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: 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.
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.
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.
This new edition of Daniel J. Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.
Reasoning under uncertainty is always based on a specified language or for malism, including its particular syntax and semantics, but also on its associated inference mechanism. In the present volume of the handbook the last aspect, the algorithmic aspects of uncertainty calculi are presented. Theory has suffi ciently advanced to unfold some generally applicable fundamental structures and methods. On the other hand, particular features of specific formalisms and ap proaches to uncertainty of course still influence strongly the computational meth ods to be used. Both general as well as specific methods are included in this volume. Broadly speaking, symbolic or logical approaches to uncertainty and nu merical approaches are often distinguished. Although this distinction is somewhat misleading, it is used as a means to structure the present volume. This is even to some degree reflected in the two first chapters, which treat fundamental, general methods of computation in systems designed to represent uncertainty. It has been noted early by Shenoy and Shafer, that computations in different domains have an underlying common structure. Essentially pieces of knowledge or information are to be combined together and then focused on some particular question or domain. This can be captured in an algebraic structure called valuation algebra which is described in the first chapter. Here the basic operations of combination and focus ing (marginalization) of knowledge and information is modeled abstractly subject to simple axioms.
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.
Propositional logic has been recognized throughout the centuries as one of the cornerstones of reasoning in philosophy and mathematics. Over time, its formalization into Boolean algebra was accompanied by the recognition that a wide range of combinatorial problems can be expressed as propositional satisfiability (SAT) problems. Because of this dual role, SAT developed into a mature, multi-faceted scientific discipline, and from the earliest days of computing a search was underway to discover how to solve SAT problems in an automated fashion. This book, the Handbook of Satisfiability, is the second, updated and revised edition of the book first published in 2009 under the same name. The handbook aims to capture the full breadth and depth of SAT and to bring together significant progress and advances in automated solving. Topics covered span practical and theoretical research on SAT and its applications and include search algorithms, heuristics, analysis of algorithms, hard instances, randomized formulae, problem encodings, industrial applications, solvers, simplifiers, tools, case studies and empirical results. SAT is interpreted in a broad sense, so as well as propositional satisfiability, there are chapters covering the domain of quantified Boolean formulae (QBF), constraints programming techniques (CSP) for word-level problems and their propositional encoding, and satisfiability modulo theories (SMT). An extensive bibliography completes each chapter. This second edition of the handbook will be of interest to researchers, graduate students, final-year undergraduates, and practitioners using or contributing to SAT, and will provide both an inspiration and a rich resource for their work. Edmund Clarke, 2007 ACM Turing Award Recipient: "SAT solving is a key technology for 21st century computer science." Donald Knuth, 1974 ACM Turing Award Recipient: "SAT is evidently a killer app, because it is key to the solution of so many other problems." Stephen Cook, 1982 ACM Turing Award Recipient: "The SAT problem is at the core of arguably the most fundamental question in computer science: What makes a problem hard?"
