Generalized implicature

A generalized implicature is a conversational implicature that is inferable without reference to a special context (Grice 1975:56, Levinson 1983:126).

Example
Expressions with the form an X usually imply that X is not closely related to the speaker or subject, as in the following expression:

John walked into a house yesterday and saw a tortoise.

This expression implies that the house is not John’s house (Grice 1975:56).