Topics In Logic Philosophy And Foundations Of Mathematics And Computer Science

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Topics in Logic, Philosophy and Foundations of Mathematics, and Computer Science

Author : Stanisław Krajewski
Publisher : IOS Press
ISBN 13 : 9781586038144
Total Pages : 380 pages
Book Rating : 4.0/5 (381 download)

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Book Synopsis Topics in Logic, Philosophy and Foundations of Mathematics, and Computer Science by : Stanisław Krajewski

Download or read book Topics in Logic, Philosophy and Foundations of Mathematics, and Computer Science written by Stanisław Krajewski and published by IOS Press. This book was released on 2007 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume honors Professor Andrzej Grzegorczyk, the nestor of Polish logicians, on his 85th anniversary. The editors would like to express the respect and sympathy they have for him. His textbook The Outline of Mathematical Logic has been published in many editions and translated into several languages. It was this textbook that introduced many of us into the world of mathematical logic. Professor Grzegorczyk has made fundamental contributions to logic and to philosophy. His results, mainly on hierarchy of primitive recursive functions, known as the Grzegorczyk hierarchy, are of fundamental importance to theoretical computer science. In particular, they were precursory for the computational complexity theory. The editors would like to stress that this special publication celebrates a scientist who is still actively pursuing genuinely innovative directions of research. Quite recently, Andrzej Grzegorczyk gave a new proof of undecidability of the first order functional calculus. His proof does not use the arithmetization of Kurt Gödel. In recognition of his merits, the University of Clermont-Ferrand conferred to Professor Andrzej Grzegorczyk the Doctorat Honoris Causa. The work and life of Professor Andrzej Grzegorczyk is presented in the article by Professors Stanislaw Krajewski and Jan Wolenski. The papers in this collection have been submitted on invitational basis.

LOGIC: Lecture Notes for Philosophy, Mathematics, and Computer Science

Author : Andrea Iacona
Publisher : Springer Nature
ISBN 13 : 3030648117
Total Pages : 228 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis LOGIC: Lecture Notes for Philosophy, Mathematics, and Computer Science by : Andrea Iacona

Download or read book LOGIC: Lecture Notes for Philosophy, Mathematics, and Computer Science written by Andrea Iacona and published by Springer Nature. This book was released on 2021-05-10 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a logic manual which includes an elementary course and an advanced course. It covers more than most introductory logic textbooks, while maintaining a comfortable pace that students can follow. The technical exposition is clear, precise and follows a paced increase in complexity, allowing the reader to get comfortable with previous definitions and procedures before facing more difficult material. The book also presents an interesting overall balance between formal and philosophical discussion, making it suitable for both philosophy and more formal/science oriented students. This textbook is of great use to undergraduate philosophy students, graduate philosophy students, logic teachers, undergraduates and graduates in mathematics, computer science or related fields in which logic is required.

Three Views of Logic

Author : Donald W. Loveland
Publisher : Princeton University Press
ISBN 13 : 140084875X
Total Pages : 344 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Three Views of Logic by : Donald W. Loveland

Download or read book Three Views of Logic written by Donald W. Loveland and published by Princeton University Press. This book was released on 2014-01-26 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses

Lectures on the Philosophy of Mathematics

Author : Joel David Hamkins
Publisher : MIT Press
ISBN 13 : 0262542234
Total Pages : 350 pages
Book Rating : 4.2/5 (625 download)

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Book Synopsis Lectures on the Philosophy of Mathematics by : Joel David Hamkins

Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-03-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

Johan van Benthem on Logic and Information Dynamics

Author : Alexandru Baltag
Publisher : Springer
ISBN 13 : 3319060252
Total Pages : 1072 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Johan van Benthem on Logic and Information Dynamics by : Alexandru Baltag

Download or read book Johan van Benthem on Logic and Information Dynamics written by Alexandru Baltag and published by Springer. This book was released on 2014-08-27 with total page 1072 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book illustrates the program of Logical-Informational Dynamics. Rational agents exploit the information available in the world in delicate ways, adopt a wide range of epistemic attitudes, and in that process, constantly change the world itself. Logical-Informational Dynamics is about logical systems putting such activities at center stage, focusing on the events by which we acquire information and change attitudes. Its contributions show many current logics of information and change at work, often in multi-agent settings where social behavior is essential, and often stressing Johan van Benthem's pioneering work in establishing this program. However, this is not a Festschrift, but a rich tapestry for a field with a wealth of strands of its own. The reader will see the state of the art in such topics as information update, belief change, preference, learning over time, and strategic interaction in games. Moreover, no tight boundary has been enforced, and some chapters add more general mathematical or philosophical foundations or links to current trends in computer science. The theme of this book lies at the interface of many disciplines. Logic is the main methodology, but the various chapters cross easily between mathematics, computer science, philosophy, linguistics, cognitive and social sciences, while also ranging from pure theory to empirical work. Accordingly, the authors of this book represent a wide variety of original thinkers from different research communities. And their interconnected themes challenge at the same time how we think of logic, philosophy and computation. Thus, very much in line with van Benthem's work over many decades, the volume shows how all these disciplines form a natural unity in the perspective of dynamic logicians (broadly conceived) exploring their new themes today. And at the same time, in doing so, it offers a broader conception of logic with a certain grandeur, moving its horizons beyond the traditional study of consequence relations.

Gödel '96

Author : Petr Hájek
Publisher : Cambridge University Press
ISBN 13 : 1107168023
Total Pages : 331 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Gödel '96 by : Petr Hájek

Download or read book Gödel '96 written by Petr Hájek and published by Cambridge University Press. This book was released on 2017-03-02 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings of the conference 'Logical Foundations of Mathematics, Computer Science, and Physics - Kurt Gödel's Legacy', held in Brno, Czech Republic, on the 90th anniversary of Gödel's birth. The papers in this volume cover the wide range of topics Gödel's work touched, and affirm its continuing importance.

Algebraic Varieties

Author : G. Kempf
Publisher : Cambridge University Press
ISBN 13 : 9780521426138
Total Pages : 180 pages
Book Rating : 4.4/5 (261 download)

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Book Synopsis Algebraic Varieties by : G. Kempf

Download or read book Algebraic Varieties written by G. Kempf and published by Cambridge University Press. This book was released on 1993-09-09 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint.

Philosophical and Mathematical Logic

Author : Harrie de Swart
Publisher : Springer
ISBN 13 : 3030032558
Total Pages : 539 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Philosophical and Mathematical Logic by : Harrie de Swart

Download or read book Philosophical and Mathematical Logic written by Harrie de Swart and published by Springer. This book was released on 2018-11-28 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was written to serve as an introduction to logic, with in each chapter – if applicable – special emphasis on the interplay between logic and philosophy, mathematics, language and (theoretical) computer science. The reader will not only be provided with an introduction to classical logic, but to philosophical (modal, epistemic, deontic, temporal) and intuitionistic logic as well. The first chapter is an easy to read non-technical Introduction to the topics in the book. The next chapters are consecutively about Propositional Logic, Sets (finite and infinite), Predicate Logic, Arithmetic and Gödel’s Incompleteness Theorems, Modal Logic, Philosophy of Language, Intuitionism and Intuitionistic Logic, Applications (Prolog; Relational Databases and SQL; Social Choice Theory, in particular Majority Judgment) and finally, Fallacies and Unfair Discussion Methods. Throughout the text, the author provides some impressions of the historical development of logic: Stoic and Aristotelian logic, logic in the Middle Ages and Frege's Begriffsschrift, together with the works of George Boole (1815-1864) and August De Morgan (1806-1871), the origin of modern logic. Since "if ..., then ..." can be considered to be the heart of logic, throughout this book much attention is paid to conditionals: material, strict and relevant implication, entailment, counterfactuals and conversational implicature are treated and many references for further reading are given. Each chapter is concluded with answers to the exercises. Philosophical and Mathematical Logic is a very recent book (2018), but with every aspect of a classic. What a wonderful book! Work written with all the necessary rigor, with immense depth, but without giving up clarity and good taste. Philosophy and mathematics go hand in hand with the most diverse themes of logic. An introductory text, but not only that. It goes much further. It's worth diving into the pages of this book, dear reader! Paulo Sérgio Argolo

Feferman on Foundations

Author : Gerhard Jäger
Publisher : Springer
ISBN 13 : 3319633341
Total Pages : 551 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Feferman on Foundations by : Gerhard Jäger

Download or read book Feferman on Foundations written by Gerhard Jäger and published by Springer. This book was released on 2018-04-04 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman’s work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman’s work was largely based in mathematical logic (namely model theory, set theory, proof theory and computability theory), but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With regard to methodological issues, Feferman supported concrete projects. On the one hand, these projects calibrate the proof theoretic strength of subsystems of analysis and set theory and provide ways of overcoming the limitations imposed by Gödel’s incompleteness theorems through appropriate conceptual expansions. On the other, they seek to identify novel axiomatic foundations for mathematical practice, truth theories, and category theory. In his philosophical research, Feferman explored questions such as “What is logic?” and proposed particular positions regarding the foundations of mathematics including, for example, his “conceptual structuralism.” The contributing authors of the volume examine all of the above issues. Their papers are accompanied by an autobiography presented by Feferman that reflects on the evolution and intellectual contexts of his work. The contributing authors critically examine Feferman’s work and, in part, actively expand on his concrete mathematical projects. The volume illuminates Feferman’s distinctive work and, in the process, provides an enlightening perspective on the foundations of mathematics and logic.

Kurt Gödel and the Foundations of Mathematics

Author : Matthias Baaz
Publisher : Cambridge University Press
ISBN 13 : 1139498436
Total Pages : 541 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Kurt Gödel and the Foundations of Mathematics by : Matthias Baaz

Download or read book Kurt Gödel and the Foundations of Mathematics written by Matthias Baaz and published by Cambridge University Press. This book was released on 2011-06-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.

Martin Davis on Computability, Computational Logic, and Mathematical Foundations

Author : Eugenio G. Omodeo
Publisher : Springer
ISBN 13 : 3319418424
Total Pages : 438 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Martin Davis on Computability, Computational Logic, and Mathematical Foundations by : Eugenio G. Omodeo

Download or read book Martin Davis on Computability, Computational Logic, and Mathematical Foundations written by Eugenio G. Omodeo and published by Springer. This book was released on 2017-01-27 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a set of historical recollections on the work of Martin Davis and his role in advancing our understanding of the connections between logic, computing, and unsolvability. The individual contributions touch on most of the core aspects of Davis’ work and set it in a contemporary context. They analyse, discuss and develop many of the ideas and concepts that Davis put forward, including such issues as contemporary satisfiability solvers, essential unification, quantum computing and generalisations of Hilbert’s tenth problem. The book starts out with a scientific autobiography by Davis, and ends with his responses to comments included in the contributions. In addition, it includes two previously unpublished original historical papers in which Davis and Putnam investigate the decidable and the undecidable side of Logic, as well as a full bibliography of Davis’ work. As a whole, this book shows how Davis’ scientific work lies at the intersection of computability, theoretical computer science, foundations of mathematics, and philosophy, and draws its unifying vision from his deep involvement in Logic.

Foundations of Logic and Mathematics

Author : Yves Nievergelt
Publisher : Springer Science & Business Media
ISBN 13 : 146120125X
Total Pages : 425 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Foundations of Logic and Mathematics by : Yves Nievergelt

Download or read book Foundations of Logic and Mathematics written by Yves Nievergelt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This modern introduction to the foundations of logic and mathematics not only takes theory into account, but also treats in some detail applications that have a substantial impact on everyday life (loans and mortgages, bar codes, public-key cryptography). A first college-level introduction to logic, proofs, sets, number theory, and graph theory, and an excellent self-study reference and resource for instructors.

An Introduction to Mathematical Logic

Author : Richard E. Hodel
Publisher : Courier Corporation
ISBN 13 : 0486497852
Total Pages : 514 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis An Introduction to Mathematical Logic by : Richard E. Hodel

Download or read book An Introduction to Mathematical Logic written by Richard E. Hodel and published by Courier Corporation. This book was released on 2013-01-01 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.

Reflections on the Foundations of Mathematics

Author : Stefania Centrone
Publisher : Springer Nature
ISBN 13 : 3030156559
Total Pages : 511 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Reflections on the Foundations of Mathematics by : Stefania Centrone

Download or read book Reflections on the Foundations of Mathematics written by Stefania Centrone and published by Springer Nature. This book was released on 2019-11-11 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The volume is divided into three sections, the first two of which focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics.

Logic for Computer Scientists

Author : Uwe Schöning
Publisher : Springer Science & Business Media
ISBN 13 : 0817647627
Total Pages : 172 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Logic for Computer Scientists by : Uwe Schöning

Download or read book Logic for Computer Scientists written by Uwe Schöning and published by Springer Science & Business Media. This book was released on 2008-01-11 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the notions and methods of formal logic from a computer science standpoint, covering propositional logic, predicate logic, and foundations of logic programming. The classic text is replete with illustrative examples and exercises. It presents applications and themes of computer science research such as resolution, automated deduction, and logic programming in a rigorous but readable way. The style and scope of the work, rounded out by the inclusion of exercises, make this an excellent textbook for an advanced undergraduate course in logic for computer scientists.

Concepts of Proof in Mathematics, Philosophy, and Computer Science

Author : Dieter Probst
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 150150262X
Total Pages : 384 pages
Book Rating : 4.5/5 (15 download)

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Book Synopsis Concepts of Proof in Mathematics, Philosophy, and Computer Science by : Dieter Probst

Download or read book Concepts of Proof in Mathematics, Philosophy, and Computer Science written by Dieter Probst and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-07-25 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.

Undergraduate Algebraic Geometry

Author : Miles Reid
Publisher : Cambridge University Press
ISBN 13 : 9780521356626
Total Pages : 144 pages
Book Rating : 4.3/5 (566 download)

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Book Synopsis Undergraduate Algebraic Geometry by : Miles Reid

Download or read book Undergraduate Algebraic Geometry written by Miles Reid and published by Cambridge University Press. This book was released on 1988-12-15 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time. With the minimum of prerequisites, Dr Reid introduces the reader to the basic concepts of algebraic geometry including: plane conics, cubics and the group law, affine and projective varieties, and non-singularity and dimension. He is at pains to stress the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book arises from an undergraduate course given at the University of Warwick and contains numerous examples and exercises illustrating the theory.