Displaying Modal Logic

1. Front Matter

   Pages i-xi

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2. Introduction

   • Heinrich Wansing

   Pages 1-14

3. Sequents Generalized

   • Heinrich Wansing

   Pages 15-25

4. Display Logic

   • Heinrich Wansing

   Pages 27-46

5. Properly Displayable Logics, Displayable Logics and Strong Cut-Elimination

   • Heinrich Wansing

   Pages 47-64

6. A Proof-Theoretic Proof of Functional Completeness for Many Modal and Tense Logics

   • Heinrich Wansing

   Pages 65-73

7. Modal Tableaux Based on Residuation

   • Heinrich Wansing

   Pages 75-85

8. Strong Cut-Elimination and Labelled Modal Tableaux

   • Heinrich Wansing

   Pages 87-102

9. Tarskian Structured Consequence Relations and Functional Completeness

   • Heinrich Wansing

   Pages 103-126

10. Constructive Negation and the Modal Logic of Consistency

    • Heinrich Wansing

    Pages 127-154

11. Displaying as Temporalizing

    • Heinrich Wansing

    Pages 155-170

12. Translation of Hypersequents into Display Sequents

    • Heinrich Wansing

    Pages 171-187

13. Predicate Logics on Display

    • Heinrich Wansing

    Pages 189-210

14. Appendix

    • Heinrich Wansing

    Pages 211-234

15. Back Matter

    Pages 235-252

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The present monograph is a slightly revised version of my Habilitations­ schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics, successfully defended at Leipzig University, November 1997. It collects work on proof systems for modal and constructive logics I have done over the last few years. The main concern is display logic, a certain refinement of Gentzen's sequent calculus developed by Nuel D. Belnap. This book is far from offering a comprehensive presentation of generalized sequent systems for modal logics broadly conceived. The proof-theory of non-classical logics is a rapidly developing field, and even the generalizations of the ordinary notion of sequent listed in Chapter 1 can hardly be presented in great detail within a single volume. In addition to further investigating the various approaches toward generalized Gentzen systems, it is important to compare them and to discuss their relative advantages and disadvantages. An initial attempt at bringing together work on different kinds of proof systems for modal logics has been made in [188]. Another step in the same direction is [196]. Since Chapter 1 contains introductory considerations and, moreover, every remaining chapter begins with some surveying or summarizing remarks, in this preface I shall only emphasize a relation to philosophy that is important to me, register the sources of papers that have entered this book in some form or another, and acknowledge advice and support.

• Cut-elimination theorem
• Extension
• logic
• modal logic
• nonmonotonic reasoning
• predicate logic
• proof
• semantics
• sequent calculus

• Institute of Logic and Philosophy of Science, University of Leipzig, Leipzig, Germany

  Heinrich Wansing

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