A First Course in Logic

An Introduction to Model Theory, Proof Theory, Computability, and Complexity

Author: Shawn Hedman

Publisher: Oxford University Press on Demand

ISBN: 9780198529811

Category: Mathematics

Page: 431

View: 8584

"The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, thistext covers the fundamental topics in classical logic in a clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, andmodel theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course."--BOOK JACKET.

A First Course in Logic

An Introduction to Model Theory, Proof Theory, Computability, and Complexity

Author: Shawn Hedman

Publisher: OUP Oxford

ISBN: 9780198529804

Category: Mathematics

Page: 452

View: 6582

"The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, thistext covers the fundamental topics in classical logic in a clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, andmodel theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course."--BOOK JACKET.

Automata, Languages, and Programming

42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6-10, 2015, Proceedings

Author: Magnús M. Halldórsson,Kazuo Iwama,Naoki Kobayashi,Bettina Speckmann

Publisher: Springer

ISBN: 366247672X

Category: Computers

Page: 1111

View: 5507

The two-volume set LNCS 9134 and LNCS 9135 constitutes the refereed proceedings of the 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015, held in Kyoto, Japan, in July 2015. The 143 revised full papers presented were carefully reviewed and selected from 507 submissions. The papers are organized in the following three tracks: algorithms, complexity, and games; logic, semantics, automata, and theory of programming; and foundations of networked computation: models, algorithms, and information management.

Mathematical Foundations of Computer Science 2010

35th International Symposium, MFCS 2010, Brno, Czech Republic, August 23-27, 2010, Proceedings

Author: Petr Hlineny

Publisher: Springer Science & Business Media

ISBN: 364215154X

Category: Computers

Page: 714

View: 4106

This volume constitutes the refereed proceedings of the 35th International Symposium on Mathematical Foundations of Computer Science, MFCS 2010, held in Brno, Czech Republic, in August 2010. The 56 revised full papers presented together with 5 invited talks were carefully reviewed and selected from 149 submissions. Topics covered include algorithmic game theory, algorithmic learning theory, algorithms and data structures, automata, grammars and formal languages, bioinformatics, complexity, computational geometry, computer-assisted reasoning, concurrency theory, cryptography and security, databases and knowledge-based systems, formal specifications and program development, foundations of computing, logic in computer science, mobile computing, models of computation, networks, parallel and distributed computing, quantum computing, semantics and verification of programs, and theoretical issues in artificial intelligence.

Computer Science

Author: N.A

Publisher: PediaPress

ISBN: N.A

Category:

Page: N.A

View: 387

Logic and Metalogic

Author: N.A

Publisher: PediaPress

ISBN: N.A

Category:

Page: N.A

View: 2662

Fundamentals of Mathematical Logic

Author: Peter G. Hinman

Publisher: CRC Press

ISBN: 1439864276

Category: Mathematics

Page: 896

View: 7600

This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.

A Friendly Introduction to Mathematical Logic

Author: Christopher C. Leary,Lars Kristiansen

Publisher: Lulu.com

ISBN: 1942341075

Category:

Page: 380

View: 1669

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 Godel'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."

Computability and Randomness

Author: André Nies

Publisher: OUP Oxford

ISBN: 0191627887

Category: Philosophy

Page: 456

View: 3947

The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts and methods originating from randomness enrich computability theory. The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory.

A First Course in Logic

Author: K. Codell Carter

Publisher: Addison-Wesley Longman

ISBN: 9780321277329

Category: Philosophy

Page: 560

View: 4569

Providing students with a more understandable introduction to logic without sacrificing rigor, A First Course in Logic presents topics and methods in a highly accessible and integrated manner. By integrating and comparing topics throughout and using the same examples in different chapters, the author shows the utility and limitations of each method of logic. Consistent pedagogical structure helps students learn and study better; the introduction now emphasizes strategies and tactics for applying memorization rules. One-of-a-kind LSAT-type exercises apply logic to pre-professional exams. This Gold Edition of the text now uses more standard notation and has been thoroughly class-tested and revised for absolute accuracy of information.

Proof and Disproof in Formal Logic

An Introduction for Programmers

Author: Richard Bornat

Publisher: Oxford University Press, USA

ISBN: 9780198530268

Category: Mathematics

Page: 243

View: 3875

Aimed at undergraduates and graduates in computer science, logic, mathematics, and philosophy, this text is a lively and entertaining introduction to formal logic and provides an excellent insight into how a simple logic works.

Logic for Philosophy

Author: Theodore Sider

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Philosophy

Page: 289

View: 7511

Logic for Philosophy is an introduction to logic for students of contemporary philosophy. It is suitable both for advanced undergraduates and for beginning graduate students in philosophy. It covers (i) basic approaches to logic, including proof theory and especially model theory, (ii)extensions of standard logic that are important in philosophy, and (iii) some elementary philosophy of logic. It emphasizes breadth rather than depth. For example, it discusses modal logic and counterfactuals, but does not prove the central metalogical results for predicate logic (completeness,undecidability, etc.) Its goal is to introduce students to the logic they need to know in order to read contemporary philosophical work. It is very user-friendly for students without an extensive background in mathematics. In short, this book gives you the understanding of logic that you need to dophilosophy.

Introduction to the Theory of Computation

Author: Michael Sipser

Publisher: Cengage Learning

ISBN: 1285401069

Category: Computers

Page: 504

View: 8789

Now you can clearly present even the most complex computational theory topics to your students with Sipser's distinct, market-leading INTRODUCTION TO THE THEORY OF COMPUTATION, 3E. The number one choice for today's computational theory course, this highly anticipated revision retains the unmatched clarity and thorough coverage that make it a leading text for upper-level undergraduate and introductory graduate students. This edition continues author Michael Sipser's well-known, approachable style with timely revisions, additional exercises, and more memorable examples in key areas. A new first-of-its-kind theoretical treatment of deterministic context-free languages is ideal for a better understanding of parsing and LR(k) grammars. This edition's refined presentation ensures a trusted accuracy and clarity that make the challenging study of computational theory accessible and intuitive to students while maintaining the subject's rigor and formalism. Readers gain a solid understanding of the fundamental mathematical properties of computer hardware, software, and applications with a blend of practical and philosophical coverage and mathematical treatments, including advanced theorems and proofs. INTRODUCTION TO THE THEORY OF COMPUTATION, 3E's comprehensive coverage makes this an ideal ongoing reference tool for those studying theoretical computing. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Mathematical Logic and Model Theory

A Brief Introduction

Author: Alexander Prestel,Charles N. Delzell

Publisher: Springer Science & Business Media

ISBN: 1447121767

Category: Mathematics

Page: 194

View: 7300

Mathematical Logic and Model Theory: A Brief Introduction offers a streamlined yet easy-to-read introduction to mathematical logic and basic model theory. It presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra. As a profound application of model theory in algebra, the last part of this book develops a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields. The character of model theoretic constructions and results differ quite significantly from that commonly found in algebra, by the treatment of formulae as mathematical objects. It is therefore indispensable to first become familiar with the problems and methods of mathematical logic. Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic treatment of several algebraic theories (Chapter 4). This book will be of interest to both advanced undergraduate and graduate students studying model theory and its applications to algebra. It may also be used for self-study.

A Logical Introduction to Proof

Author: Daniel W. Cunningham

Publisher: Springer Science & Business Media

ISBN: 1461436311

Category: Mathematics

Page: 356

View: 8342

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.

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 4568

An Introduction to Quantum Computing

Author: Phillip Kaye,Raymond Laflamme,Michele Mosca

Publisher: Oxford University Press

ISBN: 0198570007

Category: Computers

Page: 274

View: 8866

The authors provide an introduction to quantum computing. Aimed at advanced undergraduate and beginning graduate students in these disciplines, this text is illustrated with diagrams and exercises.

The Philosopher's Index

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Philosophy

Page: N.A

View: 2139

Vols. for 1969- include a section of abstracts.

Mathematical Logic

Author: Ian Chiswell,Wilfrid Hodges

Publisher: Oxford University Press on Demand

ISBN: 0198571003

Category: Mathematics

Page: 250

View: 9021

Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't becalculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assumingMatiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optional sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics andcomputer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in Logic,Mathematics, Philosophy, and Computer Science.

First Course in Mathematical Logic

Author: Patrick Suppes,Shirley Hill

Publisher: Courier Corporation

ISBN: 0486150941

Category: Mathematics

Page: 288

View: 3790

Rigorous introduction is simple enough in presentation and context for wide range of students. Symbolizing sentences; logical inference; truth and validity; truth tables; terms, predicates, universal quantifiers; universal specification and laws of identity; more.