Composition of hierarchic default specifications
نویسنده
چکیده
The main contribution of this work has been the establishment of an institution independent theory of composition of hierarchic specifications. Hierarchic specifications consist of formulas (“defaults”) from an underlying logic (institution), organized by priority levels (related by a partial order). These formulas can be defeated when in contradiction with more reliable information (at more important priority levels). Hierarchic specifications model structures with several levels of overriding of general properties, such as those occurring in the specification of classes and subclasses. Composition of hierarchic specifications is formalized in the syntactic and semantic levels by canonical operations in appropriate categories. This composition generalizes the classical framework of institutions (Goguen and Burstall, 1989) and defines the semantics of the syntactic composition of hierarchic specifications (Braß, Lipeck, Ryan, 1991). The following concepts and properties have been introduced in this thesis. • Minimal Semantics. A new semantics for hierarchic specifications, a hierarchy of preference relations, has been defined. This semantics is shown to be the minimal semantics satisfying certain logical and compositional conditions. • Galois Connection. We have shown a Galois connection between hierarchic specifications and their semantics. It expresses the one to one mapping between the theories of hierarchic specifications and their semantics. It implies a one to one mapping between syntactic and semantic operations. It is the basic mechanism of the theory of composition. • Categorial Constructions. A category (hieSpec) of hierarchic specifications and a “mirror” category of their semantics (hiePref) have been defined. Hierarchic specification morphisms consist of signature and priority structure morphisms. Composition of hierarchic specifications is formalized by colimits in the category hieSpec, or by limits in the semantic category hiePref. Existence of these constructions (both in hieSpec and hiePref) is guaranteed by existence of the corresponding signature and priority structure constructions.
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