Logic Lecture Notes For Philosophy Mathematics And Computer Science

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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.

Logicism Renewed

Author : Paul C. Gilmore
Publisher : Cambridge University Press
ISBN 13 : 1108676936
Total Pages : pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Logicism Renewed by : Paul C. Gilmore

Download or read book Logicism Renewed written by Paul C. Gilmore and published by Cambridge University Press. This book was released on 2017-03-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Logicism, as put forward by Bertrand Russell, was predicated on a belief that all of mathematics can be deduced from a very small number of fundamental logical principles. In this volume, the twenty-third publication in the Lecture Notes in Logic series, Paul C. Gilmore revisits logicism in light of recent advances in mathematical logic and theoretical computer science. Gilmore addresses the need for languages which can be understood by both humans and computers and, using Intensional Type Theory (ITT), provides a unified basis for mathematics and computer science. This yields much simpler foundations for recursion theory and the semantics of computer programs than those currently provided by category theory.

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

Intensionality

Author : Reinhard Kähle
Publisher : Cambridge University Press
ISBN 13 : 1108634001
Total Pages : pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Intensionality by : Reinhard Kähle

Download or read book Intensionality written by Reinhard Kähle and published by Cambridge University Press. This book was released on 2017-03-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twenty-second publication in the Lecture Notes in Logic series, will launch a discussion about the concept of intensionality in philosophy, logic, linguistics and mathematics. These articles grew out of a workshop held at the University of Munich in October, 2000. Some articles address philosophical issues raised by the possible worlds approach to intensionality; others are devoted to technical aspects of modal logic. The volume highlights the particular interdisciplinary nature of intensionality with articles spanning philosophy, linguistics, mathematics and computer science.

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.

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.

Logic Colloquium 2007

Author : Françoise Delon
Publisher : Cambridge University Press
ISBN 13 : 1139488937
Total Pages : 282 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Logic Colloquium 2007 by : Françoise Delon

Download or read book Logic Colloquium 2007 written by Françoise Delon and published by Cambridge University Press. This book was released on 2010-06-07 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume, Logic Colloquium 2007, with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. This volume covers many areas of contemporary logic: model theory, proof theory, set theory, and computer science, as well as philosophical logic, including tutorials on cardinal arithmetic, on Pillay's conjecture, and on automatic structures. This volume will be invaluable for experts as well as those interested in an overview of central contemporary themes in mathematical logic.

Logic Colloquium '01

Author : Matthias Baaz
Publisher : A K Peters/CRC Press
ISBN 13 :
Total Pages : 502 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Logic Colloquium '01 by : Matthias Baaz

Download or read book Logic Colloquium '01 written by Matthias Baaz and published by A K Peters/CRC Press. This book was released on 2005-03-07 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: A compilation of papers presented at the 2001 European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium '01 includes surveys and research articles from some of the world's preeminent logicians. Two long articles are based on tutorials given at the meeting and present accessible expositions of research in two active areas of logic, geometric model theory and descriptive set theory of group actions. The remaining articles cover seperate research topics in many areas of mathematical logic, including applications in Computer Science, Proof Theory, Set Theory, Model Theory, Computability Theory, and aspects of Philosophy. This collection will be of interest not only to specialists in mathematical logic, but also to philosophical logicians, historians of logic, computer scientists, formal linguists and mathematicians in the areas of algebra, abstract analysis and topology. A number of the articles are aimed at non-specialists and serve as good introductions for graduate students.

Logics for Computer Science

Author : Anita Wasilewska
Publisher : Springer
ISBN 13 : 3319925911
Total Pages : 535 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Logics for Computer Science by : Anita Wasilewska

Download or read book Logics for Computer Science written by Anita Wasilewska and published by Springer. This book was released on 2018-11-03 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an in-depth introduction to fundamental classical and non-classical logics, this textbook offers a comprehensive survey of logics for computer scientists. Logics for Computer Science contains intuitive introductory chapters explaining the need for logical investigations, motivations for different types of logics and some of their history. They are followed by strict formal approach chapters. All chapters contain many detailed examples explaining each of the introduced notions and definitions, well chosen sets of exercises with carefully written solutions, and sets of homework. While many logic books are available, they were written by logicians for logicians, not for computer scientists. They usually choose one particular way of presenting the material and use a specialized language. Logics for Computer Science discusses Gentzen as well as Hilbert formalizations, first order theories, the Hilbert Program, Godel's first and second incompleteness theorems and their proofs. It also introduces and discusses some many valued logics, modal logics and introduces algebraic models for classical, intuitionistic, and modal S4 and S5 logics. The theory of computation is based on concepts defined by logicians and mathematicians. Logic plays a fundamental role in computer science, and this book explains the basic theorems, as well as different techniques of proving them in classical and some non-classical logics. Important applications derived from concepts of logic for computer technology include Artificial Intelligence and Software Engineering. In addition to Computer Science, this book may also find an audience in mathematics and philosophy courses, and some of the chapters are also useful for a course in Artificial Intelligence.

A Concise Introduction to Mathematical Logic

Author : Wolfgang Rautenberg
Publisher : Springer
ISBN 13 : 1441912215
Total Pages : 337 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis A Concise Introduction to Mathematical Logic by : Wolfgang Rautenberg

Download or read book A Concise Introduction to Mathematical Logic written by Wolfgang Rautenberg and published by Springer. This book was released on 2010-07-01 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.

A Friendly Introduction to Mathematical Logic

Author : Christopher C. Leary
Publisher : Lulu.com
ISBN 13 : 1942341075
Total Pages : 382 pages
Book Rating : 4.9/5 (423 download)

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Book Synopsis A Friendly Introduction to Mathematical Logic by : Christopher C. Leary

Download or read book A Friendly Introduction to Mathematical Logic written by Christopher C. Leary and published by Lulu.com. This book was released on 2015 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.

Logic Colloquium 2000 (hardcover)

Author : Rene Cori
Publisher : A K Peters/CRC Press
ISBN 13 :
Total Pages : 432 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Logic Colloquium 2000 (hardcover) by : Rene Cori

Download or read book Logic Colloquium 2000 (hardcover) written by Rene Cori and published by A K Peters/CRC Press. This book was released on 2005-04-25 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This compilation of papers presented at the 2000 European Summer Meeting of the Association for Symbolic Logic marks the centenial anniversery of Hilbert's famous lecture. Held in the same hall at La Sorbonne where Hilbert first presented his famous problems, this meeting carries special significance to the Mathematics and Logic communities. The presentations include tutorials and research articles from some of the world's preeminent logicians. Three long articles are based on tutorials given at the meeting, and present accessible expositions of devloping research in three active areas of logic: model theory, computability, and set theory. The eleven subsequent articles cover seperate research topics in all areas of mathematical logic, including: aspects in Computer Science, Proof Theory, Set Theory, Model Theory, Computability Theory, and aspects of Philosophy.

Lectures in Logic and Set Theory: Volume 1, Mathematical Logic

Author : George Tourlakis
Publisher : Cambridge University Press
ISBN 13 : 9780521753739
Total Pages : 342 pages
Book Rating : 4.7/5 (537 download)

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Book Synopsis Lectures in Logic and Set Theory: Volume 1, Mathematical Logic by : George Tourlakis

Download or read book Lectures in Logic and Set Theory: Volume 1, Mathematical Logic written by George Tourlakis and published by Cambridge University Press. This book was released on 2003-01-09 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work bridges the gap between introductory expositions of logic (or set theory) and the research literature. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly lecture style that makes them equally effective for self-study or class use. Volume I includes formal proof techniques, applications of compactness (including nonstandard analysis), computability and its relation to the completeness phenonmenon, and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen.

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.

Computation, Logic, Philosophy

Author : Wang Hao
Publisher : Springer Science & Business Media
ISBN 13 : 9400923562
Total Pages : 394 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Computation, Logic, Philosophy by : Wang Hao

Download or read book Computation, Logic, Philosophy written by Wang Hao and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: ~Et moi ... si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non· The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Bridging the Gap: Philosophy, Mathematics, and Physics

Author : Giovanna Corsi
Publisher : Springer Science & Business Media
ISBN 13 : 9780792317616
Total Pages : 356 pages
Book Rating : 4.3/5 (176 download)

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Book Synopsis Bridging the Gap: Philosophy, Mathematics, and Physics by : Giovanna Corsi

Download or read book Bridging the Gap: Philosophy, Mathematics, and Physics written by Giovanna Corsi and published by Springer Science & Business Media. This book was released on 1993 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundational questions in logic, mathematics, computer science and physics are constant sources of epistemological debate in contemporary philosophy. To what extent is the transfinite part of mathematics completely trustworthy? Why is there a general malaise' concerning the logical approach to the foundations of mathematics? What is the role of symmetry in physics? Is it possible to build a coherent worldview compatible with a macroobjectivistic position and based on the quantum picture of the world? What account can be given of opinion change in the light of new evidence? These are some of the questions discussed in this volume, which collects 14 lectures on the foundation of science given at the School of Philosophy of Science, Trieste, October 1989. The volume will be of particular interest to any student or scholar engaged in interdisciplinary research into the foundations of science in the context of contemporary debates.