An Introduction To Mathematical Logic And Type Theory
Download An Introduction To Mathematical Logic And Type Theory full books in PDF, epub, and Kindle. Read online free An Introduction To Mathematical Logic And Type Theory ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
An Introduction to Mathematical Logic and Type Theory
Author | : Peter B. Andrews |
Publsiher | : Springer Science & Business Media |
Total Pages | : 404 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 9789401599344 |
Download An Introduction to Mathematical Logic and Type Theory Book in PDF, Epub and Kindle
In case you are considering to adopt this book for courses with over 50 students, please contact [email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.
An Introduction to Mathematical Logic and Type Theory
Author | : Peter B. Andrews |
Publsiher | : Unknown |
Total Pages | : 414 |
Release | : 2014-01-15 |
Genre | : Electronic Book |
ISBN | : 9401599351 |
Download An Introduction to Mathematical Logic and Type Theory Book in PDF, Epub and Kindle
Categorical Logic and Type Theory
Author | : B. Jacobs |
Publsiher | : Gulf Professional Publishing |
Total Pages | : 784 |
Release | : 2001-05-10 |
Genre | : Computers |
ISBN | : 0444508538 |
Download Categorical Logic and Type Theory Book in PDF, Epub and Kindle
This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.
An Introduction to Mathematical Logic
Author | : Richard E. Hodel |
Publsiher | : Courier Corporation |
Total Pages | : 514 |
Release | : 2013-01-01 |
Genre | : Mathematics |
ISBN | : 9780486497853 |
Download An Introduction to Mathematical Logic Book in PDF, Epub and Kindle
This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.
Homotopy Type Theory Univalent Foundations of Mathematics
Author | : Anonim |
Publsiher | : Univalent Foundations |
Total Pages | : 484 |
Release | : 2024 |
Genre | : Electronic Book |
ISBN | : 9182736450XXX |
Download Homotopy Type Theory Univalent Foundations of Mathematics Book in PDF, Epub and Kindle
A Friendly Introduction to Mathematical Logic
Author | : Christopher C. Leary,Lars Kristiansen |
Publsiher | : Lulu.com |
Total Pages | : 382 |
Release | : 2015 |
Genre | : Education |
ISBN | : 9781942341079 |
Download A Friendly Introduction to Mathematical Logic Book in PDF, Epub and Kindle
At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.
Type Theory and Formal Proof
Author | : Rob Nederpelt,Herman Geuvers |
Publsiher | : Cambridge University Press |
Total Pages | : 465 |
Release | : 2014-11-06 |
Genre | : Computers |
ISBN | : 9781107036505 |
Download Type Theory and Formal Proof Book in PDF, Epub and Kindle
A gentle introduction for graduate students and researchers in the art of formalizing mathematics on the basis of type theory.
Twenty Five Years of Constructive Type Theory
Author | : Giovanni Sambin,Jan M. Smith |
Publsiher | : Clarendon Press |
Total Pages | : 294 |
Release | : 1998-10-15 |
Genre | : Mathematics |
ISBN | : 9780191589034 |
Download Twenty Five Years of Constructive Type Theory Book in PDF, Epub and Kindle
Per Martin-Löf's work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has important applications in areas such as computing science and linguistics. This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Löf over the last twenty-five years. As well as celebrating the anniversary of the birth of the subject it covers many of the diverse fields which are now influenced by type theory. It is an invaluable record of areas of current activity, but also contains contributions from N. G. de Bruijn and William Tait, both important figures in the early development of the subject. Also published for the first time is one of Per Martin-Löf's earliest papers.