Domainincluding

Domainincluding is a neologism used in some technical discussions to describe the relation in which one domain is formally included within another. Broadly, it denotes the act or property of including all elements of a source domain inside a target domain, typically via an inclusion map or embedding. The term is not standard across disciplines, but it is used to discuss subdomain relationships and their consequences when combining systems or theories.

In mathematics, domainincluding formalizes the idea of a subdomain. If D1 and D2 are domains in a given setting, domainincluding asserts that D1 is contained in D2 through an inclusion function i: D1 -> D2 that identifies D1 with a subdomain of D2. In domain theory, this aligns with the usual order-theoretic inclusion of domains, where the inclusion is monotone and preserves structure relevant to computation.

In computer science and data integration, domainincluding is used to describe efforts to unify or extend the domain of discourse when combining components. Practically, it involves extending a target domain to include the elements of a source domain, ensuring compatibility of identifiers, types, and operations. Techniques include mapping, schema alignment, and the use of inclusion morphisms to avoid data loss.

Examples include merging taxonomies, integrating APIs with overlapping concept spaces, or extending a programming language's type domain to accommodate new constructs while preserving existing behavior. Potential challenges include name collisions, semantic drift, and ensuring that the inclusion is lossless for intended queries.

Related concepts include domain, subdomain, inclusion map, and domain adaptation.