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Advances in Proof Theory
The aim of this volume is to collect original contributions by the best specialists from the area of proof theory, constructivity, and computation and discuss recent trends and results in these areas. Some emphasis will be put on ordinal analysis, reductive proof theory, explicit mathematics and type-theoretic formalisms, and abstract computations. The volume is dedicated to the 60th birthday of Professor Gerhard Jäger, who has been instrumental in shaping and promoting logic in Switzerland for the last 25 years. It comprises contributions from the symposium “Advances in Proof Theory”, which was held in Bern in December 2013. Proof theory came into being in the twenties of the last c...
Concepts of Proof in Mathematics, Philosophy, and Computer Science
A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.
Variation, Selection, Development
Can language change be modelled as an evolutionary process? Can notions like variation, selection and competition be fruitfully applied to facts of language development? The present volume ties together various strands of linguistic research which can bring us towards an answer to these questions. In one of the youngest and rapidly growing areas of linguistic research, mathematical models and simulations of competition based developments have been applied to instances of language change. By matching the predicted and observed developmental trends, researchers gauge existing models to the needs of linguistic applications and evaluate the fruitfulness of evolutionary models in linguistics. The...
Proof Theory in Computer Science
Proof theory has long been established as a basic discipline of mathematical logic. It has recently become increasingly relevant to computer science. The - ductive apparatus provided by proof theory has proved useful for metatheoretical purposes as well as for practical applications. Thus it seemed to us most natural to bring researchers together to assess both the role proof theory already plays in computer science and the role it might play in the future. The form of a Dagstuhl seminar is most suitable for purposes like this, as Schloß Dagstuhl provides a very convenient and stimulating environment to - scuss new ideas and developments. To accompany the conference with a proc- dings volume appeared to us equally appropriate. Such a volume not only ?xes basic results of the subject and makes them available to a broader audience, but also signals to the scienti?c community that Proof Theory in Computer Science (PTCS) is a major research branch within the wider ?eld of logic in computer science.
Logic and Foundations of Mathematics
The IOth International Congress of Logic, Methodology and Philosophy of Science, which took place in Florence in August 1995, offered a vivid and comprehensive picture of the present state of research in all directions of Logic and Philosophy of Science. The final program counted 51 invited lectures and around 700 contributed papers, distributed in 15 sections. Following the tradition of previous LMPS-meetings, some authors, whose papers aroused particular interest, were invited to submit their works for publication in a collection of selected contributed papers. Due to the large number of interesting contributions, it was decided to split the collection into two distinct volumes: one coveri...
Handbook of Constructive Mathematics
Gives a complete overview of modern constructive mathematics and its applications through surveys by leading experts.
The Indo-European Language Family
Modern languages like English, Spanish, Russian and Hindi as well as ancient languages like Greek, Latin and Sanskrit all belong to the Indo-European language family, which means that they all descend from a common ancestor. But how, more precisely, are the Indo-European languages related to each other? This book brings together pioneering research from a team of international scholars to address this fundamental question. It provides an introduction to linguistic subgrouping as well as offering comprehensive, systematic and up-to-date analyses of the ten main branches of the Indo-European language family: Anatolian, Tocharian, Italic, Celtic, Germanic, Greek, Armenian, Albanian, Indo-Iranian and Balto-Slavic. By highlighting that these branches are saliently different from each other, yet at the same time display striking similarities, the book demonstrates the early diversification of the Indo-European language family, spoken today by half the world's population. This title is also available as open access on Cambridge Core.
Semantics - Interfaces
Explore the exciting research where semantics meets morphology, syntax and pragmatics. In this book, leading researchers use in-depth articles to explain a wide range of topics at these interfaces, including the semantics of intonation, inflection, compounding, argument structure, type shifting, compositionality, implicature, context dependence, deixis and presupposition. Now in paperback for the first time since its original publication, the highly cited material in this book is an ideal starting point for anyone interested in semantics where it crosses over with other dimensions of grammar.
Pragmatics, Semantics and the Case of Scalar Implicatures
This book is an advanced debate on the nature of scalar implicatures, one of the most popular topics in philosophical linguistics in the last 20 years. Leading theorists in the field offer an up-to-date presentation of the subject in a way that will help readers to orient themselves in the vast literature on the topic.
