The main aim of this monograph is to provide a structured study of
the algebraic method in metalogic. In contrast to traditional
algebraic logic, where the focus is on the algebraic forms of
specific deductive systems, abstract algebraic logic is concerned
with the process of algebraization itself. This book presents in a
systematic way recent ideas in abstract algebraic logic centered
around the notion of the Leibniz operator. The stress is put on the
taxonomy of deductive systems. Isolating a list of plausible
properties of the Leibniz operator serves as a basis for
distinguishing certain natural classes of sentential logics. The
hierarchy of deductive systems presented in the book comprises,
among others, the following classes: protoalgebraic logics,
equivalential logics, algebraizable logics, and Fregean logics.
Because of the intimate connection between algebraic and logical
structures, the book also provides a uniform treatment of various
topics concerning deduction theorems and quasivarieties of
algebras. The presentation of the above classes of logics is
accompanied by a wealth of examples illustrating the general
theory. An essential part of the book is formed by the numerous
exercises integrated into the text. This book is both suitable for
logically and algebraically minded graduate and advanced graduate
students of mathematics, computer science and philosophy, and as a
reference work for the expert.
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