Labelled Deductive Systems

This important book provides a new unifying methodology for logic. It replaces the traditional view of logic as manipulating sets of formulas by the notion of structured families of labelled formulas, the labels having algebraic structure. This simple device has far reaching consequences for the methodology of logics and their semantics. The book studies the main features of such systems as well as many applications. The framework of Labelled Deductive Systems is of interest to a large variety of readers. At one extreme there is the pure mathematical logician who likes exact formal definitions and dry theorems, who probably specializes in one logic and methodology. At the other extreme there is the practical consumer of logic, who likes to absorb the intutions and use labelling as needed to advance the cause of applications. The book begins with an intuitive presentation of LDS in the context of traditional current views of monotonic and nonmonotonic logics. It is less orientated towards the pure logician and more towards the practical consumer of logic. The main part of the book presents the formal theory of LDS for the formal logician. The author has tried to avoid the style of definition-lemma-theorem and has put in some explanation.