Quantifiers: Logics, Models and Computation

1. Front Matter

   Pages i-ix

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2. Quantifiers and Inference

   • Johan van Benthem

   Pages 1-20

3. Operators on Branched Quantifiers

   • Mark A. Brown

   Pages 21-61

4. Hilbert’s ε-Symbol in the Presence of Generalized Quantifiers

   • Xavier Caicedo

   Pages 63-78

5. Partially Ordered Connectives and Finite Graphs

   • Lauri Hella, Gabriel Sandu

   Pages 79-88

6. Theories of Finitely Determinate Linear Orderings in Stationary Logic

   • Heinrich Herre

   Pages 89-113

7. Definable Second-Order Quantifiers and Quasivarieties

   • Alexandre A. Ivanov

   Pages 115-123

8. Quantifiers Determined by Classes of Binary Relations

   • Michał Krynicki

   Pages 125-138

9. Decidability Results for Classes of Ordered Abelian Groups in Logics with Ramsey-Quantifiers

   • Wolfgang Lenski

   Pages 139-168

10. On the Eliminability of the Quantifier “There Exist Uncountably Many”

    • Žarko Mijajlović

    Pages 169-179

11. Quantifiers Definable by Second Order Means

    • Marcin Mostowski

    Pages 181-214

12. Generalized Quantifiers in Algebra

    • Alexandre G. Pinus

    Pages 215-228

13. On Ordering of the Family of Logics with Skolem-Löwenheim Property and Countable Compactness Property

    • Marek Wacławek

    Pages 229-236

14. Pre-Ordered Quantifiers in Elementary Sentences of Natural Language

    • Marek W. Zawadowski

    Pages 237-253

15. Some Remarks on Zawadowski’s Theory of Preordered Quantifiers

    • Mark A. Brown

    Pages 255-264

16. Back Matter

    Pages 265-278

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This volume contains a collection of research papers centered around the concept of quantifier. Recently this concept has become the central point of research in logic. It is one of the important logical concepts whose exact domain and applications have so far been insufficiently explored, especially in the area of inferential and semantic properties of languages. It should thus remain the central point of research in the future. Moreover, during the last twenty years generalized quantifiers and logical technics based on them have proved their utility in various applications. The example of natu­ rallanguage semantics has been partcularly striking. For a long time it has been belived that elementary logic also called first-order logic was an ade­ quate theory of logical forms of natural language sentences. Recently it has been accepted that semantics of many natural language constructions can­ not be properly represented in elementary logic. It has turned out, however, that they can be described by means of generalized quantifiers. As far as computational applications oflogic are concerned, particulary interesting are semantics restricted to finite models. Under this restriction elementary logic looses several of its advantages such as axiomatizability and compactness. And for various purposes we can use equally well some semantically richer languages of which generalized quantifiers offer the most universal methods of describing extensions of elementary logic. Moreover we can look at generalized quantifiers as an explication of some specific mathematical concepts, e. g.

• Index
• Symbol
• logic
• proof
• quantifiers
• semantic
• semantics

• Department of Mathematics, University of Warsaw, Poland

  Michał Krynicki

• Department of Philosophy, University of Warsaw, Poland

  Marcin Mostowski

• Siedlce University, Poland

  Lesław W. Szczerba

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