Author: A. S. TroelstraPublisher:
ISBN:
Category :
Languages : en
Pages : 215
Book Description
Lectures on Linear Logic
Author: A. S. TroelstraLectures on Linear Logic
Author: Anne Sjerp TroelstraPublisher: Center for the Study of Language and Information Publications
ISBN: 9780937073773
Category : Mathematics
Languages : en
Pages : 215
Book Description
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.
Lectures on Linear Logic
Author: A. S. TroelstraLinear Logic in Computer Science
Author: Thomas EhrhardPublisher: Cambridge University Press
ISBN: 0521608570
Category : Computers
Languages : en
Pages : 393
Book Description
This book illustrates linear logic in the application of proof theory to computer science.
Advances in Linear Logic
Author: Jean-Yves GirardPublisher: Cambridge University Press
ISBN: 0521559618
Category : Mathematics
Languages : en
Pages : 401
Book Description
This volume gives an overview of linear logic that will be useful to mathematicians and computer scientists working in this area.
The Blind Spot
Author: Jean-Yves GirardPublisher: European Mathematical Society
ISBN: 9783037190883
Category : Logic
Languages : en
Pages : 554
Book Description
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.
Probability Theory
Author: Nikolai DokuchaevPublisher: World Scientific Publishing Company
ISBN: 9814678058
Category : Business & Economics
Languages : en
Pages : 224
Book Description
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.
Mathematical Foundations of Computer Science 1993
Author: Andrzej M. BorzyszkowskiPublisher: Springer
ISBN: 9783662162651
Category : Mathematics
Languages : en
Pages : 786
Book Description
This volume contains the proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science, MFCS '93, held in Gdansk, Poland, August-September 1993. The MFCS symposia, organized annually in Poland and the former Czechoslovakia since 1972, have a long and well-established tradition. Over the years they have served as a meeting ground for specialists from all branches of theoretical computer science, in particular - algorithms and complexity, automata theory and theory of languages, - concurrent, distributed and real-time systems, - the theory of functional, logic and object-oriented programming, - lambda calculus and type theory, - semantics and logics of programs, and others. The volume contains 12 invitedlectures and 56 contributed papers selected from 133 submissions.
Introduction to Logic, Second Edition
Author: Genesereth MichaelPublisher: Springer Nature
ISBN: 3031017994
Category : Mathematics
Languages : en
Pages : 155
Book Description
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/
Logic and Scientific Methods
Author: Maria Luisa Dalla ChiaraPublisher: Springer Science & Business Media
ISBN: 9780792343837
Category : Science
Languages : en
Pages : 564
Book Description
This is the first of two volumes comprising the papers submitted for publication by the invited participants to the Tenth International Congress of Logic, Methodology and Philosophy of Science, held in Florence, August 1995. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science. The invited lectures published in the two volumes demonstrate much of what goes on in the fields of the Congress and give the state of the art of current research. The two volumes cover the traditional subdisciplines of mathematical logic and philosophical logic, as well as their interfaces with computer science, linguistics and philosophy. Philosophy of science is broadly represented, too, including general issues of natural sciences, social sciences and humanities. The papers in Volume One are concerned with logic, mathematical logic, the philosophy of logic and mathematics, and computer science.