An Introduction To Mathematical Logic And Type Theory
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An Introduction To Mathematical Logic And Type Theory
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Author : Peter B. Andrews
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
An Introduction To Mathematical Logic And Type Theory written by Peter B. Andrews and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
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
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Author : Peter B. Andrews
language : en
Publisher:
Release Date : 2014-01-15
An Introduction To Mathematical Logic And Type Theory written by Peter B. Andrews and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Type Theory And Formal Proof
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Author : Rob Nederpelt
language : en
Publisher: Cambridge University Press
Release Date : 2014-11-06
Type Theory And Formal Proof written by Rob Nederpelt and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-06 with Computers categories.
A gentle introduction for graduate students and researchers in the art of formalizing mathematics on the basis of type theory.
Basic Simple Type Theory
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Author : J. Roger Hindley
language : en
Publisher: Cambridge University Press
Release Date : 1997
Basic Simple Type Theory written by J. Roger Hindley and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Computers categories.
Type theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. By concentrating on the principles that make the theory work in practice, the author covers all the key ideas without getting involved in the complications of more advanced systems. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm that lies at the heart of every such system. Also featured are two other interesting algorithms that until now have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making it the first book at this level that can be used as an introduction to type theory for computer scientists.
Mathematical Logic And Theoretical Computer Science
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Author : David Kueker
language : en
Publisher: CRC Press
Release Date : 2020-12-22
Mathematical Logic And Theoretical Computer Science written by David Kueker and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-22 with Mathematics categories.
Mathematical Logic and Theoretical Computer Science covers various topics ranging from recursion theory to Zariski topoi. Leading international authorities discuss selected topics in a number of areas, including denotational semanitcs, reccuriosn theoretic aspects fo computer science, model theory and algebra, Automath and automated reasoning, stability theory, topoi and mathematics, and topoi and logic. The most up-to-date review available in its field, Mathematical Logic and Theoretical Computer Science will be of interest to mathematical logicians, computer scientists, algebraists, algebraic geometers, differential geometers, differential topologists, and graduate students in mathematics and computer science.
Intelligent Computer Mathematics
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Author : Michael Kohlhase
language : en
Publisher: Springer
Release Date : 2016-07-11
Intelligent Computer Mathematics written by Michael Kohlhase and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-11 with Computers categories.
This book constitutes the refereed proceedings of the 9th International Conference on Intelligent Computer Mathematics, CICM 2016, held in Bialystok, Poland, in July 2016. The 10 full papers and 2 short papers presented were carefully reviewed and selectedfrom a total of 41 submissions. The papers are organized in topical sections according to the five tracks of the conference: Calculemus; Digital Mathematics Libraries; Mathematical Knowledge Management; Surveys and Projects; and Systems and Data.
Handbook Of Logic And Language
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Author : J. van Benthem
language : en
Publisher: Elsevier
Release Date : 1997
Handbook Of Logic And Language written by J. van Benthem and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Computers categories.
This Handbook documents the main trends in current research between logic and language, including its broader influence in computer science, linguistic theory and cognitive science. The history of the combined study of Logic and Linguistics goes back a long way, at least to the work of the scholastic philosophers in the Middle Ages. At the beginning of this century, the subject was revitalized through the pioneering efforts of Gottlob Frege, Bertrand Russell, and Polish philosophical logicians such as Kazimierz Ajdukiewicz. Around 1970, the landmark achievements of Richard Montague established a junction between state-of-the-art mathematical logic and generative linguistic theory. Over the subsequent decades, this enterprise of Montague Grammar has flourished and diversified into a number of research programs with empirical and theoretical substance. This appears to be the first Handbook to bring logic-language interface to the fore. Both aspects of the interaction between logic and language are demonstrated in the book i.e. firstly, how logical systems are designed and modified in response to linguistic needs and secondly, how mathematical theory arises in this process and how it affects subsequent linguistic theory. The Handbook presents concise, impartial accounts of the topics covered. Where possible, an author and a commentator have cooperated to ensure the proper breadth and technical content of the papers. The Handbook is self-contained, and individual articles are of the highest quality.
Frege
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Author : Dale Jacquette
language : en
Publisher: Cambridge University Press
Release Date : 2019-04-04
Frege written by Dale Jacquette and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-04 with Biography & Autobiography categories.
A rich and informative biography of one of the most important and influential figures of analytic philosophy.
Theorem Proving In Higher Order Logics
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Author : Joe Hurd
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-08-08
Theorem Proving In Higher Order Logics written by Joe Hurd and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-08 with Computers categories.
This book constitutes the refereed proceedings of the 18th International Conference on Theorem Proving in Higher Order Logics, TPHOLs 2005, held in Oxford, UK, in August 2005. The 20 revised full papers presented together with 2 invited papers and 4 proof pearls (concise and elegant presentations of interesting examples) were carefully reviewed and selected from 49 submissions. All current issues in HOL theorem proving and formal verification of software and hardware systems are addressed. Among the topics of this volume are theorem proving, verification, recursion and induction, mechanized proofs, mathematical logic, proof theory, type systems, program verification, and proving systems like HOL, Coq, ACL2, Isabelle/HOL and Isabelle/HOLCF.
Theorem Proving With Analytic Tableaux And Related Methods
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Author : P. Miglioli
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-04-24
Theorem Proving With Analytic Tableaux And Related Methods written by P. Miglioli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-04-24 with Computers categories.
This books presents the refereed proceedings of the Fifth International Workshop on Analytic Tableaux and Related Methods, TABLEAUX '96, held in Terrasini near Palermo, Italy, in May 1996. The 18 full revised papers included together with two invited papers present state-of-the-art results in this dynamic area of research. Besides more traditional aspects of tableaux reasoning, the collection also contains several papers dealing with other approaches to automated reasoning. The spectrum of logics dealt with covers several nonclassical logics, including modal, intuitionistic, many-valued, temporal and linear logic.