Algebraic Methods In Philosophical Logic

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Algebraic Methods in Philosophical Logic

Author : J. Michael Dunn
Publisher : OUP Oxford
ISBN 13 : 0191589225
Total Pages : 490 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Algebraic Methods in Philosophical Logic by : J. Michael Dunn

Download or read book Algebraic Methods in Philosophical Logic written by J. Michael Dunn and published by OUP Oxford. This book was released on 2001-06-28 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive text demonstrates how various notions of logic can be viewed as notions of universal algebra. It is aimed primarily for logisticians in mathematics, philosophy, computer science and linguistics with an interest in algebraic logic, but is also accessible to those from a non-logistics background. It is suitable for researchers, graduates and advanced undergraduates who have an introductory knowledge of algebraic logic providing more advanced concepts, as well as more theoretical aspects. The main theme is that standard algebraic results (representations) translate into standard logical results (completeness). Other themes involve identification of a class of algebras appropriate for classical and non-classical logic studies, including: gaggles, distributoids, partial- gaggles, and tonoids. An imporatant sub title is that logic is fundamentally information based, with its main elements being propositions, that can be understood as sets of information states. Logics are considered in various senses e.g. systems of theorems, consequence relations and, symmetric consequence relations.

Algebraic Methods in Philosophical Logic

Author : J. Michael Dunn
Publisher :
ISBN 13 :
Total Pages : 470 pages
Book Rating : 4.:/5 (468 download)

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Book Synopsis Algebraic Methods in Philosophical Logic by : J. Michael Dunn

Download or read book Algebraic Methods in Philosophical Logic written by J. Michael Dunn and published by . This book was released on 2001 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Interpolation and Definability

Author : Dov M. Gabbay
Publisher : Oxford University Press
ISBN 13 : 0198511744
Total Pages : 524 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Interpolation and Definability by : Dov M. Gabbay

Download or read book Interpolation and Definability written by Dov M. Gabbay and published by Oxford University Press. This book was released on 2005-05-12 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a specialized monograph on interpolation and definability, a notion central in pure logic and with significant meaning and applicability in all areas where logic is applied, especially computer science, artificial intelligence, logic programming, philosophy of science and natural language.Suitable for researchers and graduate students in mathematics, computer science and philosophy, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (second edition), J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and NonmonotonicReasoning, P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2, and David J. Pym and Eike Ritter's Reductive Logic and Proof Search: Proof theory, semantics and control.

Philosophy of Mathematics and Deductive Structure in Euclid's Elements

Author : Ian Mueller
Publisher : Courier Dover Publications
ISBN 13 :
Total Pages : 404 pages
Book Rating : 4.3/5 (555 download)

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Book Synopsis Philosophy of Mathematics and Deductive Structure in Euclid's Elements by : Ian Mueller

Download or read book Philosophy of Mathematics and Deductive Structure in Euclid's Elements written by Ian Mueller and published by Courier Dover Publications. This book was released on 2006 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of Euclid's Elements, this text provides an understanding of the classical Greek conception of mathematics and its similarities to modern views as well as its differences. It focuses on philosophical, foundational, and logical questions -- rather than focusing strictly on historical and mathematical issues -- and features several helpful appendixes.

An Algebraic Introduction to Mathematical Logic

Author : D.W. Barnes
Publisher : Springer Science & Business Media
ISBN 13 : 1475744897
Total Pages : 129 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis An Algebraic Introduction to Mathematical Logic by : D.W. Barnes

Download or read book An Algebraic Introduction to Mathematical Logic written by D.W. Barnes and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for mathematicians. Its origins lie in a course of lectures given by an algebraist to a class which had just completed a substantial course on abstract algebra. Consequently, our treatment of the subject is algebraic. Although we assume a reasonable level of sophistication in algebra, the text requires little more than the basic notions of group, ring, module, etc. A more detailed knowledge of algebra is required for some of the exercises. We also assume a familiarity with the main ideas of set theory, including cardinal numbers and Zorn's Lemma. In this book, we carry out a mathematical study of the logic used in mathematics. We do this by constructing a mathematical model of logic and applying mathematics to analyse the properties of the model. We therefore regard all our existing knowledge of mathematics as being applicable to the analysis of the model, and in particular we accept set theory as part of the meta-Ianguage. We are not attempting to construct a foundation on which all mathematics is to be based--rather, any conclusions to be drawn about the foundations of mathematics come only by analogy with the model, and are to be regarded in much the same way as the conclusions drawn from any scientific theory.

Knowledge, Proof and Dynamics

Author : Fenrong Liu
Publisher : Springer
ISBN 13 : 9789811522208
Total Pages : 217 pages
Book Rating : 4.5/5 (222 download)

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Book Synopsis Knowledge, Proof and Dynamics by : Fenrong Liu

Download or read book Knowledge, Proof and Dynamics written by Fenrong Liu and published by Springer. This book was released on 2020-03-24 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers selected papers presented at the Fourth Asian Workshop on Philosophical Logic, held in Beijing in October 2018. The contributions cover a wide variety of topics in modal logic (epistemic logic, temporal logic and dynamic logic), proof theory, algebraic logic, game logics, and philosophical foundations of logic. They also reflect the interdisciplinary nature of logic – a subject that has been studied in fields as diverse as philosophy, linguistics, mathematics, computer science and artificial intelligence. More specifically. The book also presents the latest developments in logic both in Asia and beyond.

Principia Mathematica

Author : Alfred North Whitehead
Publisher :
ISBN 13 :
Total Pages : 688 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Principia Mathematica by : Alfred North Whitehead

Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Algebraic Approach to Non-classical Logics

Author : Helena Rasiowa
Publisher :
ISBN 13 :
Total Pages : 428 pages
Book Rating : 4.:/5 (45 download)

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Book Synopsis An Algebraic Approach to Non-classical Logics by : Helena Rasiowa

Download or read book An Algebraic Approach to Non-classical Logics written by Helena Rasiowa and published by . This book was released on 1974 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main aim of this book is to formulate an algebraic approach to a carefully selected widest possible class of logics and to prove fundamental theorems for it, which previously have usually been proved for each of those logics separately. The second aim of this book has been to give a number of examples of logics which belong to the class above.

An Investigation of the Laws of Thought

Author : George Boole
Publisher :
ISBN 13 :
Total Pages : 450 pages
Book Rating : 4.B/5 (1 download)

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Book Synopsis An Investigation of the Laws of Thought by : George Boole

Download or read book An Investigation of the Laws of Thought written by George Boole and published by . This book was released on 1854 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Model Theory and the Philosophy of Mathematical Practice

Author : John T. Baldwin
Publisher : Cambridge University Press
ISBN 13 : 1107189217
Total Pages : 365 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Model Theory and the Philosophy of Mathematical Practice by : John T. Baldwin

Download or read book Model Theory and the Philosophy of Mathematical Practice written by John T. Baldwin and published by Cambridge University Press. This book was released on 2018-01-25 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.

Ewa Orłowska on Relational Methods in Logic and Computer Science

Author : Joanna Golińska-Pilarek
Publisher : Springer
ISBN 13 : 9783319978789
Total Pages : 0 pages
Book Rating : 4.9/5 (787 download)

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Book Synopsis Ewa Orłowska on Relational Methods in Logic and Computer Science by : Joanna Golińska-Pilarek

Download or read book Ewa Orłowska on Relational Methods in Logic and Computer Science written by Joanna Golińska-Pilarek and published by Springer. This book was released on 2018-12-20 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tribute to Professor Ewa Orłowska, a Polish logician who was celebrating the 60th year of her scientific career in 2017. It offers a collection of contributed papers by different authors and covers the most important areas of her research. Prof. Orłowska made significant contributions to many fields of logic, such as proof theory, algebraic methods in logic and knowledge representation, and her work has been published in 3 monographs and over 100 articles in internationally acclaimed journals and conference proceedings. The book also includes Prof. Orłowska’s autobiography, bibliography and a trialogue between her and the editors of the volume, as well as contributors' biographical notes, and is suitable for scholars and students of logic who are interested in understanding more about Prof. Orłowska’s work.

Symbolic Logic

Author : Gary M. Hardegree
Publisher :
ISBN 13 : 9780078039812
Total Pages : 418 pages
Book Rating : 4.0/5 (398 download)

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Book Synopsis Symbolic Logic by : Gary M. Hardegree

Download or read book Symbolic Logic written by Gary M. Hardegree and published by . This book was released on 2011 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Evolution of Logic

Author : W. D. Hart
Publisher : Cambridge University Press
ISBN 13 : 1139491202
Total Pages : pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis The Evolution of Logic by : W. D. Hart

Download or read book The Evolution of Logic written by W. D. Hart and published by Cambridge University Press. This book was released on 2010-08-23 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines the relations between logic and philosophy over the last 150 years. Logic underwent a major renaissance beginning in the nineteenth century. Cantor almost tamed the infinite, and Frege aimed to undercut Kant by reducing mathematics to logic. These achievements were threatened by the paradoxes, like Russell's. This ferment generated excellent philosophy (and mathematics) by excellent philosophers (and mathematicians) up to World War II. This book provides a selective, critical history of the collaboration between logic and philosophy during this period. After World War II, mathematical logic became a recognized subdiscipline in mathematics departments, and consequently but unfortunately philosophers have lost touch with its monuments. This book aims to make four of them (consistency and independence of the continuum hypothesis, Post's problem, and Morley's theorem) more accessible to philosophers, making available the tools necessary for modern scholars of philosophy to renew a productive dialogue between logic and philosophy.

Algebraic Methods of Mathematical Logic

Author : Ladislav Rieger
Publisher : Elsevier
ISBN 13 : 1483270521
Total Pages : 213 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Algebraic Methods of Mathematical Logic by : Ladislav Rieger

Download or read book Algebraic Methods of Mathematical Logic written by Ladislav Rieger and published by Elsevier. This book was released on 2014-05-12 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Methods of Mathematical Logic focuses on the algebraic methods of mathematical logic, including Boolean algebra, mathematical language, and arithmetization. The book first offers information on the dialectic of the relation between mathematical and metamathematical aspects; metamathematico-mathematical parallelism and its natural limits; practical applications of methods of mathematical logic; and principal mathematical tools of mathematical logic. The text then elaborates on the language of mathematics and its symbolization and recursive construction of the relation of consequence. Discussions focus on recursive construction of the relation of consequence, fundamental descriptively-semantic rules, mathematical logic and mathematical language as a material system of signs, and the substance and purpose of symbolization of mathematical language. The publication examines expressive possibilities of symbolization; intuitive and mathematical notions of an idealized axiomatic mathematical theory; and the algebraic theory of elementary predicate logic. Topics include the notion of Boolean algebra based on joins, meets, and complementation, logical frame of a language and mathematical theory, and arithmetization and algebraization. The manuscript is a valuable reference for mathematicians and researchers interested in the algebraic methods of mathematical logic.

The Structure of Models of Peano Arithmetic

Author : Roman Kossak
Publisher : Oxford University Press
ISBN 13 : 0198568274
Total Pages : 326 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis The Structure of Models of Peano Arithmetic by : Roman Kossak

Download or read book The Structure of Models of Peano Arithmetic written by Roman Kossak and published by Oxford University Press. This book was released on 2006-06-29 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at graduate students, research logicians and mathematicians, this much-awaited text covers over 40 years of work on relative classification theory for nonstandard models of arithmetic. The book covers basic isomorphism invariants: families of type realized in a model, lattices of elementary substructures and automorphism groups.

A Book of Abstract Algebra

Author : Charles C Pinter
Publisher : Courier Corporation
ISBN 13 : 0486474178
Total Pages : 402 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis A Book of Abstract Algebra by : Charles C Pinter

Download or read book A Book of Abstract Algebra written by Charles C Pinter and published by Courier Corporation. This book was released on 2010-01-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.

Philosophy of Logic

Author :
Publisher : Elsevier
ISBN 13 : 008046663X
Total Pages : 1219 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Philosophy of Logic by :

Download or read book Philosophy of Logic written by and published by Elsevier. This book was released on 2006-11-29 with total page 1219 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.- Written by leading logicians and philosophers- Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic- Clear, in-depth expositions of technical detail- Progressive organization from general considerations to informal to symbolic logic to nonclassical logics- Presents current work in symbolic logic within a unified framework- Accessible to students, engaging for experts and professionals- Insightful philosophical discussions of all aspects of logic- Useful bibliographies in every chapter