-004-6044-z