Abstract Algebraic Logic an Introductory Textbook

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 ...

Abstract Algebraic Logic  an Introductory Textbook

Author: Josep Maria Font

Publisher:

ISBN: 9781848902077

Page: 554

View: 940

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.

Related Books:

Abstract Algebraic Logic. an Introductory Textbook
Language: un
Pages: 554
Authors: Josep Maria Font
Categories: Computers
Type: BOOK - Published: 2016-04-11 - Publisher:

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
Abstract Algebraic Logic
Language: un
Pages:
Authors: Joseph Maria Font
Categories: Computers
Type: BOOK - Published: 2013 - Publisher:

Books about Abstract Algebraic Logic
Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science
Language: en
Pages: 454
Authors: Janusz Czelakowski
Categories: Philosophy
Type: BOOK - Published: 2018-03-20 - Publisher: Springer

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
The Equationally-Defined Commutator
Language: en
Pages: 292
Authors: Janusz Czelakowski
Categories: Mathematics
Type: BOOK - Published: 2015-09-08 - Publisher: Birkhäuser

This monograph introduces and explores the notions of a commutator equation and the equationally-defined commutator from the perspective of abstract algebraic logic. An account of the commutator operation associated with equational deductive systems is presented, with an emphasis placed on logical aspects of the commutator for equational systems determined by
Proof Theory and Algebra in Logic
Language: en
Pages: 160
Authors: Hiroakira Ono
Categories: Philosophy
Type: BOOK - Published: 2019-08-02 - Publisher: Springer

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