Displaying Modal Logic

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Springer Science & Business Media, 14.03.2013 - 252 Seiten
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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.
 

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Inhalt

CHAPTER THREE DISPLAY LOGIC
27
CHAPTER FOUR PROPERLY DISPLAYABLE LOGICs
47
CHAPTER FIVE A PROOFTHEORETIC PROOF
65
CHAPTER SIX MoDAL TABLEAUx BASED ON RESIDUATION
75
CHAPTER SEVEN STRONG CUTELIMINATION
87
CHAPTER EIGHT TARSKIAN STRUCTURED CONSEQUENCE
103
CHAPTER NINE CONSTRUCTIVE NEGATION AND THE MODAL
127
CHAPTER TEN DISPLAYING As TEMPORALIZING
155
CHAPTER ELEVEN TRANSLATION OF HYPERSEQUENTs
171
CHAPTER TWELVE PREDICATE LOGICs on DISPLAY
189
CHAPTER THIRTEEN APPENDIx
211
BIBLIOGRAPHY
235
INDEX
247
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