The Formal Semantics of Programming Languages provides the basic mathematical techniques necessary for those who are beginning a study of the semantics and logics of programming languages. These techniques will allow students to invent, formalize, and justify rules with which to reason about a variety of programming languages. Although the treatment is elementary, several of the topics covered are drawn from recent research, including the vital area of concurency. The book contains many exercises ranging from simple to miniprojects.Starting with basic set theory, structural operational semantics is introduced as a way to define the meaning of programming languages along with associated proof techniques. Denotational and axiomatic semantics are illustrated on a simple language of while-programs, and fall proofs are given of the equivalence of the operational and denotational semantics and soundness and relative completeness of the axiomatic semantics. A proof of Godel's incompleteness theorem, which emphasizes the impossibility of achieving a fully complete axiomatic semantics, is included. It is supported by an appendix providing an introduction to the theory of computability based on while-programs. Following a presentation of domain theory, the semantics and methods of proof for several functional languages are treated. The simplest language is that of recursion equations with both call-by-value and call-by-name evaluation. This work is extended to lan guages with higher and recursive types, including a treatment of the eager and lazy lambda-calculi. Throughout, the relationship between denotational and operational semantics is stressed, and the proofs of the correspondence between the operation and denotational semantics are provided. The treatment of recursive types - one of the more advanced parts of the book - relies on the use of information systems to represent domains. The book concludes with a chapter on parallel programming languages, accompanied by a discussion of methods for specifying and verifying nondeterministic and parallel programs.

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.

What is Meaning? Fundamentals of Formal Semantics is a concise introduction to the field of semantics as it is actually practiced. Through simple examples, pictures, and metaphors, Paul Portner presents the field’s key ideas about how language works. Explains the fundamental ideas and some of the most significant results of modern semantic theory Combines foundational discussion with simplified analyses of complex phenomena to provide readers with a sense of the fascination to be found in the details of the human language Includes exercises and thought-provoking questions to facilitate learning

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.

Formal semantics - the scientific study of meaning in natural language - is one of the most fundamental and long-established areas of linguistics. This Handbook offers a comprehensive, yet compact guide to the field, bringing together research from a wide range of world-leading experts. Chapters include coverage of the historical context and foundation of contemporary formal semantics, a survey of the variety of formal/logical approaches to linguistic meaning and an overview of the major areas of research within current semantic theory, broadly conceived. The Handbook also explores the interfaces between semantics and neighbouring disciplines, including research in cognition and computation. This work will be essential reading for students and researchers working in linguistics, philosophy, psychology and computer science.

The essays in this collection are the outgrowth of a workshop, held in June 1976, on formal approaches to the semantics and pragmatics of natural languages. They document in an astoundingly uniform way the develop ments in the formal analysis of natural languages since the late sixties. The avowed aim of the' workshop was in fact to assess the progress made in the application of formal methods to semantics, to confront different approaches to essentially the same problems on the one hand, and, on the other, to show the way in relating semantic and pragmatic explanations of linguistic phenomena. Several of these papers can in fact be regarded as attempts to close the 'semiotic circle' by bringing together the syntactic, semantic and pragmatic properties of certain constructions in an explanatory framework thereby making it more than obvious that these three components of an integrated linguistic theory cannot be as neatly separated as one would have liked to believe. In other words, not only can we not elaborate a syntactic description of (a fragment of) a language and then proceed to the semantics (as Montague pointed out already forcefully in 1968), we cannot hope to achieve an adequate integrated syntax and semantics without paying heed to the pragmatic aspects of the constructions involved. The behavior of polarity items, 'quantifiers' like any, conditionals or even logical particles like and and or in non-indicative sentences is clear-cut evidence for the need to let each component of the grammar inform the other.