I am interested in giving a course on Computational Semantics and Natural Language Processing (NLP).

It should provide an introduction to modern logical and grammatical theories for natural language.

A possible textbook is Bob Carpenter: Type-Logical Semantics, MIT Press 1997.

Based on an introductory course on natural-language semantics, this book provides an introduction to type-logical grammar and the range of linguistic phenomena that can be handled in categorial grammar.

It also contains a great deal of original work on categorial grammar and its application to natural-language semantics.

The author chose the type-logical categorial grammar as his grammatical basis because of its broad syntactic coverage and its strong linkage of syntax and semantics.

Although its basic orientation is linguistic, the book should also be of interest to logicians and computer scientists seeking connections between logical systems and natural language.

*Table of Contents*

Preface Acknowledgments 1 Introduction 1.1 Truth and Reference 1.1.1 Truth 1.1.2 Reference 1.1.3 Conventionalism and Realism 1.2 Topics in Semantics 1.2.1 Synonymy, Entailment, and Contradiction 1.2.2 Presupposition 1.2.3 Ambiguity and Vagueness 1.2.4 Indexicality and the Situation of an Utterance 1.2.5 Sense and Reference 1.2.6 Lexical Semantics 1.3 Topics in Pragmatics 1.3.1 Conversational Implicature 1.3.2 Speech Acts 1.3.3 Discourse Structure 1.3.4 Metaphors, Idioms, and Language Change 1.4 Methodology 1.4.1 Productivity 1.4.2 Compositionality 1.4.3 Model Theory and Grammar Fragments Exercises 2 Simply Typed l-Calculus 2.1 Simple Types 2.2 l-Terms 2.3 Functional Models 2.3.1 Frames 2.3.2 Models 2.4 Proof Theory for Simply Typed l-Calculus 2.5 Combinators and Variable-Free Logic 2.6 Products 2.7 Sums Exercises 3 Higher-Order Logic 3.1 Higher-Order Syntax 3.2 Higher-Order Models 3.3 Quantifiers in Natural Language 3.3.1 A Compositional Approach to Quantifiers 3.3.2 Properties of Natural-Language Quantifiers 3.4 Negative Polarity Items 3.5 Definite Descriptions 3.5.1 Quantificational Definites 3.5.2 Referential Definites 3.5.3 Contextual Elaboration 3.5.4 Nominal Type Shifting 3.6 Proof Theory for Higher-Order Logic Exercises 4 Applicative Categorial Grammar 4.1 The Category System 4.2 Semantic Domains 4.3 Categorial Lexicons 4.4 Phrase Structure 4.5 A Categorial Lexicon 4.6 Tree Admissibility 4.7 Ambiguity, Vagueness, and Meaning Postulates 4.7.1 Lexical Ambiguity and Vagueness 4.7.2 Derivational Ambiguity 4.7.3 Local and Global Ambiguity 4.7.4 Meaning Postulates Exercises 5 The Lambek Calculus 5.1 Lambek's Sequent Calculus 5.1.1 Applicative Fragment 5.1.2 Abstraction Schemes 5.1.3 Associativity, Cut Elimination, and Decidability 5.2 The Natural-Deduction Lambek Calculus 5.2.1 Applicative Natural Deduction 5.2.2 The Natural-Deduction Lambek Calculus 5.2.3 Proof Normalization 5.3 Products 5.4 Categorial Grammar Aas Logic 5.4.1 Substructural Logic 5.4.2 The Curry-Howard Isomorphism Exercises 6 Coordination and Unbounded Dependencies 6.1 Coordination 6.1.1 Boolean Coordination 6.1.2 Distributivity and Type Raising 6.1.3 Nonconstituent Coordination 6.2 Conjunctive and Disjunctive Categories 6.2.1 The Conjunction Constructor 6.2.2 The Disjunction Constructor 6.2.3 Natural-Deduction Conjunction and Disjunction 6.2.4 Copular Complements and Predicatives 6.2.5 Incompleteness of Conjunction and Disjunction 6.3 Unbounded Dependency Constructions 6.3.1 The Lambek Calculus and Unbounded Dependencies 6.3.2 "Disharmonic" Combinations 6.3.3 Moortgat's Approach to Unboundedness 6.3.4 Islands and Extractability 6.3.5 Incompleteness of the Extraction Constructor Exercises 7 Quantifiers and Scope 7.1 Quantifying In 7.2 Cooper Storage 7.3 Scoping Constructor 7.4 Type Raising and Quantifier Coordinations 7.5 Embedded Quantifiers 7.6 Quantifiers and Coordinate Structures 7.7 Quantification and Negation 7.8 Quantification and Definite Descriptions 7.9 Possessives 7.10 Indefinites 7.11 Generics 7.12 Comparatives 7.12.1 Gradability and Measurability 7.12.2 The Grammar of Comparatives 7.13 Expletives and the Unit Type Exercises 8 Plurals 8.1 An Ontology of Groups 8.2 A Plural Grammar 8.3 Distributors and Collectors 8.4 Coordination, Negation, and Argument Lowering 8.5 Adverbial Distribution 8.6 Plural Quantification 8.7 Partitives and Pseudopartitives 8.8 Nonboolean Coordination 8.9 Comitative Complements 8.10 Mass Terms Exercises 9 Pronouns and Dependency 9.1 Pronouns and Reflexives 9.2 Pronouns and Agreement 9.3 Pronouns as Variables 9.4 A Quantificational Approach to Reflexives 9.5 Plural Pronouns 9.6 Reciprocals and Generalized Quantification 9.7 Pied Piping 9.8 Ellipsis and Sloppy Anaphora 9.9 Interrogatives Exercises 10 Modal Logic 10.1 Modes of Truth 10.2 S5: A Modal Logic of Necessity 10.2.1 The Model Theory of S5 10.2.2 S5 Proof Theory 10.3 Indexicality 10.4 General Modal Logics 10.4.1 Classifying Modal Logics 10.5 Strict Implication and Counterfactuals 10.6 First-Order Tense Logics 10.7 Tense Logic And Natural Language 10.8 Temporal-Period Structures 10.8.1 Constructing Periods from Moments 10.8.2 Constructing Moments from Periods 10.8.3 Duration and Measure 10.9 Higher-Order Modal Logic Exercises 11 Intensionality 11.1 An Intensional Grammar 11.1.1 Type Logic and Categorial Grammar 11.1.2 Propositional Attitudes 11.1.3 Complementized Sentences 11.1.4 Sentential, Infinitival, and Gerundive Subjects 11.1.5 Nominalization, Self-Reference, and Semantic Paradoxes 11.1.6 Gerunds, Naked Infinitives, and Event-Based Semantics 11.1.7 Modal Adverbs and Modal Auxiliaries 11.1.8 Control Verbs 11.1.9 Control Predicatives 11.1.10 Nonobligatory Control and Purpose Clauses 11.1.11 Intensional Transitive Verbs 11.1.12 Intensional Adjectives 11.2 Individual Concepts and Quantificational Definites 11.2.1 Definite Descriptions and Scope 11.2.2 Individual Concepts and Rigid Designation 11.3 Alternatives to Possible Worlds 11.3.1 Logical Omniscience and the Granularity of Propositions 11.3.2 Quotational Theories 11.3.3 Structured Meanings and General Intensional Models 11.3.4 Situation Semantics 11.3.5 Truth-Value Gaps and Partial Possible Worlds 11.4 Lexical Relations Exercises 12 Tense and Aspect 12.1 Reichenbach's Approach to Simple and Perfect Tenses 12.2 Tense and Discourse 12.3 Vendler's Verb Classes 12.4 A Semantic Approach to Aspect 12.5 A Grammar of Tense and Aspect 12.5.1 Verb Forms 12.5.2 Simple Finite Verbs and Auxiliary Verbs 12.5.3 Intersective Temporal Modifiers 12.5.4 The Perfect 12.5.5 The Progressive 12.5.6 Tense and Nominal Quantification 12.5.7 Tense, Nominals, and Quantification 12.5.8 Adverbs of Quantification and Negation Exercises Appendix A Mathematical Preliminaries A.1 Set Theory A.2 Functions and Relations A.3 Orderings, Well Orderings, and Lattices A.4 Proof by Induction A.5 Formal Languages A.6 Trees A.7 First-Order Logic A.7.1 First-Order Terms and Formulas A.7.2 First-Order Model Theory A.7.3 First-Order Proof Theory A.8 Algebras and Equality A.8.1 Algebras A.8.2 Boolean Algebras A.8.3 First-Order Logic with Equality References Index