Lectures on Linear Logic
Author | : A. S. Troelstra |
Publisher | : |
Total Pages | : 215 |
Release | : 2000 |
Genre | : |
ISBN | : |
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Author | : A. S. Troelstra |
Publisher | : |
Total Pages | : 215 |
Release | : 2000 |
Genre | : |
ISBN | : |
Author | : Anne Sjerp Troelstra |
Publisher | : Center for the Study of Language and Information Publications |
Total Pages | : 215 |
Release | : 1992-05-01 |
Genre | : Mathematics |
ISBN | : 9780937073773 |
The initial sections of this text deal with syntactical matters such as logical formalism, cut-elimination, and the embedding of intuitionistic logic in classical linear logic. Concluding chapters focus on proofnets for the multiplicative fragment and the algorithmic interpretation of cut-elimination in proofnets.
Author | : A. S. Troelstra |
Publisher | : |
Total Pages | : 115 |
Release | : 1990 |
Genre | : |
ISBN | : |
Author | : Thomas Ehrhard |
Publisher | : Cambridge University Press |
Total Pages | : 393 |
Release | : 2004-11-15 |
Genre | : Computers |
ISBN | : 0521608570 |
This book illustrates linear logic in the application of proof theory to computer science.
Author | : Jean-Yves Girard |
Publisher | : Cambridge University Press |
Total Pages | : 401 |
Release | : 1995-06-22 |
Genre | : Mathematics |
ISBN | : 0521559618 |
This volume gives an overview of linear logic that will be useful to mathematicians and computer scientists working in this area.
Author | : Jean-Yves Girard |
Publisher | : European Mathematical Society |
Total Pages | : 554 |
Release | : 2011 |
Genre | : Logic |
ISBN | : 9783037190883 |
These lectures on logic, more specifically proof theory, are basically intended for postgraduate students and researchers in logic. The question at stake is the nature of mathematical knowledge and the difference between a question and an answer, i.e., the implicit and the explicit. The problem is delicate mathematically and philosophically as well: the relation between a question and its answer is a sort of equality where one side is ``more equal than the other'': one thus discovers essentialist blind spots. Starting with Godel's paradox (1931)--so to speak, the incompleteness of answers with respect to questions--the book proceeds with paradigms inherited from Gentzen's cut-elimination (1935). Various settings are studied: sequent calculus, natural deduction, lambda calculi, category-theoretic composition, up to geometry of interaction (GoI), all devoted to explicitation, which eventually amounts to inverting an operator in a von Neumann algebra. Mathematical language is usually described as referring to a preexisting reality. Logical operations can be given an alternative procedural meaning: typically, the operators involved in GoI are invertible, not because they are constructed according to the book, but because logical rules are those ensuring invertibility. Similarly, the durability of truth should not be taken for granted: one should distinguish between imperfect (perennial) and perfect modes. The procedural explanation of the infinite thus identifies it with the unfinished, i.e., the perennial. But is perenniality perennial? This questioning yields a possible logical explanation for algorithmic complexity. This highly original course on logic by one of the world's leading proof theorists challenges mathematicians, computer scientists, physicists, and philosophers to rethink their views and concepts on the nature of mathematical knowledge in an exceptionally profound way.
Author | : |
Publisher | : |
Total Pages | : |
Release | : 1999 |
Genre | : Logic, Symbolic and mathematical |
ISBN | : |
Author | : Andrej Ščedrov |
Publisher | : |
Total Pages | : 110 |
Release | : 1993 |
Genre | : |
ISBN | : |
Author | : Nikolai Dokuchaev |
Publisher | : World Scientific Publishing Company |
Total Pages | : 224 |
Release | : 2015-06-12 |
Genre | : Business & Economics |
ISBN | : 9814678058 |
This book provides a systematic, self-sufficient and yet short presentation of the mainstream topics on introductory Probability Theory with some selected topics from Mathematical Statistics. It is suitable for a 10- to 14-week course for second- or third-year undergraduate students in Science, Mathematics, Statistics, Finance, or Economics, who have completed some introductory course in Calculus. There is a sufficient number of problems and solutions to cover weekly tutorials.
Author | : Genesereth Michael |
Publisher | : Springer Nature |
Total Pages | : 155 |
Release | : 2013-08-16 |
Genre | : Mathematics |
ISBN | : 3031017994 |
This book is a gentle but rigorous introduction to Formal Logic. It is intended primarily for use at the college level. However, it can also be used for advanced secondary school students, and it can be used at the start of graduate school for those who have not yet seen the material. The approach to teaching logic used here emerged from more than 20 years of teaching logic to students at Stanford University and from teaching logic to tens of thousands of others via online courses on the World Wide Web. The approach differs from that taken by other books in logic in two essential ways, one having to do with content, the other with form. Like many other books on logic, this one covers logical syntax and semantics and proof theory plus induction. However, unlike other books, this book begins with Herbrand semantics rather than the more traditional Tarskian semantics. This approach makes the material considerably easier for students to understand and leaves them with a deeper understanding of what logic is all about. In addition to this text, there are online exercises (with automated grading), online logic tools and applications, online videos of lectures, and an online forum for discussion. They are available at logic.stanford.edu/intrologic/