Editing Graph theory (section)

=== Subsumption and unification ===
Constraint modeling theories concern families of directed graphs related by a [[partial order]]. In these applications, graphs are ordered by specificity, meaning that more constrained graphs—which are more specific and thus contain a greater amount of information—are subsumed by those that are more general. Operations between graphs include evaluating the direction of a subsumption relationship between two graphs, if any, and computing graph unification. The unification of two argument graphs is defined as the most general graph (or the computation thereof) that is consistent with (i.e. contains all of the information in) the inputs, if such a graph exists; efficient unification algorithms are known.

For constraint frameworks which are strictly [[Principle of Compositionality|compositional]], graph unification is the sufficient satisfiability and combination function. Well-known applications include [[Automatic theorem prover|automatic theorem proving]] and modeling the [[Parsing|elaboration of linguistic structure]].