Meaning, Logic and Ludics

1. Introduction. 1.1. The logical space of meaning. 1.2. The aim of this book. 1.3. Starting from traditional formal semantics. 1.4. Semantics and the History of Logic (1) : Intuitionism. 1.5. 1.5. Semantics and the History of Logic (2) : Classicism. 1.6. Semantics and the History of Logic (3) : Linear logic. 1.7. Presentation of the book -- pt. I. Truth-conditional meaning. 2. Compositional approaches and binding. 2.1. Representing logical meaning : The binding issue. 2.2. Syntactic derivations and semantic composition. 2.3. Montague grammar revisited. 2.4. A theory of simple types. 2.5. Heim and Kratzer's theory. 3. Derivationalism. 3.1. Introduction. 3.2. Categorial grammars. 3.3. The (pure) Lambek Calculus. 3.4. Minimalist grammars. 3.5. Concluding remarks -- pt. II. Logic. 4. Deductive systems. 4.1. Fitch's natural deduction system. 4.2. Natural deduction in intuitionistic logic. 4.3. Intuitionistic sequent calculus. 4.4. Classical sequent calculus. 4.5. Some properties of the sequent calculus. 4.6. Linear logic. 4.7. Back to the Lambek Calculus. 4.8. Linguistic applications of the additives. 4.9. Proof nets. 4.10. Proof nets for the Lambek Calculus. 4.11. Concluding remarks. 5. Curry-Howard correspondence. 5.1. Introduction. 5.2. A correspondence between types and formula. 5.3. An example of a combinator. 5.4. Concluding remarks -- pt. III. Proof theory applied to linguistics. 6. Using the Lambek Calculus and its variants. 6.1. Introduction. 6.2. Using the Lambek Calculus. 6.3. Flexible types. 6.4. Non-associative Lambek Calculus. 6.5. Semantics of the Lambek Calculus. 6.6. An extension of the Lambek Calculus : The Lambek-Grishin Calculus