13.3 Comparing Feature Structures: Subsumption

We said above that feature structures are essentially sets of properties. Given two different sets of properties an obvious thing to do is to compare the information they contain. A particularly important concept for comparing two feature structures is subsumption.

A feature structure subsumes ( $\sqsubseteq$ ) another feature structure , iff all the information that is contained in is also contained in .

The following two feature structures for instance subsume each other.

The both contain exactly the same information, since the order in which the features are listed in the matrix is not important.

And how about the following two feature structures?

Well, the first one subsumes the second, but not vice versa. Every piece of information that is contained in the first feature structure is also contained in the second, but the second feature structure contains additional information.

A final example: Do the following feature structures subsume each other?

The first one doesn't subsume the second, because it contains information that the second doesn't contain, namely $\textsc{gender}\ \textit{masc}$ . But, the second one doesn't subsume the first one either, as it contains $\textsc{person}\ \textit{3}$ which is not part of the first feature structure.

Notice that the subsumption relation between feature structures is somewhat similar to the subset relation between sets: Feature structure F_1 subsumes features structure F_2 iff all the information of F_1 is also in F_2 . Set S_1 is a subset of set S_2 iff all elements of S_1 are also elements of S_2 .