Kooperativer Bibliotheksverbund

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Format: 1 online resource (641 p.)

Edition: 1st ed.

ISBN: 1-282-12103-0 , 9786612121036 , 0-08-093112-X

Series Statement: Studies in logic and the foundations of mathematics ; v. 153:1

Content: Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy andlanguage in ancient times; they were studied by traditional informalmethods until the 20th century. In the last century the tools becamehighly mathematical, and both modal logic and quantification found numerous applications in Computer Science. At the same time many other kinds of nonclassical logics were investigated and applied to Computer Science. Although there exist several good books in propositional modal logics, this book is the first d

Note: Description based upon print version of record. , Front Cover; Quantification in Nonclassical Logic; Copyright Page; Contents; Preface; Introduction; Part I Preliminaries; Chapter 1 Basic propositional logic; 1.1 Propositional syntax; 1.2 Algebraic semantics; 1.3 Relational semantics (the modal case); 1.4 Relational semantics (the intuitionistic case); 1.5 Modal counterparts; 1.6 General Kripke frames; 1.7 Canonical Kripke models; 1.8 First-order translations and definability; 1.9 Some general completeness theorems; 1.10 Trees and unravelling; 1.11 PTC-logics and Horn closures; 1.12 Subframe and cofinal subframe logics; 1.13 Splittings , 1.14 Tabularity1.15 Transitive logics of finite depth; 1.16 ?-operation; 1.17 Neighbourhood semantics; Chapter 2 Basic predicate logic; 2.1 Introduction; 2.2 Formulas; 2.3 Variable substitutions; 2.4 Formulas with constants; 2.5 Formula substitutions; 2.6 First-order logics; 2.7 First-order theories; 2.8 Deduction theorems; 2.9 Perfection; 2.10 Intersections; 2.11 Cödel-Tarski translation; 2.12 The Glivenko theorem; 2.13 ?-operation; 2.14 Adding equality; 2.15 Propositional parts; 2.16 Semantics from an abstract viewpoint; Part II Semantics; Introduction: What is semantics? , Chapter 3 Kripke semantics3.1 Preliminary discussion; 3.2 Predicate Kripke frames; 3.3 Morphisms of Kripke frames; 3.4 Constant domains; 3.5 Kripke frames with equality; 3.6 Kripke sheaves; 3.7 Morphisms of Kripke sheaves; 3.8 Transfer of completeness; 3.9 Simulation of varying domains; 3.10 Examples of Kripke semantics; 3.11 On logics with closed or decidable equality; 3.12 Translations into classical logic; Chapter 4 Algebraic semantics; 4.1 Modal and Heyting valued structures; 4.2 Algebraic models; 4.3 Soundness; 4.4 Morphisms of algebraic structures; 4.5 Presheaves and O-sets , 4.6 Morphisms of presheaves4.7 Sheaves; 4.8 Fibrewise models; 4.9 Examples of algebraic semantics; Chapter 5 Metaframe semantics; 5.1 Preliminary discussion; 5.2 Kripke bundles; 5.3 More on forcing in Kripke bundles; 5.4 Morphisms of Kripke bundles; 5.5 Intuitionistic Kripke bundles; 5.6 Functor semantics; 5.7 Morphisms of presets; 5.8 Bundles over precategories; 5.9 Metaframes; 5.10 Permutability and weak functoriality; 5.11 Modal metaframes; 5.12 Modal soundness; 5.13 Representation theorem for modal metaframes; 5.14 Intuitionistic forcing and monotonicity; 5.15 Intuitionistic soundness , 5.16 Maximality theorem5.17 Kripke quasi-bundles; 5.18 Some constructions on metaframes; 5.19 On semantics of intuitionistic sound metaframes; 5.20 Simplicial frames; Part III Completeness; Chapter 6 Kripke completeness for varying domains; 6.1 Canonical models for modal logics; 6.2 Canonical models for superintuitionistic logics; 6.3 Intermediate logics of finite depth; 6.4 Natural models; 6.5 Refined completeness theorem for QH + K F; 6.6 Directed frames; 6.7 Logics of linear frames; 6.8 Properties of ?-operation; 6.9 ?-operation preserves completeness , 6.10 Trees of bounded branching and depth , English

Additional Edition: ISBN 0-444-52012-0

Language: English

UID:

Format: XXIV, 615 S , graph. Darst , 23 cm

Edition: 1. ed

ISBN: 9780444520128

Series Statement: Studies in logic and the foundations of mathematics 153

Note: Includes bibliographical references (p. 593 - 602) and index

In: Vol. 1

Language: English

URL: Inhaltstext

Author information: Gabbay, Dov M. 1945-

UID:

Format: 253 S , mit Notenbeisp , 8

Note: Mit Bibliogr , Münster, Phil. Fak., Diss. v. 14. Febr. 1969

Language: German

Keywords: Deutsch ; Lyrik ; Sapphische Strophe ; Geschichte 1600-1700 ; Hochschulschrift

Author information: Derks, Paul 1944-

UID:

Format: 1 Online-Ressource (615 S.).

ISBN: 978-0-08-093112-8 , 0-08-093112-X

Series Statement: Studies in logic and the foundations of mathematics 153

Note: Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy and language in ancient times; they were studied by traditional informal methods until the 20th century. In the last century the tools became highly mathematical, and both modal logic and quantification found numerous applications in computer science. At the same time many other kinds of nonclassical logics were investigated and applied to computer science. Although there exist several good books in propositional modal logics, this book is the first detailed monograph in nonclassical first-order quantification. It includes results obtained during the past thirty years. The field is very large, so we confine ourselves with only two kinds of logics: modal and superintuitionistic. The main emphasis of volume 1 is model-theoretic, and it concentrates on descriptions of different sound semantics and completeness problem --- even for these seemingly simple questions we have our hands full. The major part of the presented material has never been published before. Some results are very recent, and for other results we either give new proofs or first proofs in full detail. - Includes bibliographical references and indexes

In: Quantification in nonclassical logic.

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-0-44452012-8

Language: English

URL: Volltext  (URL des Erstveröffentlichers)

UID:

Format: 1 Online-Ressource (615 S.).

ISBN: 978-0-08-093112-8 , 0-08-093112-X

Series Statement: Studies in logic and the foundations of mathematics 153

Note: Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy and language in ancient times; they were studied by traditional informal methods until the 20th century. In the last century the tools became highly mathematical, and both modal logic and quantification found numerous applications in computer science. At the same time many other kinds of nonclassical logics were investigated and applied to computer science. Although there exist several good books in propositional modal logics, this book is the first detailed monograph in nonclassical first-order quantification. It includes results obtained during the past thirty years. The field is very large, so we confine ourselves with only two kinds of logics: modal and superintuitionistic. The main emphasis of volume 1 is model-theoretic, and it concentrates on descriptions of different sound semantics and completeness problem --- even for these seemingly simple questions we have our hands full. The major part of the presented material has never been published before. Some results are very recent, and for other results we either give new proofs or first proofs in full detail. - Includes bibliographical references and indexes

In: Quantification in nonclassical logic.

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-0-44452012-8

Language: English

URL: Volltext  (URL des Erstveröffentlichers)