Logic as Algebra

by Paul Halmos
Logic as Algebra
Author: Paul Halmos
Publisher: American Mathematical Soc.
Total Pages: 141
Release: 2019-01-30
Genre: Mathematics
ISBN: 1470451662
GET BOOK

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

by Aldo Ursini
Logic and Algebra
Author: Aldo Ursini
Publisher: Routledge
Total Pages: 728
Release: 2017-10-05
Genre: Mathematics
ISBN: 1351434721
GET BOOK

""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

by D.W. Barnes
An Algebraic Introduction to Mathematical Logic
Author: D.W. Barnes
Publisher: Springer Science & Business Media
Total Pages: 129
Release: 2013-06-29
Genre: Mathematics
ISBN: 1475744897
GET BOOK

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.

Algebraic Logic

by Paul R. Halmos
Algebraic Logic
Author: Paul R. Halmos
Publisher: Courier Dover Publications
Total Pages: 276
Release: 2016-03-17
Genre: Mathematics
ISBN: 0486810410
GET BOOK

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.

Logic and Boolean Algebra

by Bradford Henry Arnold
Logic and Boolean Algebra
Author: Bradford Henry Arnold
Publisher: Courier Corporation
Total Pages: 163
Release: 2011-01-01
Genre: Mathematics
ISBN: 0486483851
GET BOOK

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

Algebraic Methods in Philosophical Logic

by J. Michael Dunn
Algebraic Methods in Philosophical Logic
Author: J. Michael Dunn
Publisher: OUP Oxford
Total Pages: 490
Release: 2001-06-28
Genre:
ISBN: 0191589225
GET BOOK

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.

Proof Theory and Algebra in Logic

by Hiroakira Ono
Proof Theory and Algebra in Logic
Author: Hiroakira Ono
Publisher: Springer
Total Pages: 164
Release: 2019-08-02
Genre: Philosophy
ISBN: 9811379971
GET BOOK

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.

Abstract Algebraic Logic. an Introductory Textbook

by Josep Maria Font
Abstract Algebraic Logic. an Introductory Textbook
Author: Josep Maria Font
Publisher:
Total Pages: 554
Release: 2016-04-11
Genre: Computers
ISBN: 9781848902077
GET BOOK

Abstract algebraic logic is the more general and abstract side of algebraic logic, the branch of mathematics that studies the connections between logics and their algebra-based semantics. This emerging subfield of mathematical logic consolidated since the 1980s, and is considered as the algebraic logic of the twenty-first century; as such it is increasingly becoming an indispensable tool to approach the algebraic study of any (mainly sentential) logic in a systematic way. This book is an introductory textbook on abstract algebraic logic, and takes a bottom-up approach, treating first logics with a simpler algebraic study, such as Rasiowa's implicative logics, and then guides readers, by means of successive steps of generalization and abstraction, to meet more and more complicated algebra-based semantics. An entire chapter is devoted to Blok and Pigozzi's theory of algebraizable logics, proving the main theorems and incorporating later developments by other scholars. After a chapter with the basics of the classical theory of matrices, one chapter is devoted to an in-depth exposition of the semantics of generalized matrices. There are also two more avanced chapters providing introductions to the two hierachies that organize the logical landscape according to the criteria of abstract algebraic logic, the Leibniz hierarchy and the Frege hierarchy. All throughout the book, particular care is devoted to the presentation and classification of dozens of examples of particular logics. The book is addressed to mathematicians and logicians with little or no previous exposure to algebraic logic. Some acquaintance with examples of non-classical logics is desirable in order to appreciate the extremely general theory. The book is written with students (or beginners in the field) in mind, and combines a textbook style in its main sections, including more than 400 carefully graded exercises, with a survey style in the exposition of some research directions. The book includes scattered historical notes and numerous bibliographic references.

Universal Algebra, Algebraic Logic, and Databases

by Boris Isaakovich Plotkin
Universal Algebra, Algebraic Logic, and Databases
Author: Boris Isaakovich Plotkin
Publisher: Boom Koninklijke Uitgevers
Total Pages: 462
Release: 1994-01-31
Genre: Computers
ISBN: 9780792326656
GET BOOK

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.