Displaying Modal Logic
Springer Science & Business Media, 14.03.2013 - 252 Seiten
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 . Another step in the same direction is . 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.
Was andere dazu sagen - Rezension schreiben
Es wurden keine Rezensionen gefunden.
CHAPTER THREE DISPLAY LOGIC
CHAPTER FOUR PROPERLY DISPLAYABLE LOGICs
CHAPTER FIVE A PROOFTHEORETIC PROOF
CHAPTER SIX MoDAL TABLEAUx BASED ON RESIDUATION
CHAPTER SEVEN STRONG CUTELIMINATION
CHAPTER EIGHT TARSKIAN STRUCTURED CONSEQUENCE
CHAPTER NINE CONSTRUCTIVE NEGATION AND THE MODAL
Andere Ausgaben - Alle anzeigen
A D B antecedent application of cut atomic axiom schemata axiomatic basic structural rules Belnap Chapter clause closed tableau conclusion sequent consider cut-formula cut-free defined definition derivation display calculus display logic display sequent disproof equivalent F](A D B finite sets first-order first-order logic formula functionally complete Gabbay's Gentzen H X1 h(II hypersequents implies ind(II induction hypothesis instantiation introduction rules intuitionistic logic KFOL Kripke frame Kripke models Lemma logical operations modal and tense Moreover Mp Dh natural deduction negation as falsity negation as inconsistency nonmonotonic normal modal logic notion obtain occurrence parametric moves predicate logic proof systems proof-theoretic semantics propositional logic provable refutation schema sequent calculus sequent systems single-conclusion strong cut-elimination structural sequent rules structure connectives structure operations subformula property substructural substructural logics succedent position Suppose CT(III tense logic Theorem Y H X