Boolean Semantics for Natural Language


Book Description

In the spring of 1978, one of the authors of this book was sitting in on a course in logic for linguists given by the other author. In attempting to present some of Montague's insights in an elementary way (hopefully avoid ing the notation which many find difficult at first), the authors began dis cussions aimed towards the construction of a simple model-theoretical semantic apparatus which could be applied directly to a small English-like language and used to illustrate the methods of formal logical interpretation. In these discussions two points impressed themselves on us. First, our task could be simplified by using boolean algebras and boolean homomorphisms in the models; and second, the boolean approach we were developing had much more widespread relevance to the logical structure of English than we first thought. During the summer and fall of 1978 we continued work on the system, proving the more fundamental theorems (including what we have come to call the Justification Theorem) and outlining the way in which an intensional interpretation scheme could be developed which made use of the boolean approach (which was originally strictly extensional). We presented our findings in a monograph (Keenan and Faltz, 1978) which the UCLA Linguistics Department kindly published as part of their series called Occa sional Papers in Linguistics; one of the authors also presented the system at a colloquium held at the Winter Meeting of the Linguistic Society of America in December 1978.




Flexibility Principles in Boolean Semantics


Book Description

An investigation of the logical flexibility principles needed for a formal semantic account of coordination, plurality, and scope in natural language. Since the early work of Montague, Boolean semantics and its subfield of generalized quantifier theory have become the model-theoretic foundation for the study of meaning in natural languages. This book uses this framework to develop a new semantic theory of central linguistic phenomena involving coordination, plurality, and scope. The proposed theory makes use of the standard Boolean interpretation of conjunction, a choice-function account of indefinites, and a novel semantics of plurals that is not based on the distributive/collective distinction. The key to unifying these mechanisms is a version of Montagovian semantics that is augmented by flexibility principles: semantic operations that have no counterpart in phonology. This is the first book to cover these areas in a way that is both linguistically comprehensive and formally explicit. On one hand, it addresses questions of primarily linguistic concern: the semantic functions of words like and and or in different languages, the interpretation of indefinites and their scope, and the semantic typology of noun phrases and predicates. On the other hand, it addresses formal questions that are motivated by the treatment of these linguistic problems: the use of Boolean algebras in linguistics, the proper formalization of choice functions within generalized quantifier theory, and the extension of this theory to the domain of plurality. While primarily intended for readers with a background in theoretical linguistics, the book will also be of interest to researchers and advanced students in logic, computational linguistics, philosophy of language, and artificial intelligence.




Semantics of Natural Language


Book Description

"The idea that prompted the conferenee for which many of these papers were written, and that inspired this book, is stated in the Editorial Introduction reprinted below from Volume 21 of Synthese. The present volume contains the artieles in Synthese 21, Numbers 3-4 and Synthese 22, Numbers 1-2. In addition, it ineludes new papers by Saul Kripke, James McCawley, John R. Ross, and Paul Ziff, and reprints 'Grammar and Philosophy' by P. F. Strawson. Strawson's artiele first appeared in the Proceedings of the Aristotelian Society, Volume 70, and is reprinted with the kind permission of the author and the Aristotelian Society. We also repeat our thanks to the Olivetti Companyand Edizione di Comunita of Milan for permission to inelude the paper by Dana Scott; it also appeared in Synthese 21. DONALO DAVIDSON GILBERT HARMAN EDITORIAL INTRODUCTION The success of linguistics in treating naturallanguages as formal syntactic systems has aroused the interest of a number of linguists in a paralleI or related development of semantics. For the most part quite independ ently, many philosophers and logicians have reeently been applying formai semantic methods to structures increasingly like naturallanguages. While differenees in training, method and vocabulary tend to veil the fact, philosophers and linguists are converging, it seerns, on a common set of interrelated probiems. Sinee philosophers and linguists are working on the same, or very similar, probiems, it would obviously be instructive to compare notes." --




Handbook of Quantifiers in Natural Language


Book Description

Covering a strikingly diverse range of languages from 12 linguistic families, this handbook is based on responses to a questionnaire constructed by the editors. Focusing on the formation, distribution and semantic interpretation of quantificational expressions, the book explores 17 languages including German, Italian, Russian, Mandarin Chinese, Malagasy, Hebrew, Pima, Basque, and more. The language data sets enable detailed crosslinguistic comparison of numerous features. These include semantic classes of quantifiers (generalized existential, generalized universal, proportional, partitive), syntactically complex quantifiers (intensive modification, Boolean compounding, exception phrases) and several others such as quantifier scope ambiguities, quantifier float, and binary quantifiers. Its theory-independent content extends earlier work by Matthewson (2008) and Bach et al. (1995), making this handbook suitable for linguists, semanticians, philosophers of language and logicians alike.




Natural Language Semantics


Book Description

An introduction to natural language semantics that offers an overview of the empirical domain and an explanation of the mathematical concepts that underpin the discipline. This textbook offers a comprehensive introduction to the fundamentals of those approaches to natural language semantics that use the insights of logic. Many other texts on the subject focus on presenting a particular theory of natural language semantics. This text instead offers an overview of the empirical domain (drawn largely from standard descriptive grammars of English) as well as the mathematical tools that are applied to it. Readers are shown where the concepts of logic apply, where they fail to apply, and where they might apply, if suitably adjusted. The presentation of logic is completely self-contained, with concepts of logic used in the book presented in all the necessary detail. This includes propositional logic, first order predicate logic, generalized quantifier theory, and the Lambek and Lambda calculi. The chapters on logic are paired with chapters on English grammar. For example, the chapter on propositional logic is paired with a chapter on the grammar of coordination and subordination of English clauses; the chapter on predicate logic is paired with a chapter on the grammar of simple, independent English clauses; and so on. The book includes more than five hundred exercises, not only for the mathematical concepts introduced, but also for their application to the analysis of natural language. The latter exercises include some aimed at helping the reader to understand how to formulate and test hypotheses.




Type-Logical Semantics


Book Description

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.







Semantik / Semantics


Book Description

During the past 20 years the investigation into meaning of natural languages has emerged into one of the most active disciplines in theoretical linguistics. The different traditions of linguistics, philosophy of language and philosophical logic converged in the paradigm of truth conditional semantics, which now plays a central role in the cognitive sciences. From empirical research in particular languages more principal questions arise of how the speaker succeeds in expressing particular types of meaning by use of formal combination of signs. The theories developed to cope with the question assume that for a hearer, the meaning of a complex expression must be "computable", and therefore, modern theoretical semantics uses formal algebraic methods to construct the meaning compositionally in view of syntactic structur. Furthermore, meaning need to be "anchored" in the experience available to hearer. In order to deal with this, theoretical semantics extensivly uses the concept of truth conditions, which roughly explain how a world must be structured in order to be matched by certain linguistic expressions. Semantic analyses are complemented by context theory and the theory of speech acts. Thus, linguistic meaning must be related to human cognitive capacities, and therefore, theoretical semantics is tightly connected with philosophical logic as well as cognitive sciences in general. The aim of this handbook is to represent the body of theoretical knowledge which has evolved in the international research of the last two decades. Some of the theories can now be termed "classical" in that they belong to the commonly accepted base of theoretical semantics. Other theories are still disputed, and there areproblems still to be solved - as normal in a more developed science. The authors, who are leading experts in the field of semantics, try to balance the accepted and the questionable results. It goes without saying that each author hold a particular position in this respect. Some articles are written in English, some in German. Since semantics is considered to be a subfield of linguistics, the articles are arranged due to linguistic points of view. In the first 5 chapters (comprising 15 articles) the common principles of semantics are presented: ontological foundations of semantics, composition of meaning, problems of use (context, speech acts, and lexical base of meaning. The next 5 chapters (comprising 25 articles) are concerned with semantic phenomena, theories and problems which are specific for a particular class of linguistic expressions. These are arranged according to parts of speech: nouns, functional categories, verbs, adjectives and so on.This division does not reflect a theoretical position by itself, however it allows one to recognize problems connected with one another. Some more general questions are discussed in more than one article, in different perspective and vicinity. The Handbook is complemented by a service article on formal methods in semantics, followed by a comprehensive bibliography including about 1700 entries, and both a subject and a name index. This handbook is indispensable for all research in linguistics and neighboring disciplines (philosophy of language, cognitive sciences). Some of the articles can serve as basic literature for classes of advanced students.




Word Meaning and Montague Grammar


Book Description

The most general goal of this book is to propose and illustrate a program of research in word semantics that combines some of the methodology and results in linguistic semantics, primarily that of the generative semantics school, with the rigorously formalized syntactic and semantic framework for the analysis of natural languages developed by Richard Montague and his associates, a framework in which truth and denotation with respect to a model are taken as the fundamental semantic notions. I hope to show, both from the linguist's and the philosopher's point of view, not only why this synthesis can be undertaken but also why it will be useful to pursue it. On the one hand, the linguists' decompositions of word meanings into more primitive parts are by themselves inherently incomplete, in that they deal only in distinctions in meaning without providing an account of what mean ings really are. Not only can these analyses be made complete by a model theoretic semantics, but also such an account of these analyses renders them more exact and more readily testable than they could ever be otherwise.




Proceedings of the 10th West Coast Conference on Formal Linguistics


Book Description

Forty-one papers from the 1991 West Coast Conference on Formal Linguistics are included. The papers deal with diverse topics ranging from the traditional linguistic fields of phonology, morphology, syntax, and semantics to the rapidly developing areas of cognitive and discourse linguistics.