Consequence Relations

Abstract

AbstractAn in-depth study of the concept of a consequence relation, culminating in the concept of a Lindenbaum-Tarski algebra, intended for advanced undergraduate and graduate students in mathematics and graduate students in philosophy, as well as researchers in the field of mathematical and philosophical logic. The book is aimed to fill the niche left after the publication of Rasiowa and Sikorski’s The Mathematics of Metamathematics (1970), Rasiowa’s An Algebraic Approach to Non-Classical Logics (1974), and Wójcicki’s Theory of Logical Calculi (1988). The problem of obtaining confirmation that a statement is a consequence of a set of statements as prerequisites, on the one hand, and the problem of demonstrating that such confirmation does not exist in the structure under consideration, on the other hand, are considered in a balanced way, using predominantly algebraic methods, as one two-sided problem. Namely, for the second part of this problem, the concept of the Lindenbaum-Tarski algebra plays a key role, which becomes even more important when the considered consequence relation is placed in the context of decidability. This role is traced in the book for various formal objective languages. The included exercises are an essential component of the reader’s assimilation of the book’s material.