Composition of Default Specifications

In this paper we develop a theory of composition of default specifications. This theory generalizes the work by Goguen and Burstall, where specifications written in an arbitrary logical system (institution) are structured as combinations of theories. It extends the classical composition by allowing partial re-use (and overriding) of specification modules. The modularisation units are hierarchic specifications, i.e. axioms and defaults organized by priority levels. The semantics are given by default institutions, which are a generalisation of institutions in order to enable partial reuse of specifications. Composition is formalized by the use of appropriate categories, both at the syntactic and semantic levels. The theory of composition with overriding is illustrated with an example of an object-oriented specification.