Logic as Algebra

Author: Paul Halmos,Steven Givant

Publisher: American Mathematical Soc.

ISBN: 1470451131

Category:

Page: 141

View: 3398

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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 to understand the book is some basic acquaintance with algebra.
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Algebraic Formalization of Smart Systems

Theory and Practice

Author: Natalia Serdyukova,Vladimir Serdyukov

Publisher: Springer

ISBN: 3319770519

Category: Computers

Page: 189

View: 2880

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This book reveals the general laws of the theory of smart systems with the help of a very powerful and expressive language of algebraic formalization. It also shows how this language can be used to substantiate practical results in the field of smart systems, which previously had only an empirical justification. Further, it proposes a translation of the theory of smart systems from verbal language to a much more expressive language of algebraic formalization, allowing the laws of the theory of smart systems to be seen in a different light. In 1937 L. Bertalanffy proposed the concept of an algebraic system and the development of a mathematical apparatus for describing systems. In the 1970s, A.I. Mal'tsev developed a theory of algebraic systems connecting algebra and logic for studying algebraic and logical objects. In the 1990s, the concept of purities by predicates was introduced by one of the authors, and the book includes some of its applications. The concept, which is based on the theory of algebraic systems, allows clarification of the connections between quantitative and qualitative analysis of a system. The book is intended for readers who use elements of artificial intelligence in their work.
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Proof Theory and Algebra in Logic

Author: Hiroakira Ono

Publisher: Springer

ISBN: 9811379971

Category: Philosophy

Page: 160

View: 895

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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.
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Encyclopedia of Physical Science and Technology

Author: Robert Allen Meyers

Publisher: N.A

ISBN: 9780122274121

Category: Physical sciences

Page: 841

View: 9611

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Following in the footsteps of the earlier editions, hundreds of the most respected scientists and engineers participated in the creation of this new edition, including many Nobel Laureates. The articles are in-depth, yet accessible, and address all of the key areas of physical science--including aeronautics, astronomy, chemistry, communications, computers, earth sciences, electronics, engineering, materials science, mathematics, nuclear technology, physics, power systems, propulsion, and space technology. (Midwest).
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CMUC

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 6073

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