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Formal compositional relationships, a subsumption relationship over sorts, and a behavioral specification for sorts, allow sortal structures to be compared and related with respect to scope and coverage,
and data loss to be assessed when converting data from one sortal structure to another.
Syntax and Semantics
Sortal structures can be distinguished and compared syntactically and semantically.
- Comparing sortal structures syntactically requires a comparison of the overall structure, their compositional relationships and their individual components.
- The semantic distinction of syntactically identical sorts relies on the naming of sorts.
Sorts can be named and renamed.
- A simple sort always requires a name; primitive sorts and the aspects of aspect sorts are all simple sorts.
- The name of a composite sort is generally optional; attribute and disjunctive sorts are examples. Recursive sorts form an exception: their recursive definition necessitates a name.
The (re)naming of sorts specifies a semantic relationship.
- A sort is semantically derived from another sort, if it is defined as a (re)naming of the other sort. The relationship of semantic derivation is irreflexive, asymmetric and transitive.
- A sort that is not semantically derived constitutes a semantic base. The relationship of semantic derivation relates every sort to a semantic base. Note that (only) the semantic base of a (non-recursive) composite sort has no name specified.
Sorts can be classified according to their semantic and syntactic similarity.
- Sorts are identical if they are semantically identical. When given a name, they must have the same name; otherwise, they must be identically defined and constructed.
- Sorts are denoted equivalent if they share the same semantic base.
- Sorts are considered similar if they are syntactically identical, that is, they are similarly constructed from equivalent sorts or, otherwise, from primitive sorts that share the same characteristic individual (and the same arguments, if any).
Sorts may also be related under subsumption. When a sort subsumes another sort, the individuals of the latter sort also form individuals of the former sort.
More on the subsumption relationship
- A disjunctive sort subsumes each component sort.
- An attribute sort subsumes its base sort.
A comprehensive comparison of sortal structures includes not only a comparison of their simple component sorts, of their compositional structures, and of any subsumption relationship, but also of the relative completeness of their structures.
More on data conversion and these four comparative dimensions
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