Advertisement

Studia Logica

, Volume 100, Issue 1–2, pp 1–7 | Cite as

Foreword

  • Lev Beklemishev
  • Guram Bezhanishvili
  • Daniele Mundici
  • Yde Venema
Article

Keywords

Modal Logic Intuitionistic Logic Kripke Model Heyting Algebra Topological Derivative 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abashidze, M. A., Ordinal completeness of the Gödel-Löb modal system, Intensional logics and the logical structure of theories (Telavi, 1985), “Metsniereba”, Tbilisi, 1988, pp. 49–73 (Russian).Google Scholar
  2. 2.
    Bezhanishvili G., Esakia L., Gabelaia D.: ‘Some results on modal axiomatization and definability for topological spaces’. Studia Logica 81(3), 325–355 (2005)CrossRefGoogle Scholar
  3. 3.
    Bezhanishvili, G., L. Esakia, and D. Gabelaia, ‘K4.Grz and hereditarily irresolvable spaces’, in S. Feferman, W. Sieg, V. Kreinovich, V. Lifschitz, and R. de Queiroz (eds.), Proofs, Categories and Computations. Essays in honor of Grigori Mints. College Publications, 2010, pp. 61–69.Google Scholar
  4. 4.
    Bezhanishvili G., Esakia L., Gabelaia D.: ‘The modal logic of Stone spaces: diamond as derivative’. Rev. Symb. Log. 3(1), 26–40 (2010)CrossRefGoogle Scholar
  5. 5.
    Bezhanishvili, G., L. Esakia, and D. Gabelaia, ‘Spectral and T 0-spaces in dsemantics’, in N. Bezhanishvili, S. Löbner, K. Schwabe, and L. Spada (eds.), Lecture Notes in Artificial Intelligence. Springer, 2011, pp. 16–29.Google Scholar
  6. 6.
    Blass A.: ‘Infinitary combinatorics and modal logic’. J. Symbolic Logic 55(2), 761–778 (1990)CrossRefGoogle Scholar
  7. 7.
    Blok, W., Varieties of interior algebras, Ph.D. thesis, University of Amsterdam, 1976.Google Scholar
  8. 8.
    Chagrov A., Zakharyaschev M.: Modal logic, Oxford Logic Guides, vol. 35. The Clarendon Press Oxford University Press, New York (1997)Google Scholar
  9. 9.
    Esakia L.: ‘Topological Kripke models’. Soviet Math. Dokl. 15, 147–151 (1974)Google Scholar
  10. 10.
    Esakia, L., The problem of dualism in the intuitionistic logic and Browerian lattices, V Inter. Congress of Logic, Methodology and Philosophy of Science, Canada, 1975, pp. 7–8.Google Scholar
  11. 11.
    Esakia, L., On modal “companions” of superintuitionistic logics, VII Soviet Symposium on Logic (Kiev, 1976), 1976, pp. 135–136 (Russian).Google Scholar
  12. 12.
    Esakia, L., Semantical analysis of bimodal (tense) systems, Logic, Semantics and Methodology, “Metsniereba”, Tbilisi, 1978, pp. 87–99 (Russian).Google Scholar
  13. 13.
    Esakia, L., On the variety of Grzegorczyk algebras, Studies in nonclassical logics and set theory, “Nauka”, Moscow, 1979, pp. 257–287 (Russian).Google Scholar
  14. 14.
    Esakia, L., Diagonal constructions, Löb’s formula, and Cantor’s scattered spaces, Studies in logic and semantics’, “Metsniereba”, Tbilisi, 1981, pp. 128–143 (Russian).Google Scholar
  15. 15.
    Esakia L.: ‘On the variety of Grzegorczyk algebras’. Sel. Sov. Math. 3(4), 343–366 (1984)Google Scholar
  16. 16.
    Esakia, L., Heyting algebras. Duality theory, “Metsniereba”, Tbilisi, 1985 (Russian).Google Scholar
  17. 17.
    Esakia, L., A classification of elements in closure algebras: Hausdorff residues, IX Soviet Conference in Logic and Philosophy of Science, Moscow, 1986, pp. 172–173 (Russian).Google Scholar
  18. 18.
    Esakia, L., On a classification of elements in closure algebras, Methods for research in logic,“Metsniereba”, Tbilisi, 1986, pp. 48–54 (Russian).Google Scholar
  19. 19.
    Esakia, L., Provability logic with quantifier modalities, Intensional logics and the logical structure of theories (Telavi, 1985). “Metsniereba”, Tbilisi, 1988, pp. 4–9 (Russian).Google Scholar
  20. 20.
    Esakia, L., Provability interpretations of intuitionistic logic, Logical investigations, No. 5 (Moscow, 1997). “Nauka”, Moscow, 1998, pp. 19–24 (Russian).Google Scholar
  21. 21.
    Esakia L.: ‘Quantification in intuitionistic logic with provability smack’. Bull. Sect. Logic 27, 26–28 (1998)Google Scholar
  22. 22.
    Esakia, L., Creative and critical points in intuitionistic Kripke models and adjoint modalities, Russian Academy of Sciences, Moscow, 1999, pp. 78–82 (Russian).Google Scholar
  23. 23.
    Esakia, L., Synopsis of fronton theory, Logical investigations, No. 7 (Moscow, 1999). “Nauka”, Moscow, 2000, pp. 137–147 (Russian).Google Scholar
  24. 24.
    Esakia, L., Weak transitivity—a restitution, Logical investigations, No. 8 (Moscow, 2001). “Nauka”, Moscow, 2001, pp. 244–255 (Russian).Google Scholar
  25. 25.
    Esakia, L., A modal version of Gödel’s second incompleteness theorem, and the McKinsey system, Logical investigations, No. 9, “Nauka”, Moscow, 2002, pp. 292– 300 (Russian).Google Scholar
  26. 26.
    Esakia L.: ‘Intuitionistic logic and modality via topology’. Ann. Pure Appl. Logic 127(1-3), 155–170 (2004)CrossRefGoogle Scholar
  27. 27.
    Esakia L.: ‘The modalized Heyting calculus: a conservative modal extension of the intuitionistic logic’. J. Appl. Non-Classical Logics 16(3-4), 349–366 (2006)CrossRefGoogle Scholar
  28. 28.
    Esakia L.: ‘Around provability logic’. Ann. Pure Appl. Logic 161(2), 174–184 (2009)CrossRefGoogle Scholar
  29. 29.
    Esakia L., Grigolia R.: ‘Christmas trees. On free cyclic algebras in some varieties of closure algebras’. Bull. Sect. Logic 4(3), 95–102 (1975)Google Scholar
  30. 30.
    Esakia L., Grigolia R.: ‘The criterion of Brouwerian and closure algebras to be finitely generated’. Bull. Sect. Logic 6(2), 46–52 (1977)Google Scholar
  31. 31.
    Esakia L., Grigolia R.: ‘Formulas of one propositional variable in intuitionistic logic with the Solovay modality’. Logic Log. Philos 17(1-2), 111–127 (2008)Google Scholar
  32. 32.
    Esakia L., M. Jibladze, Pataraia D.: ‘Scattered toposes’. Ann. Pure Appl. Logic 103(1-3), 97–107 (2000)CrossRefGoogle Scholar
  33. 33.
    Esakia, L., and S. Meskhi, On five critical systems, Theory of logical entailment, Part I, Moscow, 1974, pp. 76–79.Google Scholar
  34. 34.
    Esakia L., Meskhi S.: ‘Five critical modal systems’. Theoria 43(1), 52–60 (1977)CrossRefGoogle Scholar
  35. 35.
    Gödel K.: ‘Eine Interpretation des intuitionistischen Aussagenkalkülus’. Ergebnisse eines mathematischen Kolloquiums 4, 39–40 (1933)Google Scholar
  36. 36.
    Grzegorczyk A.: ’Some relational systems and the associated topological spaces. Fund. Math 60, 223–231 (1967)Google Scholar
  37. 37.
    Jónsson B., Tarski A.: ‘Boolean algebras with operators. I’. Amer. J. Math. 73, 891–939 (1951)CrossRefGoogle Scholar
  38. 38.
    Jónsson B., Tarski A.: ‘Boolean algebras with operators. II’. Amer. J. Math. 74, 127–162 (1952)CrossRefGoogle Scholar
  39. 39.
    Kripke S. A.: ‘Semantical analysis of modal logic. I. Normal modal propositional calculi’. Z. Math. Logik Grundlagen Math. 9, 67–96 (1963)CrossRefGoogle Scholar
  40. 40.
    Kripke, S. A., Semantical analysis of intuitionistic logic. I, Formal Systems and Recursive Functions (Proc. Eighth Logic Colloq., Oxford, 1963. North-Holland, Amsterdam, 1965, pp. 92–130.Google Scholar
  41. 41.
    Maksimova, L., ‘Pretabular extensions of Lewis’s logic S4’, Algebra i Logika 14(1):28–55, 117, 1975 (Russian).Google Scholar
  42. 42.
    Maksimova, L., and V. Rybakov, ‘The lattice of normal modal logics’, Algebra i Logika 13:188–216, 235, 1974 (Russian).Google Scholar
  43. 43.
    McKinsey J. C. C., Tarski A.: ‘The algebra of topology’. Annals of Mathematics 45, 141–191 (1944)CrossRefGoogle Scholar
  44. 44.
    McKinsey J. C. C., Tarski A.: ‘On closed elements in closure algebras’. Ann. of Math. 47(2), 122–162 (1946)CrossRefGoogle Scholar
  45. 45.
    McKinsey J. C. C., Tarski A.: ‘Some theorems about the sentential calculi of Lewis and Heyting’. J. Symbolic Logic 13, 1–15 (1948)CrossRefGoogle Scholar
  46. 46.
    Rasiowa, H., and R. Sikorski, The mathematics of metamathematics, Monografie Matematyczne, Tom 41, Państwowe Wydawnictwo Naukowe, Warsaw, 1963.Google Scholar
  47. 47.
    Sambin G., Vaccaro V.: ‘A new proof of Sahlqvist’s theorem on modal definability and completeness’. J. Symbolic Logic 54(3), 992–999 (1989)CrossRefGoogle Scholar
  48. 48.
    Stone M. H.: ‘The theory of representations for Boolean algebras’. Trans. Amer. Math. Soc. 40(1), 37–111 (1936)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Lev Beklemishev
    • 1
  • Guram Bezhanishvili
    • 2
  • Daniele Mundici
    • 3
  • Yde Venema
    • 4
  1. 1.Steklov Mathematical InstituteMoscowRussian Federation
  2. 2.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA
  3. 3.Department of MathematicsUniversity of FlorenceFlorenceItaly
  4. 4.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands

Personalised recommendations