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.

""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.

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

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.

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.

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.

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.

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.

This publication surveys some of the disciplines within ordered algebraic structures and also contains chapters highlighting a broad spectrum of research interests. In all, this book represents a reasonably accurate cross-section of the state of the art in ordered algebraic structures.