Logic as Algebra
Logic as Algebra

Author: Paul Halmos

Publisher: American Mathematical Soc.

Published: 2019-01-30

Total Pages: 153

ISBN-13: 1470451662

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Here is an introduction to modern logic that differs from others by treating logic from an algebraic perspective. What this means is that notions and results from logic become much easier to understand when seen from a familiar standpoint of algebra. The presentation, written in the engaging and provocative style that is the hallmark of Paul Halmos, from whose course the book is taken, is aimed at a broad audience, students, teachers and amateurs in mathematics, philosophy, computer science, linguistics and engineering; they all have to get to grips with logic at some stage. All that is needed.

Logic and Algebra
Logic and Algebra

Author: Aldo Ursini

Publisher: Routledge

Published: 2017-10-05

Total Pages: 728

ISBN-13: 1351434721

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""Attempts to unite the fields of mathematical logic and general algebra. Presents a collection of refereed papers inspired by the International Conference on Logic and Algebra held in Siena, Italy, in honor of the late Italian mathematician Roberto Magari, a leading force in the blossoming of research in mathematical logic in Italy since the 1960s.

An Algebraic Introduction to Mathematical Logic
An Algebraic Introduction to Mathematical Logic

Author: D.W. Barnes

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 129

ISBN-13: 1475744897

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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.

Logic as Algebra
Logic as Algebra

Author: Paul Halmos

Publisher: Cambridge University Press

Published: 1998-09-03

Total Pages: 156

ISBN-13: 9780883853276

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An introduction to logic from the perspective of algebra.

Logic and Boolean Algebra
Logic and Boolean Algebra

Author: Bradford Henry Arnold

Publisher: Courier Corporation

Published: 2011-01-01

Total Pages: 163

ISBN-13: 0486483851

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Orignally published: Englewood Cliffs, N.J.: Prentice-Hall, 1962.

Algebraic Logic
Algebraic Logic

Author: Paul R. Halmos

Publisher: Courier Dover Publications

Published: 2016-03-17

Total Pages: 276

ISBN-13: 0486810410

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Beginning with an introduction to the concepts of algebraic logic, this concise volume features ten articles by a prominent mathematician that originally appeared in journals from 1954 to 1959. Covering monadic and polyadic algebras, these articles are essentially self-contained and accessible to a general mathematical audience, requiring no specialized knowledge of algebra or logic. Part One addresses monadic algebras, with articles on general theory, representation, and freedom. Part Two explores polyadic algebras, progressing from general theory and terms to equality. Part Three offers three items on polyadic Boolean algebras, including a survey of predicates, terms, operations, and equality. The book concludes with an additional bibliography and index.

Algebraic Methods in Philosophical Logic
Algebraic Methods in Philosophical Logic

Author: J. Michael Dunn

Publisher: OUP Oxford

Published: 2001-06-28

Total Pages: 490

ISBN-13: 0191589225

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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.

Boolean Algebra and Its Applications
Boolean Algebra and Its Applications

Author: J. Eldon Whitesitt

Publisher: Courier Corporation

Published: 2012-05-24

Total Pages: 194

ISBN-13: 0486158160

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Introductory treatment begins with set theory and fundamentals of Boolean algebra, proceeding to concise accounts of applications to symbolic logic, switching circuits, relay circuits, binary arithmetic, and probability theory. 1961 edition.

Proof Theory and Algebra in Logic
Proof Theory and Algebra in Logic

Author: Hiroakira Ono

Publisher: Springer

Published: 2019-08-02

Total Pages: 164

ISBN-13: 9811379971

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This book offers a concise introduction to both proof-theory and algebraic methods, the core of the syntactic and semantic study of logic respectively. The importance of combining these two has been increasingly recognized in recent years. It highlights the contrasts between the deep, concrete results using the former and the general, abstract ones using the latter. Covering modal logics, many-valued logics, superintuitionistic and substructural logics, together with their algebraic semantics, the book also provides an introduction to nonclassical logic for undergraduate or graduate level courses.The book is divided into two parts: Proof Theory in Part I and Algebra in Logic in Part II. Part I presents sequent systems and discusses cut elimination and its applications in detail. It also provides simplified proof of cut elimination, making the topic more accessible. The last chapter of Part I is devoted to clarification of the classes of logics that are discussed in the second part. Part II focuses on algebraic semantics for these logics. At the same time, it is a gentle introduction to the basics of algebraic logic and universal algebra with many examples of their applications in logic. Part II can be read independently of Part I, with only minimum knowledge required, and as such is suitable as a textbook for short introductory courses on algebra in logic.

Universal Algebra, Algebraic Logic, and Databases
Universal Algebra, Algebraic Logic, and Databases

Author: Boris Isaakovich Plotkin

Publisher: Boom Koninklijke Uitgevers

Published: 1994-01-31

Total Pages: 462

ISBN-13: 9780792326656

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Modern algebra, which not long ago seemed to be a science divorced from real life, now has numerous applications. Many fine algebraic structures are endowed with meaningful contents. Now and then practice suggests new and unexpected structures enriching algebra. This does not mean that algebra has become merely a tool for applications. Quite the contrary, it significantly benefits from the new connections. The present book is devoted to some algebraic aspects of the theory of databases. It consists of three parts. The first part contains information about universal algebra, algebraic logic is the subject of the second part, and the third one deals with databases. The algebraic material of the flI'St two parts serves the common purpose of applying algebra to databases. The book is intended for use by mathematicians, and mainly by algebraists, who realize the necessity to unite theory and practice. It is also addressed to programmers, engineers and all potential users of mathematics who want to construct their models with the help of algebra and logic. Nowadays, the majority of professional mathematicians work in close cooperation with representatives of applied sciences and even industrial technology. It is neces sary to develop an ability to see mathematics in different particular situations. One of the tasks of this book is to promote the acquisition of such skills.