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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.
Many textbooks in formal semantics are all versions of, or introductions to, the same paradigm in semantic theory: Montague Grammar. Knowledge of Meaning is based on different assumptions and a different history. It provides the only introduction to truth-theoretic semantics for natural languages, fully integrating semantic theory into the modern Chomskyan programme in linguistic theory and connecting linguistic semantics to research elsewhere in cognitive psychology and philosophy. As such, it better fits into a modern graduate or undergraduate programme in linguistics, cognitive science, or philosophy. Furthermore, since the technical tools it employs are much simpler to teach and to master, Knowledge of Meaning can be taught by someone who is not primarily a semanticist.
This book is an introduction to the current developments in model-theoretic semantics, which has become an essential part of the work in theoretical linguistics over the last decade. The author examines the model structure of Montague's theory and then presents elaborations on this basic model that have been of particular importance in the last few years: generalized quantifiers, the introduction of more structure in the domain of individuals, properties as primitive elements in the model, situations and similar 'smaller' worldlike entities. Nothing is presupposed about knowledge of the mathematical and logical tools used in formal semantics, and Bach presents the informal with a minimum of formalism.
Introducing some of the foundational concepts, principles and techniques in the formal semantics of natural language, Elements of Formal Semantics outlines the mathematical principles that underlie linguistic meaning. Making use of a wide range of concrete English examples, the book presents the most useful tools and concepts of formal semantics in an accessible style and includes a variety of practical exercises so that readers can learn to utilise these tools effectively. For readers with an elementary background in set theory and linguistics or with an interest in mathematical modelling, this fascinating study is an ideal introduction to natural language semantics. Designed as a quick yet thorough introduction to one of the most vibrant areas of research in modern linguistics today this volume reveals the beauty and elegance of the mathematical study of meaning.
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. The book, which stepwise develops successively more powerful logical and grammatical systems, covers an unusually broad range of material. Topics covered include higher-order logic, applicative categorial grammar, the Lambek calculus, coordination and unbounded dependencies, quantifiers and scope, plurals, pronouns and dependency, modal logic, intensionality, and tense and aspect. The book contains more mathematical development than is usually found in texts on natural language; an appendix includes the basic mathematical concepts used throughout the book.
Muskens radically simplifies Montague Semantics and generalises the theory by basing it on a partial higher order logic resulting in a theory which combines important aspects of Montague Semantics and Situation Semantics. Richard Montague formulated the revolutionary insight that we can understand the concept of meaning in ordinary languages much in the same way as we understand the semantics of logical languages. Unfortunately, he formalised his idea in an unnecessarily complex way. The present work does away with unnecessary complexities, obtains a streamlined version of the theory, shows how partialising the theory automatically provides us with the most central concepts of Situation Semantics, and offers a simple logical treatment of propositional attitude verbs, perception verbs and proper names.
Montague Grammar is a collection of papers that discusses Richard Montague's work on the syntax and semantics of natural languages. The papers examine the applications of Montague's theory to problems of syntax and semantics, and compares Montague's approach to other theories of language. One paper describes the features in Montague's "The Proper Treatment of Quantification in Ordinary English" (PTQ), namely, the grammatical categories and lexicon, the rules most similar to CF-rules, and the treatment of quantification. Another paper presents mechanisms to Montague's grammatical framework which will allow a variety of English constructions—especially those involving sentence embedding. The paper discusses syntactic rules, such as noun phrases, verb phrases, subject-predicate sentences, variable binding, abstracts, verbs taking infinitive complements, the copula, participles. One paper describes a fragment of English that is a variation and extension of the fragment presented in Montague. It also analyses adjectival phrases, three-place and other kinds of verbs, the passive voice, reflexive pronouns, and sentences using the dummy subject "it." Another paper proposes rules, syntactics, and semantics for use in nonrestrictive clauses in a Montague grammar. One paper analyzes factives, their semantic and syntactic properties using the work of Kiparsky and Kiparsky (1971). Montague's "Universal Grammar" (UG) invokes expositions of Montague syntax, Cooper syntax, theorems on conversion process, semantic interpretation, semantic equivalence of the two systems, and interpretive semantics. The collection is intended for readers of Montague, as well as for linguists, philosophers, and students of language.