Trends In Logic
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Protoalgebraic Logics
Author: Janusz Czelakowski
language: en
Publisher: Boom Koninklijke Uitgevers
Release Date: 2001-04-30
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.
Trends in Logic
Author: Vincent F. Hendricks
language: en
Publisher: Springer Science & Business Media
Release Date: 2003-09-30
In 1953, exactly 50 years ago to this day, the first volume of Studia Logica appeared under the auspices of The Philosophical Committee of The Polish Academy of Sciences. Now, five decades later the present volume is dedicated to a celebration of this 50th Anniversary of Studia Logica. The volume features a series of papers by distinguished scholars reflecting both the aim and scope of this journal for symbolic logic.
Metamathematics of Fuzzy Logic
Author: Petr Hájek
language: en
Publisher: Springer Science & Business Media
Release Date: 2001-11-30
This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. It aims to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named ‘fuzzy inference’ can be naturally understood as logical deduction. It is for mathematicians, logicians, computer scientists, specialists in artificial intelligence and knowledge engineering, and developers of fuzzy logic.