Abstract Algebraic Logic An Introductory Textbook PDF Download
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| Author | : Josep Maria Font |
| Publisher | : |
| Total Pages | : 554 |
| Release | : 2016-04-11 |
| Genre | : Computers |
| ISBN | : 9781848902077 |
Download Abstract Algebraic Logic. an Introductory Textbook Book in PDF, ePub and Kindle
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.
| Author | : Joseph Maria Font |
| Publisher | : |
| Total Pages | : |
| Release | : 2013 |
| Genre | : |
| ISBN | : |
Download Abstract Algebraic Logic Book in PDF, ePub and Kindle
| Author | : Janusz Czelakowski |
| Publisher | : Springer |
| Total Pages | : 476 |
| Release | : 2018-03-20 |
| Genre | : Philosophy |
| ISBN | : 331974772X |
Download Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science Book in PDF, ePub and Kindle
This book celebrates the work of Don Pigozzi on the occasion of his 80th birthday. In addition to articles written by leading specialists and his disciples, it presents Pigozzi’s scientific output and discusses his impact on the development of science. The book both catalogues his works and offers an extensive profile of Pigozzi as a person, sketching the most important events, not only related to his scientific activity, but also from his personal life. It reflects Pigozzi's contribution to the rise and development of areas such as abstract algebraic logic (AAL), universal algebra and computer science, and introduces new scientific results. Some of the papers also present chronologically ordered facts relating to the development of the disciplines he contributed to, especially abstract algebraic logic. The book offers valuable source material for historians of science, especially those interested in history of mathematics and logic.
| Author | : D.W. Barnes |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 129 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475744897 |
Download An Algebraic Introduction to Mathematical Logic Book in PDF, ePub and Kindle
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.
| Author | : Charles C Pinter |
| Publisher | : Courier Corporation |
| Total Pages | : 402 |
| Release | : 2010-01-14 |
| Genre | : Mathematics |
| ISBN | : 0486474178 |
Download A Book of Abstract Algebra Book in PDF, ePub and Kindle
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.
| Author | : Joseph Landin |
| Publisher | : Courier Corporation |
| Total Pages | : 275 |
| Release | : 2012-08-29 |
| Genre | : Mathematics |
| ISBN | : 0486150410 |
Download An Introduction to Algebraic Structures Book in PDF, ePub and Kindle
This self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition.
| Author | : Nikolaos Galatos |
| Publisher | : Springer Nature |
| Total Pages | : 382 |
| Release | : 2021-12-13 |
| Genre | : Philosophy |
| ISBN | : 3030769208 |
Download Hiroakira Ono on Substructural Logics Book in PDF, ePub and Kindle
This volume is dedicated to Hiroakira Ono life’s work on substructural logics. Chapters, written by well-established academics, cover topics related to universal algebra, algebraic logic and the Full Lambek calculus; the book includes a short biography about Hiroakira Ono. The book starts with detailed surveys on universal algebra, abstract algebraic logic, topological dualities, and connections to computer science. It further contains specialised contributions on connections to formal languages (recognizability in residuated lattices and connections to the finite embedding property), covering systems for modal substructural logics, results on the existence and disjunction properties and finally a study of conservativity of expansions. This book will be primarily of interest to researchers working in algebraic and non-classical logic.
| Author | : Gary L. Mullen |
| Publisher | : CRC Press |
| Total Pages | : 213 |
| Release | : 2016-12-19 |
| Genre | : Mathematics |
| ISBN | : 1482250098 |
Download Abstract Algebra Book in PDF, ePub and Kindle
Abstract Algebra: A Gentle Introduction advantages a trend in mathematics textbook publishing towards smaller, less expensive and brief introductions to primary courses. The authors move away from the ‘everything for everyone’ approach so common in textbooks. Instead, they provide the reader with coverage of numerous algebraic topics to cover the most important areas of abstract algebra. Through a careful selection of topics, supported by interesting applications, the authors Intend the book to be used for a one-semester course in abstract algebra. It is suitable for an introductory course in for mathematics majors. The text is also very suitable for education majors who need to have an introduction to the topic. As textbooks go through various editions and authors employ the suggestions of numerous well-intentioned reviewers, these book become larger and larger and subsequently more expensive. This book is meant to counter that process. Here students are given a "gentle introduction," meant to provide enough for a course, yet also enough to encourage them toward future study of the topic. Features Groups before rings approach Interesting modern applications Appendix includes mathematical induction, the well-ordering principle, sets, functions, permutations, matrices, and complex nubers. Numerous exercises at the end of each section Chapter "Hint and Partial Solutions" offers built in solutions manual
| Author | : John W. Lawrence |
| Publisher | : Cambridge University Press |
| Total Pages | : 640 |
| Release | : 2021-04-15 |
| Genre | : Mathematics |
| ISBN | : 1108865518 |
Download Abstract Algebra Book in PDF, ePub and Kindle
Through this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence. Groups, rings and fields are covered in depth with a strong emphasis on irreducible polynomials, a fresh approach to modules and linear algebra, a fresh take on Gröbner theory, and a group theoretic treatment of Rejewski's deciphering of the Enigma machine. It includes a detailed treatment of the basics on finite groups, including Sylow theory and the structure of finite abelian groups. Galois theory and its applications to polynomial equations and geometric constructions are treated in depth. Those interested in computations will appreciate the novel treatment of division algorithms. This rigorous text 'gets to the point', focusing on concisely demonstrating the concept at hand, taking a 'definitions first, examples next' approach. Exercises reinforce the main ideas of the text and encourage students' creativity.
| Author | : Paul Halmos |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 141 |
| Release | : 2019-01-30 |
| Genre | : Mathematics |
| ISBN | : 1470451662 |
Download Logic as Algebra Book in PDF, ePub and Kindle
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.
