Skip to main content Accessibility help

Hereditarily structurally complete modal logics

  • V. V. Rybakov (a1)


We consider structural completeness in modal logics. The main result is the necessary and sufficient condition for modal logics over K4 to be hereditarily structurally complete: a modal logic λ is hereditarily structurally complete iff λ is not included in any logic from the list of twenty special tabular logics. Hence there are exactly twenty maximal structurally incomplete modal logics above K4 and they are all tabular.



Hide All
[1]Bellissima, F., Finitely generated free Heyting algebras, this Journal, vol. 51 (1986), pp. 152165.
[2]Blok, W. J., Pretabular varieties of modal algebras, Studia Logica, vol. 39 (1980), pp. 101124.
[3]Citkin, A. I., On admissible rules of intuitionistic propositional logic, Mathematics USSR Sbornik, vol.31 (1977), pp. 279288.
[4]Citkin, A. I., On structurally complete superintuitionistic logics, Soviet Mathematics Doklady, vol. 19 (1978), pp. 816819.
[5]de Jong, D. H. and Troelstra, A. S., On the connection of partially ordered sets with some pseudo-Boolean algebras, Indagationes Mathematicae, vol. 28 (1966), pp. 317329.
[6]Dziobiak, W., Structural completeness of modal logics containing k4, Manuscript, 1989.
[7]Fagin, R., Halpern, J. Y., and Vardi, M. Y., What is an inference rule, this Journal, vol. 57 (1992), pp. 10181045.
[8]Fine, K., Logics containing S4.3, Zeitschrift für Mathematische Logic und Grundlagen der Mathematik, vol. 17 (1971), pp. 371376.
[9]Fine, K., Logic containing K4, part I, this Journal, vol. 39 (1974), pp. 229237.
[10]Gabbay, D. M., Investigations in modal and tense logics with applications to problems in philosophy and linguistics, D. Reidel Publishing Company, Dordrecht-Holland/Boston-USA, 1976.
[11]Goldblatt, R. I., Metamathematics of modal logics (part 1), Reports on Mathematical Logic, vol. 6 (1976), pp. 4178.
[12]Goldblatt, R. I., Metamathematics of modal logics (part 2), Reports on Mathematical Logic, vol. 7 (1976), pp. 2152.
[13]Kracht, M., Prefinitely axiomatizable modal and intermediate logics, Preprint No. 73, Department of Philosophy, University of Utrecht, The Netherlands, 1992.
[14]Kracht, M., Splittings and the finite model property, this Journal, vol. 58 (1993), pp. 139154.
[15]Makinson, D., A characterization of structural completeness of a structural consequence operation, Reports on Mathematical Logic, vol. 6 (1976), pp. 99102.
[16]Maksimova, L. L., Pretabular super-intuitionistic logics, Algebra and Logic, vol. 11 (1972), pp. 558570, In Russian, English Translation in Algebra and Logic, Translations of the AMS.
[17]Maksimova, L. L. and Rybakov, V. V., A lattice of normal modal logics, Algebra and Logic, vol. 13 (1974), pp. 105122.
[18]Mints, G. E., Derivability of admissible rules, Journal of Soviet Mathematics, vol. 6 (1976), pp. 417421.
[19]Prucnal, T., Structural completeness of Medvedev's propositional calculus, Reports on Mathematical Logic, vol. 6 (1976), pp. 103105.
[20]Rautenberg, W., Der verband der normal verzweigten modallogiken, Mathematische Zeitschrift, vol. 156 (1977), pp. 123140.
[21]Rautenberg, W., Klassische und nichtklassische aussagenlogik, Braunschweig/Wiesbaden, 1979.
[22]Rybakov, V. V., A criterion for admissibility of rules in the modal system S4 and the intuitionistic logic, Algebra and Logic, vol. 23 (1984), pp. 369384, (English translation).
[23]Rybakov, V. V., Problems of substitution and admissibility in the modal system Grz and intuitionistic calculus, Annals of Pure and Applied Logic, vol. 50 (1990), pp. 71106.
[24]Rybakov, V. V., Rules of inference with parameters for intuitionistic logic, this Journal, vol. 57 (1992), pp. 912923.
[25]Segerberg, K., An essay in classical modal logic, vol. 1–3, Filosofiska Studier, Uppsala, 1971.
[26]van Benthem, J. F. A. K., Modal and classical logic, Bibliopolis, 1983.

Related content

Powered by UNSILO

Hereditarily structurally complete modal logics

  • V. V. Rybakov (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.