Abstract
We present our personal view on W.J. Blok's contribution to modal logic.
Similar content being viewed by others
References
BLOK, W. J., Varieties of interior algebras, PhD thesis, University of Amsterdam, 1976.
BLOK, W. J., ‘The lattice of modal logics (abstract)’, Bulletin of the Section of Logic of the Polish Academy of Sciences 6 (1977), 112–115.
BLOK, W. J., ‘On the degree of incompleteness of modal logics (abstract)’, Bulletin of the Section of Logic of the Polish Academy of Sciences 7 (1978), 167–175.
BLOK, W. J., ‘On the degree of incompleteness of modal logics and the covering relation in the lattice of modal logics’, Technical Report 78–07, Department of Mathematics, University of Amsterdam, 1978.
BLOK, W. J., ‘An axiomatization of the modal theory of the veiled recession frame’, Studia Logica 38 (1979) 37–47.
BLOK, W. J., ‘The lattice of modal logics: an algebraic investigation’, Journal of Symbolic Logic 45 (1980), 221–236.
BLOK, W. J., ‘The lattice of varieties of modal algebras is not strongly atomic’, Algebra Universalis 11 (1980), 285–294.
BLOK, W. J., ‘Pretabular varieties of modal algebras’, Studia Logica 39 (1980), 101–124.
BLOK, W. J., ‘Reminiscences about modal logic in the seventies’, 2000.
BLOK, W. J., and P. DWINGER, ‘Equational classes of closure algebras’, Indagationes Mathematicae 37 (1975), 189–198.
BLOK, W. J., and P. KOHLER, ‘Algebraic semantics for quasi-classical modal logics’, Journal of Symbolic Logic 48 (1983), 941–964.
CHAGROV, A., and M. ZAKHARYASCHEV, Modal Logic, volume 35 of Oxford Logic Guides, Clarendon Press, Oxford, 1997.
CHAGROV, A., ‘Nontabularity-pretabularity, antitabularity, co-antitabularity’, in Algebraic and Logical Constructions, Kalinin State University, Kalinin, 1989, pp. 105–111. (Russian).
CHAGROV, A., and M. ZAKHARYASCHEV, ‘Modal companions of intermediate prepositional logics’, Studio, Logica 51 (1992), 49–82.
CHAGROVA, L., ‘On the degree of neighbourhood incompleteness of normal modal logics’, in KRACHT, M., M. DE RIJKE, H. WANSING, and M. ZAKHARYASCHEV, (eds.) Advances in Modal Logic 1, CSLI Publications 1998, pp. 63–72.
DUMMETT, M., and E. LEMMON, ‘Modal logics between S4 and S5’, Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik 5 (1959), 250–264.
DZIOBIAK, W., ‘A note on incompleteness of modal logics with respect to neighbourhood semantics’, Bulletin of the Section of Logic 9 (1978), 136–140.
ESAKIA, L.L., ‘On varieties of Grzegorczyk algebras’, in MIKHAILOV, A. L, (ed.) Studies in Non-classical Logics and Set Theory, pp. 257–287. Moscow, Nauka, 1979. (Russian).
ESAKIA, L.L., ‘To the theory of modal and superintuitionistic systems’, in SMIRNOV, V. A., (ed.) Logical Inference. Proceedings of the USSR Symposium on the Theory of Logical Inference, pp. 147–172. Nauka, Moscow, 1979. (Russian).
ESAKIA, L.L., and V. Yu. MESKHI, ‘Five critical systems’, Theoria 40 (1977), 52–60.
FINE, K., ‘An incomplete logic containing S4’, Theoria 40 (1974), 23–29.
GOLDBLATT, R., ‘Mathematical modal logic: a view of its evolution’, Journal of Applied Logic 1 (2003), 309–392.
GRZEGORCZYK, A., ‘Some relational systems and the associated topological spaces’, Fundamenta Mathematicae 60 (1967), 223–231.
JANKOV, V. A., ‘The relationship between deducibility in the intuitionistic prepositional calculus and finite implicational structures’, Soviet Mathematics Doklady 4 (1963), 1203–1204.
JANSANA, R., ‘Willem Blok's contribution to abstract algebraic logic’, Studia Logica 31–48 of this issue.
JONSSON, B., ‘Algebras whose congruence lattices are distributive’, Mathematica Scandinavica 21 (1967), 110–121.
KRACHT, M., Tools and Techniques in Modal Logic, Studies in Logic. Elsevier, North-Holland, 1999.
KUZNETSOV, A. V., ‘Some properties of the structure of varieties of pseudo-Boolean algebras’, in Proceedings of the Xlth USSR Algebraic Colloquium, pp. 255–256, Kishinev, 1971. (Russian).
LlTAK, T., An algebraic approach to incompleteness in modal logic, Ph. D. thesis, JAIST, 2005.
MAKSIMOVA, L., ‘Modal logics of finite slices’, Algebra and Logic 14 (1975), 188–197.
MAKSIMOVA, L., ‘Pretabular extensions of Lewis 54’, Algebra and Logic 14 (1975), 16–33.
MAKSIMOVA, L., and V. RYBAKOV, ‘Lattices of modal logics’, Algebra and Logic 13 (1974), 105–122.
McKENZIE, R., ‘Equational bases and non-modular lattice varieties’, Transactions of the American Mathematical Society 174 (1972), 1–43.
McKlNSEY, J. C. C., and A. TARSKI, ‘The algebra of topology’, Annals of Mathematics, 45 (1944), 141–191.
McKlNSEY, J. C. C., and A. TARSKI, ‘On closed elements in closure algebras’, Annals of Mathematics 47 (1946), 122–162.
McKlNSEY, J. C. C., and A. TARSKI, ‘Some theorems about the sentential calculi of Lewis and Heyting’, Journal of Symbolic Logic 13 (1948), 1–15.
RAUTENBERG, W., Klassische und nichtklassische Aussagenlogik, Vieweg, Braunschweig-Wiesbaden, 1979.
RAUTENBERG, W., ‘Splitting lattices of logics’, Archiv fur Mathematische Logik 20 (1980), 155–159.
SEGERBERG, K., ‘An essay in classical modal logic’, Philosophical Studies 13 (1971).
THOMASON, S., ‘An incompleteness theorem in modal logic’, Theoria 40 (1974), 30–34.
WOLTER, P., ‘The structure of lattices of subframe logics’, Annals of Pure and Applied Logic 86 (1997), 47–100.
WOLTER, P., and M. ZAKHARYASCHEV, ‘Modal decision problems’, in BLACKBURN, P., J. VAN BENTHEM, and F. WOLTER, (eds.) Handbook of Modal Logic, Elsevier, 2006.
ZAKHARYASCHEV, M., F. WOLTER, and A. CHAGROV, ‘Advanced modal logic’, in GABBAY, D., and F. GUENTHNER, (eds.) Handbook of Philosophical Logic, vol.3, pp. 83–266. Kluwer Academic Publishers, 2nd edition, 2001.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rautenberg, W., Zakharyaschev, M. & Wolter, F. Willem Blok and Modal Logic. Stud Logica 83, 15–30 (2006). https://doi.org/10.1007/s11225-006-8296-2
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11225-006-8296-2