The English determiner 'the' can be characterized as conveying a relation between an entity and a description, where the relation is that the entity can be uniquely mutually identifiable in context by the speaker and hearer. This allows room for some of the information conveyed by the noun phrase to be new and resulting from implicature, or assumption, in the interpretation process. The various ways an entity can be mutually identifiable were catalogued. This should provide a good starting point for the commonsense theory of discourse processing that an account of mutual identifiability must tap into.
In a follow-up study I will examine the counterpart hypothesis, that the indefinite determiners, including ``a'' for singular count nouns and the empty string for plurals and singular mass nouns, also conveys a relation between the entity the noun phrase refers to and the property is expresses. This relation is that the entity is not mutually identifiable by virtue of the property.