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Introduction To Proofs And Proof Strategies

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Introduction To Proofs And Proof Strategies

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Author : Shay Fuchs
language : en
Publisher: Cambridge University Press
Release Date : 2023-06-22

Introduction To Proofs And Proof Strategies written by Shay Fuchs 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 2023-06-22 with Mathematics categories.

With a conversational style and no prerequisites, this transition to advanced mathematics emphasizes creative thinking and problem-solving.

A Logical Introduction To Proof

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Author : Daniel Cunningham
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-19

A Logical Introduction To Proof written by Daniel Cunningham 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 2012-09-19 with Mathematics categories.

The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a tool for showing students how to write correct mathematical proofs.

The Efficiency Of Theorem Proving Strategies

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Author : David A. Plaisted
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

The Efficiency Of Theorem Proving Strategies written by David A. Plaisted 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 2013-11-11 with Computers categories.

This is the second and slightly revised edition of this book. A few errors have been fixed, and some references to related work have been added. I thank the readers for their comments on the first edition. We analyze the search efficiency of a number of common refutational theorem proving strategies on propositional and near-propositional prob lems. Search efficiency is concerned with the total number of proofs and partial proofs generated, rather than with the sizes of the proofs. We show that most common strategies produce search spaces of expo nential size even on simple sets of clauses, or else are not sensitive to the goal. However, clause linking, which uses a reduction to proposi tional calculus, has behavior that is more favorable in some respects, a property that it shares with methods that cache subgoals. A strat egy which is of interest for term-rewriting based theorem proving is the A-ordering strategy, and we discuss it in some detail. We show some advantages of A-ordering over other strategies, which may help to explain its efficiency in practice. We also point out some of its com binatorial inefficiencies, especially in relation to goal-sensitivity and irrelevant clauses. In addition, SLD-resolution, which is of importance for Prolog implementation, has combinatorial inefficiencies; this may suggest basing Prolog implementations on a different theorem proving strategy. We also develop techniques for studying the asymptotic complexity of first-order theorem provers. This permits an analytic comparison of the worst-case performances of various theorem proving methods.

A Logical Introduction To Proof

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Author : Daniel W. Cunningham
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-19

A Logical Introduction To Proof written by Daniel W. Cunningham 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 2012-09-19 with Mathematics categories.

Science Of Learning Mathematical Proofs The An Introductory Course

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Author : Elana Reiser
language : en
Publisher: World Scientific
Release Date : 2020-11-25

Science Of Learning Mathematical Proofs The An Introductory Course written by Elana Reiser and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-25 with Mathematics categories.

College students struggle with the switch from thinking of mathematics as a calculation based subject to a problem solving based subject. This book describes how the introduction to proofs course can be taught in a way that gently introduces students to this new way of thinking. This introduction utilizes recent research in neuroscience regarding how the brain learns best. Rather than jumping right into proofs, students are first taught how to change their mindset about learning, how to persevere through difficult problems, how to work successfully in a group, and how to reflect on their learning. With these tools in place, students then learn logic and problem solving as a further foundation.Next various proof techniques such as direct proofs, proof by contraposition, proof by contradiction, and mathematical induction are introduced. These proof techniques are introduced using the context of number theory. The last chapter uses Calculus as a way for students to apply the proof techniques they have learned.

An Introduction To Logic Second Edition

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Author : Richard T.W. Arthur
language : en
Publisher: Broadview Press
Release Date : 2016-11-30

An Introduction To Logic Second Edition written by Richard T.W. Arthur and has been published by Broadview Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-30 with Philosophy categories.

In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python. A previous edition of this book appeared under the title Natural Deduction. This new edition adds clarifications of the notions of explanation, validity and formal validity, a more detailed discussion of derivation strategies, and another rule of inference, Reiteration.

Current Trends In Hardware Verification And Automated Theorem Proving

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Author : Graham Birtwistle
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Current Trends In Hardware Verification And Automated Theorem Proving written by Graham Birtwistle 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.

This report describes the partially completed correctness proof of the Viper 'block model'. Viper [7,8,9,11,23] is a microprocessor designed by W. J. Cullyer, C. Pygott and J. Kershaw at the Royal Signals and Radar Establishment in Malvern, England, (henceforth 'RSRE') for use in safety-critical applications such as civil aviation and nuclear power plant control. It is currently finding uses in areas such as the de ployment of weapons from tactical aircraft. To support safety-critical applications, Viper has a particulary simple design about which it is relatively easy to reason using current techniques and models. The designers, who deserve much credit for the promotion of formal methods, intended from the start that Viper be formally verified. Their idea was to model Viper in a sequence of decreasingly abstract levels, each of which concentrated on some aspect ofthe design, such as the flow ofcontrol, the processingofinstructions, and so on. That is, each model would be a specification of the next (less abstract) model, and an implementation of the previous model (if any). The verification effort would then be simplified by being structured according to the sequence of abstraction levels. These models (or levels) of description were characterized by the design team. The first two levels, and part of the third, were written by them in a logical language amenable to reasoning and proof.

7th International Conference On Automated Deduction

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Author : R. E. Shostak
language : en
Publisher: Springer
Release Date : 2011-05-09

7th International Conference On Automated Deduction written by R. E. Shostak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-09 with Mathematics categories.

The Seventh International Conference on Automated Deduction was held May 14-16, 19S4, in Napa, California. The conference is the primary forum for reporting research in all aspects of automated deduction, including the design, implementation, and applications of theorem-proving systems, knowledge representation and retrieval, program verification, logic programming, formal specification, program synthesis, and related areas. The presented papers include 27 selected by the program committee, an invited keynote address by Jorg Siekmann, and an invited banquet address by Patrick Suppes. Contributions were presented by authors from Canada, France, Spain, the United Kingdom , the United States, and West Germany. The first conference in this series was held a decade earlier in Argonne, Illinois. Following the Argonne conference were meetings in Oberwolfach, West Germany (1976), Cambridge, Massachusetts (1977), Austin, Texas (1979), Les Arcs, France (19S0), and New York, New York (19S2). Program Committee P. Andrews (CMU) W.W. Bledsoe (U. Texas) past chairman L. Henschen (Northwestern) G. Huet (INRIA) D. Loveland (Duke) past chairman R. Milner (Edinburgh) R. Overbeek (Argonne) T. Pietrzykowski (Acadia) D. Plaisted (U. Illinois) V. Pratt (Stanford) R. Shostak (SRI) chairman J. Siekmann (U. Kaiserslautern) R. Waldinger (SRI) Local Arrangements R. Schwartz (SRI) iv CONTENTS Monday Morning Universal Unification (Keynote Address) Jorg H. Siekmann (FRG) .

Ijcai Proceedings 1979

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Author : Ijcai
language : en
Publisher: Elsevier
Release Date : 1979

Ijcai Proceedings 1979 written by Ijcai and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Computers categories.

Theorem Proving In Higher Order Logics

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Author : Richard J. Boulton
language : en
Publisher: Springer
Release Date : 2003-06-30

Theorem Proving In Higher Order Logics written by Richard J. Boulton and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-30 with Computers categories.

This volume constitutes the proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2001) held 3–6 September 2001 in Edinburgh, Scotland. TPHOLs covers all aspects of theorem proving in higher order logics, as well as related topics in theorem proving and veri?cation. TPHOLs 2001 was collocated with the 11th Advanced Research Working Conference on Correct Hardware Design and Veri?cation Methods (CHARME 2001). This was held 4–7 September 2001 in nearby Livingston, Scotland at the Institute for System Level Integration, and a joint half-day session of talks was arranged for the 5th September in Edinburgh. An excursion to Traquair House and a banquet in the Playfair Library of Old College, University of Edinburgh were also jointly organized. The proceedings of CHARME 2001 have been p- lished as volume 2144 of Springer-Verlag’s Lecture Notes in Computer Science series, with Tiziana Margaria and Tom Melham as editors. Each of the 47 papers submitted in the full research category was refereed by at least 3 reviewers who were selected by the Program Committee. Of these submissions, 23 were accepted for presentation at the conference and publication in this volume. In keeping with tradition, TPHOLs 2001 also o?ered a venue for the presentation of work in progress, where researchers invite discussion by means of a brief preliminary talk and then discuss their work at a poster session. A supplementary proceedings containing associated papers for work in progress was published by the Division of Informatics at the University of Edinburgh.

Introduction To Proofs And Proof Strategies

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