This book develops model theory independently of any concrete logical system or structure, within the abstract category-theoretic framework of the so called 'institution theory'. The development includes most of the important methods and concepts of conventional concrete model theory at the abstract institution-independent level. Consequently it is easily applicable to a rather large diverse collection of logics from the mathematical and computer science practice.

This is a report on the formal definition of the CafeOBJ algebraic specification language, which is a modern successor to the famous algebraic language OBJ. While the equational core of CafeOBJ is just a reshaping of OBJ, CafeOBJ significantly extends OBJ by incorporating several recent major developments in the area of algebraic specification, such as behavioural specification and rewriting logic.

The definition of the language parallels its logical semantics based on the so-called institutions, which also provide a methodological framework for structuring the presentation of the basic...