Well-Typed Feature Structures

Appropriateness itself does not specify how type and feature restrictions are interpreted. There are several choices of interpreting the appropriateness specification, ranging from very relaxed to more severe constraints placed on types and feature values.

In a basic interpretation, the appropriateness specification can be seen as a restriction on which features a type can bear, i.e., which labels are permitted for the arcs emanating from a node [Penn2000]. A much stronger restriction (well-typedness) places constraints on the type of value those features can have [Carpenter1992]:

Definition 2.17   A feature structure $F=\langle Q, \overline{q}, \theta, \delta\rangle$ is well-typed iff $\forall q\in Q$, if $\delta(f,q)$ is defined, $Approp(f,\theta(q))$ is defined, and $Approp(f,\theta(q))\sqsubseteq\theta(\delta(f,q))$.

Well-typedness does not impose any restrictions on the existence of features. However, in TFS applications, such as ALE [Carpenter and Penn2001], it is practical to require that all features are defined (given values) for nodes for which they are appropriate. This condition, named total well-typedness, also includes the restrictions imposed by well-typedness [Carpenter1992]:

Definition 2.18   A feature structure $F=\langle Q, \overline{q}, \theta, \delta\rangle$ is totally well-typed iff it is well-typed and $\forall q\in Q$ if $Approp(f,\theta(q))$ is defined, then $\delta(f,q)$ is defined.

Imposing total well-typedness creates a distinction between absent information and irrelevant information inside a feature structure [Penn2000]. The work presented in this thesis is based on the assumption of totally well-typedness.