In this book we hope to acquaint the reader with the fundamentals of truth conditional model-theoretic semantics, and in particular with a version of this developed by Richard Montague in a series of papers published during the 1960's and early 1970's. In many ways the paper 'The Proper Treatment of Quantification in Ordinary English' (commonly abbreviated PTQ) represents the culmination of Montague's efforts to apply the techniques developed within mathematical logic to the semantics of natural languages, and indeed it is the system outlined there that people generally have in mind when they refer to "Montague Grammar". (We prefer the term "Montague Semantics" inasmuch as a grammar, as conceived of in current linguistics, would contain at least a phonological component, a morphological component, and other subsystems which are either lacking entirely or present only in a very rudi mentary state in the PTQ system. ) Montague's work has attracted increasing attention in recent years among linguists and philosophers since it offers the hope that semantics can be characterized with the same formal rigor and explicitness that transformational approaches have brought to syntax. Whether this hope can be fully realized remains to be seen, but it is clear nonetheless that Montague semantics has already established itself as a productive para digm, leading to new areas of inquiry and suggesting new ways of conceiving of theories of natural language. Unfortunately, Montague's papers are tersely written and very difficult to follow unless one has a considerable background in logical semantics.

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Introduction.- 2. The Syntax and Semantics of Two Simple Languages.- I. The Language L0.- 1. Syntax of L0.- 2. Semantics of L0.- II. The Language L0E.- 1. Syntax of L0E.- 2. Semantics of L0E.- 3. Alternative Formulations of L0E and L0.- III. A Synopsis of Truth-Conditional Semantics.- IV. The Notion of Truth Relative to a Model.- V. Validity and Entailment Defined in Terms of Possible Models.- VI. Model Theory and Deductive Systems.- Exercises.- Note.- 3. First-Order Predicate Logic.- I. The Language L1.- 1. Syntax of L1.- 2. Semantics of L1.- II. The Language L1E.- 1. Syntax of L1E.- 2. Semantics of L1E.- Exercises.- Notes.- 4. A Higher-Order Type-Theoretic Language.- I. A Notational Variant of L1.- II. The Language Ltype.- 1. Syntax of Ltype.- 2. Semantics of Ltype.- III. Lambda Abstraction and the Language L?.- Exercises.- Notes.- 5. Tense and Modal Operators.- I. Tense Operators and Their Interpretation.- II. The Other Varieties of Modal Logic; the Operators ? and ?.- III. Languages Containing Both Tense and Modal Operators: Coordinate Semantics.- Exercises.- Notes.- 6. Montague's Intensional Logic.- I. Compositionality and the Intension-Extension Distinction.- II. The Intensional Logic of PTQ.- 1. Syntax of IL.- 2. Semantics of IL.- III. Examples of 'Oblique Contexts' as Represented in IL.- IV. Some Unresolved Issues with Possible Worlds Semantics and Propositional Attitudes.- Notes.- 7. The Grammar of PTQ.- I. The Overall Organization of the PTQ Grammar.- 1. The Syntactic Categories of English in the PTQ Grammar.- 2. The Correspondence Between Categories of English and Types of IL.- II. Subject-Predicate and Determiner-Noun Rules.- III. Conjoined Sentences, Verb Phrases, and Term Phrases.- IV. Anaphoric Pronouns as Bound Variables; Scope Ambiguities and Relative Clauses.- V. Be, Transitive Verbs, Meaning Postulates, and Non-Specific Readings.- VI. Adverbs and Infinitive Complement Verbs.- VII. De dicto Pronouns and Some Pronoun Problems.- VIII. Prepositions, Tenses, and Negation.- Exercises.- Notes.- 8. Montague's General Semiotic Program.- 9. An Annotated Bibliography of Further Work in Montague Semantics.- Appendix I: Index of Symbols.- Appendix II: Variable Type Conventions for Chapter 7.- Notes.- References.- Answers to Selected Problems and Exercises.