Algebraic Logic by Hajnal Andreka, I. Nemeti, I. Sain

About this book :-
Algebraic Logic by Hajnal Andréka, István Németi, and Ildikó Sain explores the deep connections between logic and algebra, focusing especially on translating logical systems (like first-order logic) into algebraic structures such as relation and cylindric algebras. Algebraic logic can be divided into two main parts. Part I studies algebras which are relevant to logic(s). Since Part I studies algebras, its methods are, basically, algebraic. One could say that Part I belongs to ‘Algebra Country’. Continuing this metaphor, Part II deals with studying and building the bridge between Algebra Country and Logic Country. Part II deals with the methodology of solving logic problems by (i) translating them to algebra, (ii) solving the algebraic problem (this really belongs to Part I), and (iii) translating the result back to logic. There is an emphasis here on step (iii), because without such a methodological emphasis one could be tempted to play the ‘enjoyable games’ (i) and (ii), and then forget about the ‘boring duty’ of (iii). Of course, this bridge can also be used backwards, to solve algebraic problems with logical methods. We will give some simple examples for this in the present work.

Book Detail :-
Title: Algebraic Logic by Hajnal Andreka, I. Nemeti, I. Sain
Publisher: Hajnal Andréka
Year: 2003
Pages: 129
Type: PDF
Language: English
ISBN-10 #: N\A
ISBN-13 #: N\A
License: Linked Content Owned by Author
Amazon: Amazon

About Author :-
The author Hajnal Ilona Andréka (also known as Hajnalka Andréka, 1947) is a Hungarian mathematician specializing in algebraic logic. She is a research professor emeritus at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences. She completed a Ph.D. from Eötvös Loránd University in 1975, and earned a candidate's degree in 1978. In 1992, she earned a Dr. rer. nat. degree from the Hungarian Academy of Sciences. She worked in the Hungarian Ministry of Heavy Industries from 1971 to 1977, and has been affiliated with the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences since 1977. She is the author of Cylindric Set Algebras, Cylindric-like Algebras and Algebraic Logic, Universal Algebraic Logic and Simple Relation Algebras.

Book Contents :-
Part-I Algebras of relations Getting acquainted with the subject 1. Algebras of binary relations 2. Algebras of relations in general 3. Algebras for logics without identity Part-II Bridge between logic and algebra: Abstract Algebraic Logic Introduction 4. General framework for studying logics 5. The process of algebraization 6. Equivalence theorems 7. Examples and application

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