An Introduction to Mathematical Logic and Type Theory

To Truth Through Proof
Author: Peter B. Andrews
Publisher: Springer Science & Business Media
ISBN: 9401599343
Category: Mathematics
Page: 390
View: 7286
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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.

Eigenschaftsorientierte Beschreibung der logischen Architektur eingebetteter Systeme


Author: David Trachtenherz
Publisher: Springer-Verlag
ISBN: 9783834810298
Category: Computers
Page: 431
View: 2598
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David Trachtenherz entwickelt einen Lösungsansatz zur eigenschaftsorientierten Beschreibung der logischen Architektur eingebetteter Systeme, der eine präzise deklarative Spezifikation funktionaler Eigenschaften mit wählbarem Grad der Abstraktion für unterschiedliche Entwicklungsphasen und -ebenen ermöglicht.

Types for Proofs and Programs

International Conference, TYPES 2007, Cividale Del Friuli, Italy, May 2-5, 2007, Revised Selected Papers
Author: Marino Miculan,Ivan Scagnetto,Furio Honsell
Publisher: Springer Science & Business Media
ISBN: 3540680845
Category: Computers
Page: 203
View: 5696
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These proceedings contain a selection of refereed papers presented at or related totheAnnualWorkshopoftheTYPESproject(EUcoordinationaction510996), which was held during May 2–5, 2007 in Cividale del Friuli (Udine), Italy. The topic of this workshop was formal reasoning and computer progr- ming basedon type theory:languagesand computerized toolsfor reasoning,and applications in several domains such as analysis of programming languages, c- ti?ed software, formalization of mathematics and mathematics education. The workshopwasattended by morethan 100researchersandincluded morethan 40 presentations. We also had the pleasure of three invited lectures, from Fr´ ed´ eric Blanqui (INRIA, Protheo team), Peter Sewell (University of Cambridge) and Amy Felty (University of Ottawa). From 22 submitted papers, 13 were selected after a reviewing process. Each submitted paper was reviewed by three referees; the ?nal decisions were made by the editors. This workshop is the last of a series of meetings of the TYPES working group funded by the European Union (IST project 29001, ESPRIT Working Group 21900, ESPRIT BRA 6435).

Lineare Algebra


Author: Werner Greub
Publisher: Springer-Verlag
ISBN: 3642663850
Category: Mathematics
Page: 222
View: 3429
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Principia Mathematica.


Author: Alfred North Whitehead,Bertrand Russell
Publisher: N.A
ISBN: N.A
Category: Logic, Symbolic and mathematical
Page: 167
View: 1856
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Mathematical Reviews


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 2308
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Introduction to Modern Set Theory


Author: Judith Roitman
Publisher: John Wiley & Sons
ISBN: 9780471635192
Category: Mathematics
Page: 156
View: 7699
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This is modern set theory from the ground up--from partial orderings and well-ordered sets to models, infinite cobinatorics and large cardinals. The approach is unique, providing rigorous treatment of basic set-theoretic methods, while integrating advanced material such as independence results, throughout. The presentation incorporates much interesting historical material and no background in mathematical logic is assumed. Treatment is self-contained, featuring theorem proofs supported by diagrams, examples and exercises. Includes applications of set theory to other branches of mathematics.

A Modern Perspective on Type Theory

From its Origins until Today
Author: F.D. Kamareddine,T. Laan,Rob Nederpelt
Publisher: Springer Science & Business Media
ISBN: 1402023359
Category: Mathematics
Page: 360
View: 7558
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This book provides an overview of type theory. The first part of the book is historical, yet at the same time, places historical systems in the modern setting. The second part deals with modern type theory as it developed since the 1940s, and with the role of propositions as types (or proofs as terms. The third part proposes new systems that bring more advantages together.

Treatise on Intuitionistic Type Theory


Author: Johan Georg Granström
Publisher: Springer Science & Business Media
ISBN: 9789400717367
Category: Philosophy
Page: 198
View: 7624
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Intuitionistic type theory can be described, somewhat boldly, as a partial fulfillment of the dream of a universal language for science. This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book.

The British National Bibliography


Author: Arthur James Wells
Publisher: N.A
ISBN: N.A
Category: English literature
Page: N.A
View: 6510
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Lecture notes in pure and applied mathematics


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 2863
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A HOL Intepretation of Noden


Author: Brian T. Graham
Publisher: N.A
ISBN: N.A
Category: Automatic theorem proving
Page: 78
View: 6962
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Abstract: "We describe the use of the HOL system to corroborate the logical consistency of Noden, an integrated HDL and proof system. The Noden logic is interpreted by representing terms of its logic (which are terms of the Noden HDL) as logical statements in the HOL logic. We describe the abstract datatypes representing types and values, and sample the representation of built-in operations, functions and macros as HOL function specifications. An interpretation of Noden truth-valued statements is presented as a translation of these to HOL sequents, and the representation of Noden proof functions as HOL conversions. Results of the work are summarised, including exposed errors and ambiguities of the Noden logic and implementation. We conclude that this approach to providing assurance of soundness and consistency of a less secure proof system is not only useful, but is a practical method of prototyping and an aid to specifying such a system."

Library recommendations for undergraduate mathematics


Author: Lynn Arthur Steen,Mathematical Association of America
Publisher: Mathematical Assn of Amer
ISBN: N.A
Category: Mathematics
Page: 194
View: 9117
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Mathematics of dependable systems

based on the proceedings of a conference on mathematics of dependable systems, organized by the Institute of Mathematics and Its Applications and held at Royal Holloway, University of London, in September 1993
Author: Chris Mitchell,Victoria Stavridou,Institute for Mathematics and Its Applications
Publisher: Oxford University Press, USA
ISBN: N.A
Category: Computers
Page: 295
View: 6633
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Dependable systems is all about setting up controls to ensure maximum security, reliability, and safety in engineering and technology. With the increased use of computerized controls in airliners, manufacturing plants, and nuclear power stations, the topic is a significant one for computer scientists and engineers. These are the edited proceedings of the first international conference on the Mathematics of Dependable Systems, which took place at Royal Holloway, University of London in 1993. The goal of the conference was to identify unifying mathematical schemes for safety and security to enable interaction of ideas from different fields. Contributions from active researchers focus on safety-critical systems, software testing and reliability, computer security, entity authentication, formal methods, and fault tolerance.

IV Higher Order Workshop, Banff 1990

Proceedings of the IV Higher Order Workshop, 10-14 September 1990, Banff, Canada
Author: Graham M. Birtwistle
Publisher: N.A
ISBN: 9783540196600
Category: Parallel processing (Electronic computers)
Page: 283
View: 1673
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This volume contains the papers presented at a workshop held at Banff, Canada, 10-14 September 1990, which gathered together researchers interested in applying higher order techniques to: reasoning about concurrency, specifying and reasoning about synchronous circuits (specifically butterfly circuits), reasoning about delay insensitive circuits, categorical concepts for programming languages, and support for automated reasoning. In the 1960's and 70's, Landin, Burge and others showed us how to apply higher order techniques and laid practical foundations for modern functional programming. The advantage of higher order techniques is clear: they provide succinct and clear specifications that are easy to reason with. Over the past few years, higher order techniques have been applied successfully to a wide range of applications in software, hardware, and communications. While the papers present recent research results, they have been written so as to be accessible to non hard- liners. This volume will be of interest to readers who wish to gain a broad view of the subject, as well as to specialists in specific subtopics.

Intelligent systems

third golden West international conference : edited and selected papers
Author: E. A. Yfantis
Publisher: Kluwer Academic Publishers
ISBN: 9780792334200
Category: Computers
Page: 967
View: 2886
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The Bulletin of Symbolic Logic


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Logic, Symbolic and mathematical
Page: N.A
View: 720
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Subject Guide to Books in Print

An Index to the Publishers' Trade List Annual
Author: N.A
Publisher: N.A
ISBN: N.A
Category: American literature
Page: N.A
View: 4729
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Kant-Studien


Author: Hans Vaihinger,Max Scheler,Bruno Bauch,Max Frischeisen-Köhler,Arthur Liebert,Paul Menzer
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 1468
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1904-26 (includes lists of members)

Applied Elasticity


Author: John Prescott
Publisher: N.A
ISBN: N.A
Category: Elasticity
Page: 666
View: 3999
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