Studia Logica

, Volume 58, Issue 3, pp 395–401 | Cite as

Kripke Bundle Semantics and C-set Semantics

  • Eiko Isoda
Article

Abstract

Kripke bundle [3] and C-set semantics [1] [2] are known as semantics which generalize standard Kripke semantics. In [3] and in [1], [2] it is shown that Kripke bundle and C-set semantics are stronger than standard Kripke semantics. Also it is true that C-set semantics for superintuitionistic logics is stronger than Kripke bundle semantics [5].

In this paper, we show that Q-S4.1 is not Kripke bundle complete via C-set models. As a corollary we can give a simple proof showing that C-set semantics for modal logics are stronger than Kripke bundle semantics.

Kripke bundle semantics C-set semantics superintuitionistic logics 

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References

  1. [1]
    S. Ghilardi, (1989), Presheaf semantics and independence results for some non-classical first-order logics, Archive for Mathematical Logic 29 125-136.Google Scholar
  2. [2]
    S. Ghilardi, (1991), Incompleteness results in Kripke semantics, Journal of Symbolic Logic 56,517-538.Google Scholar
  3. [3]
    V.B. Shehtman and D.P. Skvortsov, 1990, Semantics of non-classical first order predicate logics, in P. Petkov, ed., Mathematical Logic, Plenum Press, New York, 105-116.Google Scholar
  4. [4]
    D.P. Skvortsov and V.B. Shehtman, (1993), Maximal Kripke-type semantics for modal and superintuitionistic predicate logics, Ann. Pure and Appl. Logic 69, 69-101.CrossRefGoogle Scholar
  5. [5]
    D.P. Skvortsov, On finite intersections of intermediate predicate logics, To appear in: Logic and algebra, Proc. Intern. Conf. on logic and algebra in memory of R.Magari, Siena April 1994.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Eiko Isoda
    • 1
  1. 1.Department of MathematicsTsuda CollegeTsuda-machi Kodaira-shi, TokyoJapan

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