Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such systems from logic to mathematics, and on the connection between the two main forms of structural proof theory - natural deduction and sequent calculus. The authors emphasize the computational content of logical results. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated.

This book constitutes the refereed proceedings of the 6th International Conference on Natural Language Processing, GoTAL 2008, Gothenburg, Sweden, August 2008.

The 44 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 107 submissions. The papers address all current issues in computational linguistics and monolingual and multilingual intelligent language processing - theory, methods and applications.

Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics, and computer science. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated.

Implementing a programming language means bridging the gap from the programmer's high-level thinking to the machine's zeros and ones. If this is done in an efficient and reliable way, programmers can concentrate on the actual problems they have to solve, rather than on the details of machines. But understanding the whole chain from languages to machines is still an essential part of the training of any serious programmer. It will result in a more competent programmer, who will moreover be able to develop new languages. A new language is often the best way to solve a problem, and less difficult than it may sound. This book follows a theory-based practical approach, where theoretical models serve as blueprint for actual coding. The reader is guided to build compilers and interpreters in a well-understood and scalable way. The solutions are moreover portable to different implementation languages. Much of the actual code is automatically generated from a grammar of the language, by using the BNF Converter tool. The rest can be written in Haskell or Java, for which the book gives detailed guidance, but with some adaptation also in C, C]+, C#, or OCaml, which are supported by the BNF Converter. The main focus of the book is on standard imperative and functional languages: a subset of C++ and a subset of Haskell are the source languages, and Java Virtual Machine is the main target. Simple Intel x86 native code compilation is shown to complete the chain from language to machine. The last chapter leaves the standard paths and explores the space of language design ranging from minimal Turing-complete languages to human-computer interaction in natural language.

Grammatical Framework is a programming language designed for writing grammars, which has the capability of addressing several languages in parallel. This thorough introduction demonstrates how to write grammars in Grammatical Framework and use them in applications such as tourist phrasebooks, spoken dialogue systems, and natural language interfaces. The examples and exercises presented here address several languages, and the readers are shown how to look at their own languages from the computational perspective.

It is the aim of INDICES to document recent explorations in the various fields of philosophical logic and formal linguistics and their applications in other disciplines. The main emphasis of this series is on self-contained monographs covering particular areas of recent research and surveys of methods, problems, and results in all fields of inquiry where recourse to logical analysis and logical methods has been fruitful. INDICES will contain monographs dealing with the central areas of philosophical logic (extensional and intensional systems, indexical logics, non-classical logics, philosophy of logic, etc.) as well as studies in which these systems are applied to specific issues in philosophy, in the formal semantics of natural languages, the foundations of linguistic theory, in computational linguistics, and in theoretical computer science. Constructive type theory was first presented in 1970, by the Swedish logician Per Martin-Lof. It has become one of the main approaches used in the foundations of mathematics and computer science. But it has remained relatively unknown among linguists and philosophers, although it provides a considerable extension of the concepts and techniques of logic. The book first gives an introduction to type theory from the point of view of linguistics and the philosophy of language. Type theory is then applied in the areas of quantification, anaphora, temporal reference, and the structure of text and discourse. By virtue of the type-theoretical concepts of proof object and context, various phenomena of dependence and progression in language can be discussed in precise terms, and several well-known problems can be solved. A categorial grammar is presented togenerate formally a fragment of English, together with an example of a computer implementation.

Grammatical Framework is a programming language designed for writing grammars, which has the capability of addressing several languages in parallel. This thorough introduction demonstrates how to write grammars in Grammatical Framework and use them in applications such as tourist phrasebooks, spoken dialogue systems, and natural language interfaces. The examples and exercises presented here address several languages, and the readers are shown how to look at their own languages from the computational perspective.