Modal Logic and Classical Logic

✍ Scribed by Johan van Benthem

• Publisher: Bibliopolis
• Year: 1983
• Tongue: English
• Leaves: 217
• Series: Indices. Monographs in Philosophical Logic and Formal Linguistics, volume 3
• Category: Library

✦ Synopsis

The present work is a rewritten version of van Benthem's dissertation Modal Correspondence Theory'' (University of Amsterdam, 1976) and a supplementary report calledModal Logic as Second-Order Logic'' (University of Amsterdam, 1977).

✦ Table of Contents

Cover ......Page 1
Table of contents ......Page 5
Preface ......Page 7
Introduction ......Page 8
Notation and terminology ......Page 12
Part I. A short survey of propositional modal logic ......Page 15
I. Historical background ......Page 16
II. Possible worlds semantics ......Page 20
III. Definability ......Page 34
IV. Modal algebras ......Page 50
V. Axiomatic theories ......Page 57
VI. Completeness ......Page 62
Part II. First-order definability of modal formulas ......Page 72
VII. Local and global first-order definability ......Page 73
VIII. A model-theoretic characterization of first-order definability ......Page 81
IX. The method of substitutions ......Page 89
X. Disproving first-order definability ......Page 104
XI. Relative first-order definability ......Page 115
XII. Modal predicate logic ......Page 124
XIII. Preservation classes of modal formulas ......Page 131
Part III. Modal definability ......Page 136
XIV. Modally definable elementary classes of frames ......Page 137
XV. Preservation results for first-order formulas ......Page 145
Appendix: Tense logic ......Page 163
XVI. Modally definable classes of frames ......Page 165
Appendix: Higher-order correspondence ......Page 172
Part IV: Higher-order definability ......Page 175
XVII. Universal second-order sentences ......Page 176
XVIII. Second-order logic ......Page 195
XIX. The theory of finite types ......Page 206
Bibliography ......Page 211