Working within an arbitrary logical system

Abstract

Different approaches to algebraic specification involve different mathematical underpinnings. These involve variations on the definitions of signature and algebra, the language of axioms used, and what it means for an algebra to satisfy an axiom. Different choices are useful for different purposes, and there appears to be no “best” choice that can be used for everything. We deal with this situation by making the theory of specification independent of this choice, using the notion of an institution which formalises the informal concept of logical system. This allows work on theories, results, and practical tools to be done just once for a wide range of logical systems, while at the same time forcing, via abstraction, deeper insight into the essence of the concepts and results. This chapter explains the basic elements of the theory of institutions on which the remaining chapters are based.