Systems of Logic

Norman M. Martin

doi:10.1017/CBO9780511625244

This is an advanced study of systems of propositional logic which offers a comprehensive account of a wide variety of logical systems and which encourages students to take a critical stance towards the subject. A great variety of systems and subsystems are defined and compared as regards their deductive power and relation to their model theory. Interesting features include a more refined treatment of modal logic and the special attention given to the weakenings of classical logic. Useful appendices provide a topical bibliography and review of basic set theory.

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Contents

Frontmatter
pp i-vi
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Contents
pp vii-viii
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Preface
pp ix-xii
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1 - Formal Systems and Structure Theory
pp 1-15
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2 - Zero-Order Logic: Proof Theory
pp 16-37
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3 - Zero-Order Model Theory
pp 38-56
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4 - Positive Implication
pp 57-71
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5 - Negation
pp 72-90
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6 - Complete Implication-Negation Logic
pp 91-110
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7 - Disjunction
pp 111-130
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8 - Conjunction
pp 131-145
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9 - Multi-Connective Systems
pp 146-179
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10 - Strict Implications: Introduction
pp 180-205
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11 - Strict Implications: Additional Results
pp 206-237
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12 - Quantification and First-Order Logic
pp 238-259
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13 - Quantification and Complete Logics
pp 260-284
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14 - Quantification and Incomplete Logics
pp 285-293
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15 - Interpretation of Formal Systems
pp 294-302
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Appendix: Historical and Bibliographical Remarks
pp 303-314
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Subject Index
pp 315-318
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Index of Systems
pp 319-319
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Index of Symbols
pp 320-320
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Systems of Logic

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Preface
pp ix-xii

1 - Formal Systems and Structure Theory
pp 1-15

2 - Zero-Order Logic: Proof Theory
pp 16-37

3 - Zero-Order Model Theory
pp 38-56

4 - Positive Implication
pp 57-71

5 - Negation
pp 72-90

6 - Complete Implication-Negation Logic
pp 91-110

7 - Disjunction
pp 111-130

8 - Conjunction
pp 131-145

9 - Multi-Connective Systems
pp 146-179

10 - Strict Implications: Introduction
pp 180-205

11 - Strict Implications: Additional Results
pp 206-237

12 - Quantification and First-Order Logic
pp 238-259

13 - Quantification and Complete Logics
pp 260-284

14 - Quantification and Incomplete Logics
pp 285-293

15 - Interpretation of Formal Systems
pp 294-302

Appendix: Historical and Bibliographical Remarks
pp 303-314

Subject Index
pp 315-318

Index of Systems
pp 319-319

Index of Symbols
pp 320-320

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Systems of Logic

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