Interactive Theorem Proving

Interactive Theorem Proving
Author: Jeremy Avigad
Publisher: Springer
Total Pages: 657
Release: 2018-07-03
Genre: Mathematics
ISBN: 3319948210

This book constitutes the refereed proceedings of the 9th International Conference on Interactive Theorem Proving, ITP 2018, held in Oxford, UK, in July 2018. The 32 full papers and 5 short papers presented were carefully reviewed and selected from 65 submissions. The papers feature research in the area of logical frameworks and interactive proof assistants. The topics include theoretical foundations and implementation aspects of the technology, as well as applications to verifying hardware and software systems to ensure their safety and security, and applications to the formal verication of mathematical results. Chapters 2, 10, 26, 29, 30 and 37 are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Resolution Proof Systems

Resolution Proof Systems
Author: Z. Stachniak
Publisher: Springer Science & Business Media
Total Pages: 216
Release: 2012-12-06
Genre: Computers
ISBN: 9400916779

Resolution Proof Systems: An Algebraic Theory presents a new algebraic framework for the design and analysis of resolution- based automated reasoning systems for a range of non-classical logics. It develops an algebraic theory of resolution proof systems focusing on the problems of proof theory, representation and efficiency of the deductive process. A new class of logical calculi, the class of resolution logics, emerges as a second theme of the book. The logical and computational aspects of the relationship between resolution logics and resolution proof systems is explored in the context of monotonic as well as nonmonotonic reasoning. This book is aimed primarily at researchers and graduate students in artificial intelligence, symbolic and computational logic. The material is suitable as a reference book for researchers and as a text book for graduate courses on the theoretical aspects of automated reasoning and computational logic.

Tests and Proofs

Tests and Proofs
Author: Gordon Fraser
Publisher: Springer Science & Business Media
Total Pages: 193
Release: 2010-06-17
Genre: Computers
ISBN: 3642139760

This volume contains the proceedings of TAP 2010, the 4th International C- ference on Tests and Proofs held during July 1–2 in M ́ alaga, Spain as part of TOOLS Federated Conferences. TAP 2010wasthe fourth event of an ongoingseriesof conferencesdevoted to the convergence of proofs and tests. In the past, proving and testing were seen as very di?erent and even competing techniques. Proving people would say: If correctness is proved, what do we need tests for? Testers, on the other hand, would claim that proving is too limited in applicability and testing is the only truepathtocorrectness. Ofcourse,bothhaveapoint,buttoquoteEdBrinksma from his 2009 keynote at the Dutch Testing Day and Testcom/FATES: “Who would want to ?y in an airplane with software proved correct, but not tested?” Indeed, the true power lies in the combination of both approaches. Today, m- ern test systems rely on techniques deeply rooted in formal proof techniques, and testing techniques make it possible to apply proof techniques where there was no possibility previously. At a time when even mainstream software engineering conferences start f- turing papers with both “testing” and “proving”in their titles, we are clearly on the verge of a new age where testing and proving are not competing but ?nally accepted as complementary techniques. Albeit, we are not quite there yet, and so the TAP conferences aim to provide a forum for researchers working on the converging topics and to raise general awareness of this convergence.

Practical Aspects of Declarative Languages

Practical Aspects of Declarative Languages
Author: Pascal van Hentenryck
Publisher: Springer Science & Business Media
Total Pages: 239
Release: 2005-12-19
Genre: Computers
ISBN: 3540309470

This volume contains the papers presented at the Eighth International S- posium on Practical Aspects of Declarative Languages (PADL 2006) held on January 9-10, 2006, in Charleston, South Carolina. Information about the c- ference can be found athttp://www.cs.brown.edu/people/pvh/PADL06.html. As is now traditional, PADL 2006 was co-located with the 33rd Annual Sym- sium on Principles of Programming Languages that was held on January 11-13, 2006. The PADL conference series is a forum for researchers and practioners to present original work emphasizing novel applications and implementation te- niques for all forms of declarative concepts. Topics of interest include, but are not limited to: – Innovative applications of declarative languages; – Declarative domain-speci?c languages and applications; – Practical applications of theoretical results; – New language developments and their impact on applications; – Evaluation of implementation techniques on practical applications; – Novel implementation techniques relevant to applications; – Novel uses of declarative languages in the classroom; – Practical experiences. This year, there were 36 submissions. Each submission was reviewed by at least three Programme Committee members. The committee decided to accept 15 papers. In addition, the programme also included three invited talks by Erik Meijer, David Roundy, and Philip Walder.

How to Prove It

How to Prove It
Author: Daniel J. Velleman
Publisher: Cambridge University Press
Total Pages: 404
Release: 2006-01-16
Genre: Computers
ISBN: 9780521675994

This new edition of Daniel J. Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.

Logical Foundations of Computer Science

Logical Foundations of Computer Science
Author: Sergei Artemov
Publisher: Springer
Total Pages: 478
Release: 2009-02-11
Genre: Computers
ISBN: 3540926879

This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2009, held in Deerfield Beach, Florida, USA in January 2008. The volume presents 31 revised refereed papers carefully selected by the program committee. All current aspects of logic in computer science are addressed, including constructive mathematics and type theory, logical foundations of programming, logical aspects of computational complexity, logic programming and constraints, automated deduction and interactive theorem proving, logical methods in protocol and program verification and in program specification and extraction, domain theory logics, logical foundations of database theory, equational logic and term rewriting, lambda and combinatory calculi, categorical logic and topological semantics, linear logic, epistemic and temporal logics, intelligent and multiple agent system logics, logics of proof and justification, nonmonotonic reasoning, logic in game theory and social software, logic of hybrid systems, distributed system logics, system design logics, as well as other logics in computer science.

Logic for Applications

Logic for Applications
Author: Anil Nerode
Publisher: Springer Science & Business Media
Total Pages: 383
Release: 2012-12-06
Genre: Computers
ISBN: 1468402110

In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the recent dramatic growth in the applications of logic to computer science. Thus our choice of topics has been heavily influenced by such applications. Of course, we cover the basic traditional topics - syntax, semantics, soundness, completeness and compactness - as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much of our book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic, especially in its application to Logic Programming and PROLOG. We deal extensively with the mathematical foundations of all three of these subjects. In addition, we include two chapters on nonclassical logic- modal and intuitionistic - that are becoming increasingly important in computer science. We develop the basic material on the syntax and se mantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method introduced for classical logic. We indicate how it can easily be adapted to various other special types of modal log ics. A number of more advanced topics (including nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.