Author: Ahti-Veikko Pietarinen Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110649659 Category : Philosophy Languages : en Pages : 447
Book Description
In three comprehensive volumes, Logic of the Future presents a full panorama of Charles S. Peirce’s important late writings. Among the most influential American thinkers, Peirce took his existential graphs to be his greatest contribution to human thought. The manuscripts from 1895—1913, most of which are published here for the first time, testify the richness and open-endedness of his theory of logic and its applications. They also invite us to reconsider our ordinary conceptions of reasoning as well as the conventional stories told about the evolution of modern logic. This second volume collects Peirce’s writings on existential graphs related to his Lowell Lectures of 1903, the annus mirabilis of his that became decisive in the development of the mature theory of the graphical method of logic.
Author: Ahti-Veikko Pietarinen Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110651408 Category : Philosophy Languages : en Pages : 684
Book Description
In three comprehensive volumes, Logic of the Future presents a full panorama of Charles S. Peirce’s most important late writings. Among the most influential American thinkers, Peirce took his existential graphs to be a significant contribution to human thought. The manuscripts from 1895–1913, with many of them being published here for the first time, testify to the richness and open-endedness of his theory of logic and its applications. They also invite us to reconsider our ordinary conceptions of reasoning as well as the conventional stories concerning the evolution of modern logic. This first volume of Logic of the Future is on the historical development, theory and application of Peirce’s graphical method and diagrammatic reasoning. It also illustrates the abundant further developments and applications Peirce envisaged existential graphs to have on the analysis of mathematics, language, meaning and mind.
Author: Steven Vickers Publisher: Cambridge University Press ISBN: 9780521576512 Category : Computers Languages : en Pages : 224
Book Description
Now in paperback, Topology via Logic is an advanced textbook on topology for computer scientists. Based on a course given by the author to postgraduate students of computer science at Imperial College, it has three unusual features. First, the introduction is from the locale viewpoint, motivated by the logic of finite observations: this provides a more direct approach than the traditional one based on abstracting properties of open sets in the real line. Second, the methods of locale theory are freely exploited. Third, there is substantial discussion of some computer science applications. Although books on topology aimed at mathematics exist, no book has been written specifically for computer scientists. As computer scientists become more aware of the mathematical foundations of their discipline, it is appropriate that such topics are presented in a form of direct relevance and applicability. This book goes some way towards bridging the gap.
Author: Zofia Adamowicz Publisher: John Wiley & Sons ISBN: 1118030796 Category : Mathematics Languages : en Pages : 276
Book Description
A thorough, accessible, and rigorous presentation of the central theorems of mathematical logic . . . ideal for advanced students of mathematics, computer science, and logic Logic of Mathematics combines a full-scale introductory course in mathematical logic and model theory with a range of specially selected, more advanced theorems. Using a strict mathematical approach, this is the only book available that contains complete and precise proofs of all of these important theorems: * Gödel's theorems of completeness and incompleteness * The independence of Goodstein's theorem from Peano arithmetic * Tarski's theorem on real closed fields * Matiyasevich's theorem on diophantine formulas Logic of Mathematics also features: * Full coverage of model theoretical topics such as definability, compactness, ultraproducts, realization, and omission of types * Clear, concise explanations of all key concepts, from Boolean algebras to Skolem-Löwenheim constructions and other topics * Carefully chosen exercises for each chapter, plus helpful solution hints At last, here is a refreshingly clear, concise, and mathematically rigorous presentation of the basic concepts of mathematical logic-requiring only a standard familiarity with abstract algebra. Employing a strict mathematical approach that emphasizes relational structures over logical language, this carefully organized text is divided into two parts, which explain the essentials of the subject in specific and straightforward terms. Part I contains a thorough introduction to mathematical logic and model theory-including a full discussion of terms, formulas, and other fundamentals, plus detailed coverage of relational structures and Boolean algebras, Gödel's completeness theorem, models of Peano arithmetic, and much more. Part II focuses on a number of advanced theorems that are central to the field, such as Gödel's first and second theorems of incompleteness, the independence proof of Goodstein's theorem from Peano arithmetic, Tarski's theorem on real closed fields, and others. No other text contains complete and precise proofs of all of these theorems. With a solid and comprehensive program of exercises and selected solution hints, Logic of Mathematics is ideal for classroom use-the perfect textbook for advanced students of mathematics, computer science, and logic.
Author: Bob Carpenter Publisher: Cambridge University Press ISBN: 0521419328 Category : Computers Languages : en Pages : 282
Book Description
This book develops the theory of typed feature structures and provides a logical foundation for logic programming and constraint-based reasoning systems.
Author: Sergei Artemov Publisher: Cambridge University Press ISBN: 1108424910 Category : Mathematics Languages : en Pages : 271
Book Description
Develops a new logic paradigm which emphasizes evidence tracking, including theory, connections to other fields, and sample applications.
Author: Ahti-Veikko Pietarinen Publisher: Springer Science & Business Media ISBN: 1402037295 Category : Philosophy Languages : en Pages : 516
Book Description
Charles Sanders Peirce (1839-1914) was one of the United States’ most original and profound thinkers, and a prolific writer. Peirce’s game theory-based approaches to the semantics and pragmatics of signs and language, to the theory of communication, and to the evolutionary emergence of signs, provide a toolkit for contemporary scholars and philosophers. Drawing on unpublished manuscripts, the book offers a rich, fresh picture of the achievements of a remarkable man.
Author: Terence Parsons Publisher: OUP Oxford ISBN: 0191002658 Category : Philosophy Languages : en Pages : 346
Book Description
Terence Parsons presents a new study of the development and logical complexity of medieval logic. Basic principles of logic were used by Aristotle to prove conversion principles and reduce syllogisms. Medieval logicians expanded Aristotle's notation in several ways, such as quantifying predicate terms, as in 'No donkey is every animal', and allowing singular terms to appear in predicate position, as in 'Not every donkey is Brownie'; with the enlarged notation come additional logical principles. The resulting system of logic is able to deal with relational expressions, as in De Morgan's puzzles about heads of horses. A crucial issue is a mechanism for dealing with anaphoric pronouns, as in 'Every woman loves her mother'. Parsons illuminates the ways in which medieval logic is as rich as contemporary first-order symbolic logic, though its full potential was not envisaged at the time. Along the way, he provides a detailed exposition and examination of the theory of modes of common personal supposition, and the useful principles of logic included with it. An appendix discusses the artificial signs introduced in the fifteenth century to alter quantifier scope.
Author: Patrick Blackburn Publisher: Cambridge University Press ISBN: 1316101959 Category : Computers Languages : en Pages : 574
Book Description
This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. Researchers in areas ranging from economics to computational linguistics have since realised its worth. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects, and applications to issues in logic and computer science such as completeness, computability and complexity are considered. Three appendices supply basic background information and numerous exercises are provided. Ideal for anyone wanting to learn modern modal logic.
Author: Ahti-Veikko Pietarinen
Author: Ahti-Veikko Pietarinen
Author: Steven Vickers
Author: Zofia Adamowicz
Author: Bob Carpenter
Author: William Stanley Jevons
Author: Sergei Artemov
Author: Ahti-Veikko Pietarinen
Author: Terence Parsons
Author: Patrick Blackburn