Contributions
著者
書誌事項
Contributions
（Synthese library, v. 249 . Quantifiers : logics,
Kluwer Academic Publishers, c1995
- : set
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注記
Includes bibliographical references and indexes
内容説明・目次
- 巻冊次
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ISBN 9780792334491
内容説明
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.
目次
- Preface. Quantifiers and Inference
- J. van Benthem. Operators on Branched Quantifiers
- M.A. Brown. Hilbert's Epsilon-Symbol in the Presence of Generalized Quantifiers
- X. Caicedo. Partially Ordered Connectives and Finite Graphs
- L. Hella, G. Sandu. Theories of Finitely Determined Linear Orderings in Stationary Logics
- H. Herre. Definable Second-Order Quantifiers and Quasivarieties
- A.A. Ivanov. Quantifiers Determined by Classes of Binary Relations
- M. Krynicki. Decidability Results for Classes of Ordered Abelian Groups in Logics with Ramsey Quantifiers
- W. Lenski. On the Eliminability of the Quantifier `There Exists Uncountably Many'
- Z. Mijajlovic. Quantifiers Definable by Second Order Means
- M. Mostowski. Generalized Quantifiers in Algebra
- A.G. Pinus. On Ordering of the Family of Logics with Skolem-Loewenheim Property and Countable Compactness Property
- M. Waclawek.DAGGER. Pre-Ordered Quantifiers in Elementary Sentences of Natural Language
- M.W. Zawadowsky. Some Remarks on Zawadowski's `Theory of Preordered Quantifiers'
- M.A. Brown. Index of Names.
- 巻冊次
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: set ISBN 9780792334507
内容説明
The quantifier concept is central to current logical investigations. Quantifiers: Logics, Models and Computation. Volume Two: Contributions contains twelve research papers devoted to generalized quantifiers and their applications. It offers an exhaustive survey of logical methods that are useful in investigations involving generalized quantifiers. Both model-theoretical and proof-theoretical approaches are well represented. Moreover, some papers focus on the applications of logical theory, particularly in relation to semantics of natural language. The volume includes a wide-ranging survey of logical methods which are useful in investigations into generalized quantifiers.
The book is the second volume of a large collection. The first volume - Quantifiers: Logics, Models and Computation. Volume One: Surveys - contains a collection of survey papers on selected, well-defined areas organized around the quantifier concept. Volumes One and Two are complementary.
For logicians, mathematicians, philosophers, linguists and computer scientists. Also suitable as a text for advanced undergraduate or graduate specialized courses in logic.
目次
- Preface. Quantifiers and Inference
- J. van Benthem. Operators on Branched Quantifiers
- M.A. Brown. Hilbert's Epsilon-Symbol in the Presence of Generalized Quantifiers
- X. Caicedo. Partially Ordered Connectives and Finite Graphs
- L. Hella, G. Sandu. Theories of Finitely Determined Linear Orderings in Stationary Logics
- H. Herre. Definable Second-Order Quantifiers and Quasivarieties
- A.A. Ivanov. Quantifiers Determined by Classes of Binary Relations
- M. Krynicki. Decidability Results for Classes of Ordered Abelian Groups in Logics with Ramsey Quantifiers
- W. Lenski. On the Eliminability of the Quantifier `There Exists Uncountably Many'
- Z. Mijajlovic. Quantifiers Definable by Second Order Means
- M. Mostowski. Generalized Quantifiers in Algebra
- A.G. Pinus. On Ordering of the Family of Logics with Skolem-Loewenheim Property and Countable Compactness Property
- M. Waclawek.DAGGER. Pre-Ordered Quantifiers in Elementary Sentences of Natural Language
- M.W. Zawadowsky. Some Remarks on Zawadowski's `Theory of Preordered Quantifiers'
- M.A. Brown. Index of Names.
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