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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 c.
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore :
World Scientific Publishing Company,
2011.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; 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; 1.4.1 Curry-Howard; 1.4.2 Lambek and the substructural hypothesis; 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; Part I. Truth-Conditional Meaning; 2. Compositional Approaches and Binding; 2.1 Representing Logical Meaning: The Binding Issue; 2.1.1 The syntactic notion of binding.
- 2.1.2 The semantic notion of binding2.1.3 The model-theoretic notion of binding; 2.2 Syntactic Derivations and Semantic Composition; 2.3 MontagueGrammar Revisited; 2.3.1 Fromrules to sequents; 2.3.2 On relatives and quantification; 2.3.3 Examples; 2.3.4 On binding; 2.4 A Theory of Simple Types; 2.5 Heim and Kratzer's Theory; 2.5.1 Interpreting derivation trees; 2.5.2 Predicate modification; 2.5.3 Variables and binding; 2.5.4 Towards a proof-theoretic account of binding; 3. Derivationalism; 3.1 Introduction; 3.2 Categorial Grammars; 3.3 The (Pure) Lambek Calculus.
- 3.3.1 The mathematics of sentence structure3.3.2 A categorical system; 3.4 Minimalist Grammars; 3.4.1 Minimalist principles; 3.4.2 Features; 3.4.3 Minimalist grammars; 3.4.4 Merge; 3.4.5 Move; 3.4.6 Minimalist grammars and categorial grammars; 3.4.7 Binding as "Cooper storage"; 3.4.8 The interpretation of derivational trees; 3.4.9 The semantic interpretation of Merge; 3.4.10 The semantic interpretation of Move; 3.5 Concluding Remarks; Part II. Logic; 4. Deductive Systems; 4.1 Fitch's Natural Deduction System; 4.1.1 Conjunction; 4.1.2 Implication; 4.1.3 Disjunction; 4.1.4 Negation.
- 4.2 Natural Deduction in Intuitionistic Logic4.2.1 Tree format; 4.2.2 Normalization; 4.2.3 Sequent format; 4.3 Intuitionistic Sequent Calculus; 4.3.1 Structural rule; 4.3.2 Identity rules; 4.3.3 Logical rules; 4.3.4 An example of a proof in intuitionistic logic; 4.3.5 The cut rule; 4.3.6 Lists and sets; 4.3.7 Structural rules; 4.4 Classical Sequent Calculus; 4.4.1 Structural rules; 4.4.2 Identity rules; 4.4.3 Logical rules .; 4.5 Some Properties of the Sequent Calculus; 4.5.1 Subformula property; 4.5.2 Cut-elimination; 4.6 Linear Logic; 4.6.1 Identity rules; 4.6.2 Logical rules.
- 4.6.3 Exponentials4.6.4 Constants; 4.6.5 The one-sided calculus; 4.6.6 Intuitive interpretation; 4.7 Back to the Lambek Calculus; 4.7.1 The Lambek calculus as non-commutative linear logic; 4.8 Linguistic Applications of the Additives; 4.9 ProofNets; 4.9.1 A geometrization of logic; 4.9.2 Cut-elimination in 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; Part III. Proof Theory Applied to Linguistics.