Meaning, Logic and Ludics

This book presents several recent advances in natural language semantics and explores the boundaries between syntax and semantics over the last two decades. It is based on some of the most recent theories in logic, such as linear logic and ludics, first created by Jean-Yves Girard, and it also provides some sharp analyses of computational semantical representations, explaining advanced theories in theoretical computer sciences, such as the lambda-mu and Lambek-Grishin calculi which were applied by Philippe de Groote and Michael Moortgat. The author also looks at Aarne Ranta's “proof as meaning”; approach, which was first based on Martin-Löf's Type Theory. Meaning, Logic and Ludics surveys the many solutions which have been proposed for the syntax-semantics interface, taking into account the specifications of linguistic signs (continuous or discontinuous) and the fundamental mechanisms developed by linguists and notable Generativists. This pioneering publication also presents ludics (in a chapter co-authored with Myriam Quatrini), a framework which allows us to characterize meaning as an invariant with regard to interaction between processes. It is an excellent book for advanced students, and academics alike, in the field of computational linguistics. 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 This book presents several recent advances in natural language semantics and explores the boundaries between syntax and semantics over the last two decades. It is based on some of the most recent theories in logic, such as linear logic and ludics, first created by Jean-Yves Girard, and it also provides some sharp analyses of computational semantical representations, explaining advanced theories in theoretical computer sciences, such as the lambda-mu and Lambek-Grishin calculi which were applied by Philippe de Groote and Michael Moortgat. The author also looks at Aarne Ranta's 'proof as meaning' approach, which was first based on Martin-Lof's Type Theory. Meaning, Logic and Ludics surveys the many solutions which have been proposed for the syntax-semantics interface, taking into account the specifications of linguistic signs (continuous or discontinuous) and the fundamental mechanisms developed by linguists and notable Generativists. This pioneering publication also presents ludics (in a chapter co-authored with Myriam Quatrini), a framework which allows us to characterize meaning as an invariant with regard to interaction between processes. It is an excellent book for advanced students and academics alike, in the field of computational linguistics 7. Grammatical reasoning. 7.1. Motivations. 7.2. Modal preliminary. 7.3. Residuation and modalities. 7.4. Linguistic applications. 7.5. Back to quantification. 7.6. Kripke semantics. 7.7. Concluding remarks and observations. 8. A type-theoretical version of minimalist grammars. 8.1. Inserting chains. 8.2. Head movement. 8.3. Adjoining and scrambling. 8.4. Semantics without cooper storage. 8.5. Concluding remarks : Some tracks to explore. 9. Grammars in deductive forms. 9.1. Introduction. 9.2. Convergent grammars. 9.3. Labelled linear grammars. 9.4. Binding in LLG. 9.5. On phases. 9.6. Comparing CVG and LLG. 9.7. Concluding remarks. 10. Continuations and contexts. 10.1. The use of continuations in semantics. 10.2. Symmetric calculi. 10.3. Concluding remarks and further works. 11. Proofs as meanings. 11.1. From intuitionistic logic to constructive type theory. 11.2. Formalizing Montague grammar in constructive type theory. 11.3. Dynamical interpretation and anaphoric expressions. 11.4. From sentences to dialogue -- pt. IV. Ludics. 12. Interaction and dialogue. 12.1. Dialogue and games. 12.2. Ludics. 12.3. Behaviours. 13. The future in conclusion Intends to present several main advances in Natural Language Semantics and the interface between syntax and semantics, based on logical theories of linear logic and ludics, and on sharp analyses of computing due to advanced theories in Theoretical Computer Sciences. Alain Lecomte. Contains Bibliographical References (p. 353-361) And Index.