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Introduction to Mathematical Proofs by Charles Roberts Pdf
Introduction to Mathematical Proofs helps students develop the necessary skills to write clear, correct, and concise proofs.Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural num
Types for Proofs and Programs by Stefano Berardi,Ferruccio Damiani,Ugo de Liguoro Pdf
These proceedings contain a selection of refereed papers presented at or - lated to the Annual Workshop of the TYPES project (EU coordination action 510996), which was held during March 26–29, 2008 in Turin, Italy. The topic of this workshop, and of all previous workshops of the same project, was f- mal reasoning and computer programming based on type theory: languages and computerized tools for reasoning, and applications in several domains such as analysis of programming languages, certi?ed software, mobile code, formali- tion of mathematics, mathematics education. The workshop was attended by more than 100 researchers and included more than 40 presentations. We also had three invited lectures, from A. Asperti (University of Bologna), G. Dowek (LIX, Ecole polytechnique, France) and J. W. Klop (Vrije Universiteit, A- terdam, The Netherlands). From 27 submitted papers, 19 were selected after a reviewing process. Each submitted paper was reviewed by three referees; the ?nal decisions were made by the editors. This workshop is the last of a series of meetings of the TYPES working group funded by the European Union (IST project 29001, ESPRIT Working Group 21900, ESPRIT BRA 6435).
Dag Prawitz on Proofs and Meaning by Heinrich Wansing Pdf
This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of p roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence.
Certified Programs and Proofs by Jean-Pierre Jouannaud,Zhong Shao Pdf
This book constitutes the referred proceedings of the First International Conference on Certified Programs and Proofs, CPP 2011, held in Kenting, Taiwan, in December 2011. The 24 revised regular papers presented together with 4 invited talks were carefully reviewed and selected from 49 submissions. They are organized in topical sections on logic and types, certificates, formalization, proof assistants, teaching, programming languages, hardware certification, miscellaneous, and proof perls.
Adapting Proofs-as-Programs by Iman Poernomo,John N. Crossley,Martin Wirsing Pdf
This monograph details several important advances in the direction of a practical proofs-as-programs paradigm, which constitutes a set of approaches to developing programs from proofs in constructive logic with applications to industrial-scale, complex software engineering problems. One of the books central themes is a general, abstract framework for developing new systems of programs synthesis by adapting proofs-as-programs to new contexts.
Hegel on the Proofs and Personhood of God by Robert R. Williams Pdf
This work considers the question of the personhood of God in Hegel. The first part examines Hegel's critique of Kant, focusing on and replying to Kant's attack on the theological proofs. The second part then explores the issue of divine personhood.
1 This volume contains the research papers and invited papers presented at the Third International Conference on Tests and Proofs (TAP 2009) held at ETH Zurich, Switzerland, during July 2–3, 2009. TheTAPconferenceisdevotedtotheconvergenceofproofsandtests. Itc- bines ideasfromboth sidesforthe advancementofsoftwarequality. Toprovethe correctness of a program is to demonstrate, through impeccable mathematical techniques, that it has no bugs; to test a program is to run it with the exp- tation of discovering bugs. The two techniques seem contradictory: if you have proved your program, it is fruitless to comb it for bugs; and if you are testing it, that is surely a sign that you have given up on any hope of proving its corre- ness. Accordingly, proofs and tests have, since the onset of software engineering research,been pursuedby distinct communities using ratherdi?erent techniques and tools. And yet the development of both approaches leads to the discovery of common issues and to the realization that each may need the other. The emergence of model checking has been one of the ?rst signs that contradiction may yield to complementarity, but in the past few years an increasing number of research e?orts have encountered the need for combining proofs and tests, dropping earlier dogmatic views of incompatibility and taking instead the best of what each of these software engineering domains has to o?er.
Aquinas’ Proofs for God’s Existence by D. Bonnette Pdf
The purpose of this study is to investigate the legitimacy of the principle, "The per accidens necessarily implies the per se," as it is found in the writings of St. Thomas Aquinas. Special emphasis will be placed upon the function of this principle in the proofs for God's existence. The relevance of the principle in this latter context can be seen at once when it is observed that it is the key to the solution of the well known "prob lem of infinite regress. " The investigation of the principle in question will be divided into two Parts. A preliminary examination of the function of the principle will be made in Part I: Domains Other Than That of Creature-God. The domains to be considered in this Part are those of accident-substance, change, and knowledge. Employing what is learned of the function of the principle in these areas of application, Part II: The Domain of Creature-God will analyze the role of the principle in the proofs for God's existence. This latter Part will constitute the greater portion of the book, since the domain of creatures in their relation to God is the most significant application of the principle in the writings of St. Thomas. In the course of this investigation, relevant analyses by St. Thomas' commentators - both classical and contemporary - will be considered. Finally, in light of the insights offered by St.
Existential Inertia and Classical Theistic Proofs by Joseph C. Schmid,Daniel J. Linford Pdf
This book critically assesses arguments for the existence of the God of classical theism, develops an innovative account of objects’ persistence, and defends new arguments against classical theism. The authors engage the following classical theistic proofs: Aquinas’s First Way, Aquinas’s De Ente argument, and Feser’s Aristotelian, Neo-Platonic, Augustinian, Thomistic, and Rationalist proofs. The authors also provide the first systematic treatment of the ‘existential inertia thesis’. By connecting the thesis to relativity theory and recent developments in the philosophy of physics, and by developing a variety of novel existential-inertia-friendly explanations of persistence, they mount a formidable new case against classical theistic proofs. Finally, they defend new arguments against classical theism based on abstract objects and changing divine knowledge. The text appeals to students, researchers, and others interested in classical theistic proofs, the existence and nature of God, and the ultimate explanations of persistence, change, and contingency.
Proofs from THE BOOK by Martin Aigner,Günter M. Ziegler Pdf
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
This text makes a great supplement and provides a systematic approach for teaching undergraduate and graduate students how to read, understand, think about, and do proofs. The approach is to categorize, identify, and explain (at the student's level) the various techniques that are used repeatedly in all proofs, regardless of the subject in which the proofs arise. How to Read and Do Proofs also explains when each technique is likely to be used, based on certain key words that appear in the problem under consideration. Doing so enables students to choose a technique consciously, based on the form of the problem.