CONTENTS

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PREFACE

   
1. A NOTE ON NOTATION
 
  Introduction
  Detachment substitution and 'application'
  The 'D-notation'
   
2. GROUNDWORK -- THE PROPOSITIONAL CALCULUS
 
  Building blocks
  Implicational systems -- positive implication
  Deduction
  Some ICI theses
  The semisubstitutivity of implication
  Classical implication
  Conjunction
  The full positive logic
  Classical C-K-A -- the redundancy of A
  Negation: the full system IC
  Relationships between IC connectives
  Classical negation: the full system PC
  Alternative bases for PC
   
3. GROUNDWORK--PROPOSITIONAL SEQUENT-LOGIC
 
  Introduction
  Formulas, sequences, and sequents
  Sequent generation
  Sequent-logic and propositional calculus
  The 'normal form' theorem
  The rule of contraction and its elimination
  Inversion of rules
  Contraction elimination once again
   
4. GROUNDWORK -- PROPOSITIONAL LOGIC AND TABLEAUX
 
  Proof tableaux
  Proof tableaux -- formal characterization
  Semantic tableaux
   
5. THE ABSOLUTELY STRICT SYSTEMS -- S1 AND S1
 
  Introduction
  The system S1
  The classical PC in S1
  Further theses and rules of S1
  The semisubstitutivity of strict implication and S1
  The system S1; truth-value systems
  Some work within the system S1
   
6. THE ABSOLUTELY STRICT SYSTEMS -- S2, S2, T, AND T
 
  The system S2
  Semisubstitutivity of strict implication in S2
  Some theorems of S2
  The system S2
  The systems T and T
  Modalities in T and its included systems
   
7. THE ABSOLUTELY STRICT SYSTEMS -- ALTERNATIVE FORMULATIONS
 
  The 'Lemmon style' bases
  Other formulations
   
8. THE ABSOLUTELY STRICT SYSTEMS -- MODAL SEQUENT-LOGIC
 
  Introduction
  Sequent-logic versions of S1 and S1
  The normal-form theorem in LS1 and LS1
  Equivalence of the systems
  Sequent-logic versions of S2 and S2
  Sequent-logic versions of T and T
  Decision procedures and the rule of contraction
  Modalities in T revisited
   
9. THE ABSOLUTELY STRICT SYSTEMS -- TABLEAUX
 
  Modal models
  Tableaux for modal systems
  Tableaux for T and T
  Tableaux for S2 and S2
  Tableaux for S1 and S1
   
10. THE SYSTEMS OF COMPLETE MODALIZATION -- S3 AND S3
 
  The system S3
  Semisubstitutivity of strict implication in S3
  More theorems of S3
  Inclusion, containment, and independence with S3 and S3
  The full system S3
  S3 and complete modalization
  The 'unreasonableness' of S3 and its included systems
   
11. THE SYSTEMS OF COMPLETE MODALIZATION -- S4, S4, AND S5
 
  The system S4
  S4, S4, and the previously discussed systems
  The full system S4
  The system S5
  Complete modalization in S5
   
12. THE SYSTEMS OF COMPLETE MODALIZATION -- ALTERNATIVE FORMULATIONS
 
  The Lemmon-style bases
  Other formulations
  Finite axiomatizability
  Formulations without axioms beyond those of the PC
  The deduction theorem for the systems of this chapter
   
13. THE SYSTEMS OF COMPLETE MODALIZATION -- SEQUENT-LOGIC, THE BASIC SYSTEMS
 
  Sequent-logic for S3 and S4
  The normal form theorem in LS3 and LS4
  The equivalence of the systems
  Sequent-logics for S3 and S4
  The normal form theorem for LS3 and LS4
  A relationship between intuitionist logic and S4
  Sequent-logic for S5
   
14. THE SYSTEMS OF COMPLETE MODALIZATION -- BASIC SYSTEMS OF TABLEAUX
 
  Tableaux for S4 and S4
  Tableaux for S3 and S3
  Tableaux for S5
   
15. THE SYSTEMS OF COMPLETE MODALIZATION -- THE S4-S5 SPECTRUM AND RELATED SYSTEMS
 
  Introduction
  The system S4.3
  The system S4.2
  The Diodorean system D
  S4.4 and some associated systems
  Sobocinski's family K of 'non-Lewis modal' systems
  Semantics for S4.9; the 'last stop' before S5
  Summary
   
APPENDIX: BASES FOR KEY SYSTEMS AND STRUCTURES STUDIED IN THIS BOOK
 
(A) Non-Modal Propositional Calculi
 
(A.1) Standard ('Hilbert-style') axiomatizations
 
(A.1.1) Intuitionistic propositional calculus (IC)
(A.1.2) Classical propositional calculus (PC).
(A.2) Non-modal sequent-logic
(A.3) Semantic tableaux for PC (structure MPC)
   
(B) Modal Calculi
 
(B.1) 'Lewis-style' axiomatizations of S1-S5
(B.2) 'Lemmon-style' bases for S1-S5
(B.3) Systems between S4 and S5, and Sobocinski's 'non-Lewis modal' systems
(B.4) Modal sequent-logic for S1-S5
(B.5) Sequent-logic for systems between S4 and S5
(B.6) Tableaux for Modal Systems
   

BIBLIOGRAPHY

   

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