Integration of Categorical Frameworks: Rule-Based Refinement and Hierarchical Composition for Components

Abstract

The integration of two important categorical frameworks -namely adhesive High-Level Replacement (HLR) systems and the generic component conceptyields a categorical approach to component transformation and refinement. The generic component concept is shown to be an adhesive HLR category, so rules and transformations as well as the corresponding results are available. Moreover, the compatibility with the hierarchical component composition is provided. The extension to rule-based refinement requires additional property-preserving morphisms and yields property-preserving rules and transformations, i.e. refinements where compatibility with the hierarchical component composition again is achieved. The categorical framework is instantiated to typed algebraic high-level (AHL) nets and illustrated with an example of AHL net components.

Managing changes in distributed biomedical ontologies using hierarchical distributed graph transformation

“…The transformation rules in ontology evolution determine what types of changes are allowed and can be performed on the ontological elements and axioms. Padberg (2008) describes the notion of rule-based refinement as an extension of transformations with added refinement morphisms alongside the rules, which can be applied for maintaining component-based applications. We found that the ontology evolution process, through subsequent refinements, is generally analogous and compatible with rule-based hierarchical graph transformation and refinement.…”