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We need to represent labeled edges between nodes. Traditionally, this is realized by means of feature structures: each node is a feature structure and an edge is represented by the presence of a feature on , such that . This, however, is a lousy idea when the goal is to take advantage of active constraint propagation. The problem is that, in the traditional view, features are partial functions: i.e. is a partial function from nodes to nodes (from now on, we will write instead of ). It is rather inconvenient to try to express constraints on when it is not always defined!

However, a slight change of representation allows us to turn into a total function. Instead of being either undefined or defined and denoting a node, we let it denote a set of nodes. Now instead of being undefined is simply empty. In the case where it was originally defined, it now denotes a singleton set.

Thus denotes the set of subjects of : empty except when is a finite verb, in which case it is a singleton. We say that is a *daughter set* of , i.e. a set of daughters. This idea has the second advantage that, in addition to complements (like subject), it also naturally accommodates modifiers (like adjectives): is the set of adjectives of . The difference is that a modifier daughter set may have any number of elements instead of at most 1 for a complement daughter set.

Formally, for each role , we introduce a function such that is the set of immediate daughters of whose dependency edge is labeled with :

in the constraint model is a finite set variable.

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Denys Duchier

Version 1.2.0 (20010221)