5.3 Improving Lexical Economy

Typically the same full form of a word corresponds to several distinct agreement tuples. The preceding formal presentation simply assumed that there would be a distinct lexical entry for each one of these tuples. In practice, this would not be very realistic. Therefore, we are going to define licensed lexical entries in terms of more economical lexicon entries.

Thus, instead of a feature agr mapping to a single agreement tuple, a lexicon entry has a feature agrs mapping to a set of agreement tuples.

Although this is much less useful, we shall do the same for category information and replace feature cat mapping to a single category by a feature cats mapping to a set of categories.

Optional complements are another source of considerable redundancy in the lexicon. Therefore, instead of modeling the valency by a single feature comps mapping to a set of complement roles, we shall have 2 features: comps_req mapping to a set of required complement roles, and comps_opt mapping to a set of optional complement roles.

We now define the lexicon as a finite set of lexicon entries, where a lexicon entry is an AVM of the form:

and the lexical entries licensed by the lexicon entry above are all AVMs of the form:

where

This simple formulation demonstrates how constraints can be used to produce compact representations of certain forms of lexical ambiguity. Note that lexicon entries as presented here do not support covariation of features: in such a case, you still need to expand into multiple lexicon entries. Covariation could easily be added and supported using the selection constraint, but I have never found the need for it: the most common application for covariation is agreement, and we have already elegantly taken care of it by means of a product of finite domains.