| An Overview of the Sequent Calculus | |
| What Is a Good Sequent Calculus? | p. 3 |
| The Sequent Calculus Gc1 | p. 3 |
| Formal Remarks | p. 7 |
| Philosophical Remarks | p. 12 |
| Analyticity | p. 12 |
| Logicality | p. 14 |
| From Logicality to Inferentialism | p. 16 |
| Harmony | p. 18 |
| Inferentialism | p. 20 |
| Concluding Remarks | p. 21 |
| Subformula Property | p. 22 |
| Admissibility of the Structural Rules | p. 24 |
| Operational vs Global Meaning | p. 26 |
| Admissibility of the Logical Rules | p. 28 |
| Explicitness, Separation and Symmetry | p. 28 |
| Uniqueness | p. 29 |
| Syntactic Purity | p. 29 |
| Dosen's Principle Redefined | p. 31 |
| Modularity | p. 34 |
| Sequent Calculi for Modal Logic | |
| Modal Logic and Ordinary Sequent Calculi | p. 39 |
| Normal Modal Logic | p. 39 |
| Ordinary Sequent Calculi for Modal Logic | p. 45 |
| The Idea of Generalising the Gentzen Calculus | p. 51 |
| Purely Syntactic Methods | p. 55 |
| Multiple Sequent Calculi | p. 56 |
| Higher-Arity Sequent Calculi | p. 62 |
| Display Sequent Calculi | p. 66 |
| Semantic Methods | p. 75 |
| Semantic Modal Sequent Calculi | p. 76 |
| Indexed Sequent Calculi | p. 84 |
| Internalised Forcing (Relation) Sequent Calculi | p. 92 |
| Comparing the Different Generalisations of the Sequent Calculus | p. 101 |
| From Multiple Sequent Calculi to Display Sequent Calculi | p. 101 |
| From Higher-Arity Sequent Calculi to Display Sequent Calculi | p. 104 |
| From Indexed Sequent Calculi to Internalised Forcing Sequent Calculi | p. 107 |
| From Indexed Sequent Calculi to Semantic Modal Sequent Calculi and Vice Versa | p. 112 |
| From Display Sequent Calculi to Internalised Forcing Sequent Calculi | p. 113 |
| Tree-Hypersequent Calculi | |
| On the Tree-Hypersequent Calculi | p. 119 |
| The Calculi Thsk* | p. 122 |
| Logical Variant of the Tree-Hypersequent Calculi | p. 126 |
| Adequacy of the Tree-Hypersequent Calculi | p. 138 |
| Syntactic Cut-Admissibility and Decidability | p. 143 |
| Cut-Admissibility in the Tree-Hypersequent Calculi | p. 143 |
| Decidability of the Tree-Hypersequent Calculi | p. 156 |
| Semantic Adequacy | p. 165 |
| Semantic Validity of the Tree-Hypersequent Calculi | p. 165 |
| Semantic Completeness of the Tree-Hypersequent Calculi | p. 170 |
| A Hypersequent Calculus for the System S5 | p. 175 |
| The Calculus ThS5L | p. 176 |
| Admissibility of the Structural Rules in ThS5L | p. 177 |
| Adequacy of ThS5L | p. 180 |
| Cut-Admissibility in ThS5L | p. 181 |
| Decidability of ThS5L | p. 183 |
| A Tree-Hypersequent Calculus for the Modal Logic of Provability | p. 187 |
| The Calculus ThsglL | p. 187 |
| Admissibility of the Structural Rules in ThsglL | p. 188 |
| Adequacy of ThsglL | p. 193 |
| Cut-Admissibility in ThsglL | p. 196 |
| Further Results on Tree-Hypersequent Calculi | p. 203 |
| Tree-Hypersequent Calculi and Other Calculi | p. 203 |
| Tree-Hypersequent Calculi and Other Logics | p. 206 |
| Tree-Hypersequent Calculi and Further Developments | p. 207 |
| References | p. 209 |
| Symbols and Notations | p. 215 |
| Index | p. 219 |
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