| Preface | p. ix |
| The philosophy of substructural logics | |
| The role of structural rules in sequent calculi | p. 3 |
| The "inferential approach" to logical calculus | p. 3 |
| Structural rules, operational rules, and meaning | p. 5 |
| Discovering the effects of structural rules | p. 11 |
| Reasons for dropping structural rules | p. 15 |
| Reasons for dropping structural rules altogether | p. 15 |
| Reasons for dropping (or eliminating) the cut rule | p. 17 |
| Reasons for dropping the weakening rules | p. 21 |
| Reasons for dropping the contraction rules | p. 25 |
| Reasons for dropping the exchange rules | p. 28 |
| Reasons for dropping the associativity of comma | p. 30 |
| Ways of reading a sequent | p. 30 |
| The truth-based reading | p. 31 |
| The proof-based reading | p. 31 |
| The informational reading | p. 32 |
| The "Hobbesian" reading | p. 34 |
| The proof theory of substructural logics | |
| Basic proof systems for substructural logics | p. 41 |
| Some basic definitions and notational conventions | p. 42 |
| Sequent calculi | p. 44 |
| The calculus LL | p. 44 |
| Adding the empty sequent: the dialethic route | p. 49 |
| Adding the lattice-theoretical constants: the bounded route | p. 49 |
| Adding contraction: the relevant route | p. 50 |
| Adding weakening: the affine route | p. 55 |
| Adding restricted structural rules | p. 57 |
| Adding the exponentials | p. 65 |
| Hilbert-style calculi | p. 68 |
| Presentation of the systems | p. 68 |
| Derivability and theories | p. 73 |
| Lindenbaum-style constructions | p. 81 |
| Equivalence of the two approaches | p. 83 |
| Cut elimination and the decision problem | p. 87 |
| Cut elimination | p. 87 |
| Cut elimination for LK | p. 87 |
| Cut elimination for calculi without the contraction rules | p. 94 |
| Cut elimination for calculi without the weakening rules | p. 97 |
| Cases where cut elimination fails | p. 99 |
| The decision problem | p. 100 |
| Gentzen's method for establishing the decidability of LK | p. 101 |
| A decision method for contraction-free systems | p. 105 |
| A decision method for weakening-free systems | p. 106 |
| Other decidability (and undecidability) results | p. 111 |
| Other formalisms | p. 115 |
| Generalizations of sequent calculi | p. 116 |
| N-sided sequents | p. 116 |
| Hypersequents | p. 121 |
| Dunn-Mints calculi | p. 127 |
| Display calculi | p. 130 |
| A comparison of these frameworks | p. 136 |
| Proofnets | p. 137 |
| Resolution calculi | p. 145 |
| Classical resolution | p. 146 |
| Relevant resolution | p. 149 |
| Resolution systems for other logics | p. 153 |
| The algebra of substructural logics | |
| Algebraic structures | p. 159 |
| *-autonomous lattices | p. 161 |
| Definitions and elementary properties | p. 161 |
| Notable *-autonomous lattices | p. 165 |
| Homomorphisms, l-filters, l-ideals, congruences | p. 171 |
| Principal, prime and regular l-ideals | p. 181 |
| Representation theory | p. 186 |
| Classical residuated lattices | p. 187 |
| Maximal, prime, and primary l-ideals | p. 188 |
| Subdirectly irreducible c.r. lattices | p. 190 |
| Weakly simple, simple and semisimple c.r. lattices | p. 192 |
| The semantics of substructural logics | |
| Algebraic semantics | p. 201 |
| Algebraic soundness and completeness theorems | p. 202 |
| Calculi without exponentials | p. 203 |
| Calculi with exponentials | p. 209 |
| Totally ordered models and the single model property | p. 213 |
| Applications | p. 219 |
| Relational semantics | p. 221 |
| Semantics for distributive logics | p. 222 |
| Routley-Meyer semantics: definitions and results | p. 223 |
| Applications | p. 235 |
| Semantics for nondistributive logics | p. 239 |
| General phase structures | p. 240 |
| General phase semantics | p. 250 |
| The exponentials | p. 252 |
| Applications | p. 254 |
| Basic glossary of algebra and graph theory | p. 257 |
| Other substructural logics | p. 271 |
| Lambek calculus | p. 271 |
| Ono's subintuitionistic logics | p. 277 |
| Basic logic | p. 281 |
| Bibliography | p. 289 |
| Index of subjects | p. 301 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
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