Semilattice structures

Connections between logic and lattices were already mentioned by Garrett Birkhoff in his monograph „Lattice Theory“ published in 1940 and a number of books appeared since then on this topic discussing semilattices and semilattice structures however only marginally. The aim of this monograph is to remedy this situation by concentrating on semilattices and semilattice structures exclusively. The authors also discuss implication logics, but focus on the collection of descriptions and properties of the corresponding algebraic structures. They present many known and new results, in particular on semilattices equipped with supplementary operations such as for example pseudocomplementation or relative pseudocomplementation and their generalizations. This book is of interest for algebraists working on semilattice structures or algebras related to logic as well as for logicians. It is hoped that the book can initiate a further development of the topic and that it can in particular be useful for mathematicians starting to work in semilattice structures.