Automated Mathematical Induction
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Automated Mathematical Induction
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Author : Hantao Zhang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Automated Mathematical Induction written by Hantao Zhang 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 2012-12-06 with Computers categories.
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.
Automated Mathematical Induction
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Author : Hantao Zhang
language : en
Publisher:
Release Date : 2014-01-15
Automated Mathematical Induction written by Hantao Zhang 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.
Automated Theorem Proving After 25 Years
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Author : W. W. Bledsoe
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
Automated Theorem Proving After 25 Years written by W. W. Bledsoe and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Thirty Five Years Of Automating Mathematics
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Author : F.D. Kamareddine
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Thirty Five Years Of Automating Mathematics written by F.D. Kamareddine 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.
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.
Proof Theory And Automated Deduction
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Author : Jean Goubault-Larrecq
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-30
Proof Theory And Automated Deduction written by Jean Goubault-Larrecq 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 2001-11-30 with Computers categories.
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
The Automation Of Proof
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Author : Donald A. MacKenzie
language : en
Publisher:
Release Date : 1994
The Automation Of Proof written by Donald A. MacKenzie and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Automatic theorem proving categories.
Proof Technology In Mathematics Research And Teaching
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Author : Gila Hanna
language : en
Publisher: Springer Nature
Release Date : 2019-10-02
Proof Technology In Mathematics Research And Teaching written by Gila Hanna and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-02 with Education categories.
This book presents chapters exploring the most recent developments in the role of technology in proving. The full range of topics related to this theme are explored, including computer proving, digital collaboration among mathematicians, mathematics teaching in schools and universities, and the use of the internet as a site of proof learning. Proving is sometimes thought to be the aspect of mathematical activity most resistant to the influence of technological change. While computational methods are well known to have a huge importance in applied mathematics, there is a perception that mathematicians seeking to derive new mathematical results are unaffected by the digital era. The reality is quite different. Digital technologies have transformed how mathematicians work together, how proof is taught in schools and universities, and even the nature of proof itself. Checking billions of cases in extremely large but finite sets, impossible a few decades ago, has now become a standard method of proof. Distributed proving, by teams of mathematicians working independently on sections of a problem, has become very much easier as digital communication facilitates the sharing and comparison of results. Proof assistants and dynamic proof environments have influenced the verification or refutation of conjectures, and ultimately how and why proof is taught in schools. And techniques from computer science for checking the validity of programs are being used to verify mathematical proofs. Chapters in this book include not only research reports and case studies, but also theoretical essays, reviews of the state of the art in selected areas, and historical studies. The authors are experts in the field.
First Order Logic And Automated Theorem Proving
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Author : Melvin Fitting
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
First Order Logic And Automated Theorem Proving written by Melvin Fitting 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 2012-12-06 with Mathematics categories.
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.
Rippling Meta Level Guidance For Mathematical Reasoning
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Author : Alan Bundy
language : en
Publisher: Cambridge University Press
Release Date : 2005-06-30
Rippling Meta Level Guidance For Mathematical Reasoning written by Alan Bundy 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 2005-06-30 with Computers categories.
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.
Handbook Of Mathematical Induction
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Author : David S. Gunderson
language : en
Publisher: CRC Press
Release Date : 2014-01-09
Handbook Of Mathematical Induction written by David S. Gunderson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-09 with Computers categories.
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 discuss