On the Logic with Rough Quantifier

  • Michał Krynicki
  • Lesław W. Szczerba
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 13)


The main aim of this paper is to present a survey of results on the logic with rough quantifier. Besides, a classification of simplicity of formulas of the logic with rough quantifier is defined and a criterion for placing a formula on the exact simplicity level is given.


Equivalence Class Equivalence Relation Order Logic Winning Strategy Existential Quantifier 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Bal]
    Barwise, J.: On Moskovakis closure ordinals. The Journal of Symbolic Logic, 42, (1977), 292–296MathSciNetMATHCrossRefGoogle Scholar
  2. [BS1.]
    Bell, J.L. and Slomson, A.B.: Models and Ultraproducts. An Introduction. North-Holland Publ. Co., (1969)Google Scholar
  3. [CK1]
    Chang, C.C. and Keisler, H.J.: Model Theory. North-Holland, Publ. Comp., (1973)MATHGoogle Scholar
  4. [Ehl]
    Ehrenfeucht, A.: An applications of games to the completeness problem for formalized theories. Fundamenta Mathematicae, 49, (1961), 129–141MathSciNetMATHGoogle Scholar
  5. [Fr1]
    Fraïssé, R.J.: Sur quelques classifications des systémes des relations. Publ. Sci. Univ. Alger, A 1, (1954), 35–182Google Scholar
  6. [Iml]
    Immerman, N.: Upper and lower bounds for first—order logic. Information and Control, 68, (1982), 76–98Google Scholar
  7. [Ke1]
    Kell Keisler, H.J.: Logic with the quantifier “there exist uncountably many” Annals of Mathematical Logic, 1, (1970), 1–93MathSciNetMATHGoogle Scholar
  8. [KV1]
    Kolaitis, P.G. and Väänänen, J.: Generalized quantifiers and pebble games on finite structures Annals of Pure and Applied Logic, 74, (1995), 23–75MATHGoogle Scholar
  9. [KK1]
    Krawczyk, A. and Krynicki, M.: Ehrenfeucht games for generalized quantifiers. In: Set Theory and Hierarchy Theory, Lecture Notes in Mathematics, 537, Springer, (1976), 145–152Google Scholar
  10. [Kr1]
    Krynicki, M.: A note on rough concepts logic. Fundamenta Informaticae, 13, (1990), 227–235MathSciNetMATHGoogle Scholar
  11. [Kr2]
    Krynicki, M.: Relational Quantifiers. Dissertationes Mathematicae, 347, (1995)Google Scholar
  12. [KS1]
    Krynicki, M., Szczerba, L.W.: On simplicity of formulas. Studia Logica, 49, (1990), 401–419MathSciNetMATHCrossRefGoogle Scholar
  13. [KT1]
    Krynicki, M. and Tuschik, H-P.: An axiomatization of the logic with the rough quantifier. The Journal of Symbolic Logic, 56, (1991), 608–617MathSciNetMATHCrossRefGoogle Scholar
  14. [MT1]
    Makowsky, J.A. and Tulipani, S.: Some model theory for monotone quanti- fiers. Archive fur Math. Logik und Grundlagenforschung, 18, (1977), 115–134MathSciNetMATHCrossRefGoogle Scholar
  15. [RS1]
    Rasiowa, H. and Skowron, A.: Rough concepts logic. In: Computation Theory, A.Skowron (ed.), Lecture Notes in Computer Science, 208, Springer, (1985), 288–297Google Scholar
  16. [Szl]
    Szczerba, L.W.: Rough Quantifiers. Bulletin of the Polish Academy of Science, Mathematics, 35, (1987), 251–254MathSciNetMATHGoogle Scholar
  17. [Sz2]
    Szczerba, L.W.: Rough Quantifiers have no Tarski property. Bulletin of the Polish Academy of Science, Mathematics, 35, (1987), 663–665MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Michał Krynicki
    • 1
  • Lesław W. Szczerba
    • 2
  1. 1.Institute of MathematicsUniversity of WarsawPoland
  2. 2.Siedlce UniversityPoland

Personalised recommendations