Download or read book Automated Mathematical Induction written by Hantao Zhang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been shown how the common structure that defines a family of proofs can be expressed as a proof plan [5]. This common structure can be exploited in the search for particular proofs. A proof plan has two complementary components: a proof method and a proof tactic. By prescribing the structure of a proof at the level of primitive inferences, a tactic [11] provides the guarantee part of the proof. In contrast, a method provides a more declarative explanation of the proof by means of preconditions. Each method has associated effects. The execution of the effects simulates the application of the corresponding tactic. Theorem proving in the proof planning framework is a two-phase process: 1. Tactic construction is by a process of method composition: Given a goal, an applicable method is selected. The applicability of a method is determined by evaluating the method's preconditions. The method effects are then used to calculate subgoals. This process is applied recursively until no more subgoals remain. Because of the one-to-one correspondence between methods and tactics, the output from this process is a composite tactic tailored to the given goal. 2. Tactic execution generates a proof in the object-level logic. Note that no search is involved in the execution of the tactic. All the search is taken care of during the planning process. The real benefits of having separate planning and execution phases become appar ent when a proof attempt fails.
Download or read book Automated Mathematical Induction written by Hantao Zhang and published by . This book was released on 2014-01-15 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Automated Mathematical Induction with Test Sets written by A. Bouhoula and published by . This book was released on 1993 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Automated Mathematical Induction written by Adel Bouhoula and published by . This book was released on 1992 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Proofs by induction are important in many computer science and artificial intelligence applications, in particular, in program verification and specification systems. We present a new method to prove (and disprove) automatically inductive properties. Given a set of axioms, a well-suited induction scheme is constructed automatically. We call such an induction scheme a test set. Then, for proving a property, we just instantiate it with terms from the test set and apply pure algebraic simplification to the result. This method needs no completion and explicit induction. However it retains their positive features, namely, the completeness of the former and the robustness of the latter. It has been implemented in the theorem-prover SPIKE."
Download or read book The Automation of Proof by Mathematical Induction written by Alan Bundy and published by . This book was released on 1998 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Automation of Proof written by Donald A. MacKenzie and published by . This book was released on 1994 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Automation of Proof by Mathematical Induction written by R. S. Boyer and published by . This book was released on 1995 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Automation of Proof by Mathematical Induction written by Robert S. Boyer and published by . This book was released on 1995 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Automated Theorem Proving After 25 Years written by W. W. Bledsoe and published by American Mathematical Soc.. This book was released on 1984 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Mathematical Induction written by David S. Gunderson and published by Chapman & Hall/CRC. This book was released on 2016-11-16 with total page 921 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics. In the first part of the book, the author discusses different inductive techniques, including well-ordered sets, basic mathematical induction, strong induction, double induction, infinite descent, downward induction, and several variants. He then introduces ordinals and cardinals, transfinite induction, the axiom of choice, Zorn's lemma, empirical induction, and fallacies and induction. He also explains how to write inductive proofs. The next part contains more than 750 exercises that highlight the levels of difficulty of an inductive proof, the variety of inductive techniques available, and the scope of results provable by mathematical induction. Each self-contained chapter in this section includes the necessary definitions, theory, and notation and covers a range of theorems and problems, from fundamental to very specialized. The final part presents either solutions or hints to the exercises. Slightly longer than what is found in most texts, these solutions provide complete details for every step of the problem-solving process.
Download or read book Thirty Five Years of Automating Mathematics written by F.D. Kamareddine and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: THIRTY FIVE YEARS OF AUTOMATING MATHEMATICS: DEDICATED TO 35 YEARS OF DE BRUIJN'S AUTOMATH N. G. de Bruijn was a well established mathematician before deciding in 1967 at the age of 49 to work on a new direction related to Automating Mathematics. By then, his contributions in mathematics were numerous and extremely influential. His book on advanced asymptotic methods, North Holland 1958, was a classic and was subsequently turned into a book in the well known Dover book series. His work on combinatorics yielded influential notions and theorems of which we mention the de Bruijn-sequences of 1946 and the de Bruijn-Erdos theorem of 1948. De Bruijn's contributions to mathematics also included his work on generalized function theory, analytic number theory, optimal control, quasicrystals, the mathematical analysis of games and much more. In the 1960s de Bruijn became fascinated by the new computer technology and as a result, decided to start the new AUTOMATH project where he could check, with the help of the computer, the correctness of books of mathematics. In each area that de Bruijn approached, he shed a new light and was known for his originality and for making deep intellectual contributions. And when it came to automating mathematics, he again did it his way and introduced the highly influential AUTOMATH. In the past decade he has also been working on theories of the human brain.
Download or read book Introducing Software Verification with Dafny Language written by Boro Sitnikovski and published by Apress. This book was released on 2022-03-01 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: Get introduced to software verification and proving correctness using the Microsoft Research-backed programming language, Dafny. While some other books on this topic are quite mathematically rigorous, this book will use as little mathematical symbols and rigor as possible, and explain every concept using plain English. It's the perfect primer for software programmers and developers with C# and other programming language skills. Writing correct software can be hard, so you'll learn the concept of computation and software verification. Then, apply these concepts and techniques to confidently write bug-free code that is easy to understand. Source code will be available throughout the book and freely available via GitHub. After reading and using this book you'll be able write correct, big free software source code applicable no matter which platform and programming language you use. What You Will Learn Discover the Microsoft Research-backed Dafny programming language Explore Hoare logic, imperative and functional programs Work with pre- and post-conditions Use data types, pattern matching, and classes Dive into verification examples for potential re-use for your own projects Who This Book Is For Software developers and programmers with at least prior, basic programming experience. No specific language needed. It is also for those with very basic mathematical experience (function, variables).
Download or read book Rippling Meta Level Guidance for Mathematical Reasoning written by Alan Bundy and published by Cambridge University Press. This book was released on 2005-06-30 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rippling is a radically new technique for the automation of mathematical reasoning. It is widely applicable whenever a goal is to be proved from one or more syntactically similar givens. It was originally developed for inductive proofs, where the goal was the induction conclusion and the givens were the induction hypotheses. It has proved to be applicable to a much wider class of tasks, from summing series via analysis to general equational reasoning. The application to induction has especially important practical implications in the building of dependable IT systems, and provides solutions to issues such as the problem of combinatorial explosion. Rippling is the first of many new search control techniques based on formula annotation; some additional annotated reasoning techniques are also described here. This systematic and comprehensive introduction to rippling, and to the wider subject of automated inductive theorem proving, will be welcomed by researchers and graduate students alike.
Download or read book Automation of Proof by Mathematical Induction written by Robert S. Boyer (et al.) and published by . This book was released on 1996 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book First Order Logic and Automated Theorem Proving written by Melvin Fitting and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many kinds of books on formal logic. Some have philosophers as their intended audience, some mathematicians, some computer scientists. Although there is a common core to all such books they will be very dif ferent in emphasis, methods, and even appearance. This book is intended for computer scientists. But even this is not precise. Within computer sci ence formal logic turns up in a number of areas, from program verification to logic programming to artificial intelligence. This book is intended for computer scientists interested in automated theorem proving in classical logic. To be more precise yet, it is essentially a theoretical treatment, not a how-to book, although how-to issues are not neglected. This does not mean, of course, that the book will be of no interest to philosophers or mathematicians. It does contain a thorough presentation of formal logic and many proof techniques, and as such it contains all the material one would expect to find in a course in formal logic covering completeness but not incompleteness issues. The first item to be addressed is, what are we talking about and why are we interested in it. We are primarily talking about truth as used in mathematical discourse, and our interest in it is, or should be, self-evident. Truth is a semantic concept, so we begin with models and their properties. These are used to define our subject.
Download or read book Automated Theorem Proving in Software Engineering written by Johann M. Schumann and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Growing demands for the quality, safety, and security of software can only be satisfied by the rigorous application of formal methods during software design. This book methodically investigates the potential of first-order logic automated theorem provers for applications in software engineering. Illustrated by complete case studies on protocol verification, verification of security protocols, and logic-based software reuse, this book provides techniques for assessing the prover's capabilities and for selecting and developing an appropriate interface architecture.
Download or read book Proof Theory and Automated Deduction written by Jean Goubault-Larrecq and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in computer applications has led to a new attitude to applied logic in which researchers tailor a logic in the same way they define a computer language. In response to this attitude, this text for undergraduate and graduate students discusses major algorithmic methodologies, and tableaux and resolution methods. The authors focus on first-order logic, the use of proof theory, and the computer application of automated searches for proofs of mathematical propositions. Annotation copyrighted by Book News, Inc., Portland, OR
