Hierarchical Defaults in Specifications

The goal of this paper is to explain the usage and semantics of hierarchical defaults in logical specifications. We discuss the usefulness of defaults for different specification scenarios like specialization, aggregation, explanation, revision, etc. To understand defaults formally, we introduce a general framework parameterized on the underlying logical institution extended by an instantiation mechanism for formulae. It is shown that hierarchical defaults have intended models if the extended institution is compact. As an example for a non-standard logic, we give the semantics of defaults in the multi-modal object calculus of the is-core project. To structure and compose specifications with defaults, default-preserving specification morphisms are defined and corresponding colimit constructions are sketched.