Syntactic Theory

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Unification

Unification is the major operation on feature structures. Other than the subsumption relation, which compares the information of feature structures, unification combines the information that is contained in two compatible feature structures. We use the term unification for both the operation and the result. Whenever two feature structures are related, they are assumed to be over the same signature.

In mathematical terms, we take the least upper bound of two operands with respect to the partial order. For feature structures, this means subsumption. If two feature structures have an upper bound, they have least upper bound.

Note: subsumption is antisymmetric for feature structures, but not for feature graphs and AVMs. A unique least upper bound can therefore not be guaranteed for all three views.

Generalisation

Generalisation is the opposite operation and rarely performed. The operation returns the most specific feature structure. Unlike unification, generalisation can never fail (as it could always return an empty feature structure as a least general feature structure).