Context

Conventional implicature is non-truth-conditional meaning arising solely because of the conventional features attached to particular lexical items and/or linguistic constructions, which is not derivable from general considerations of cooperation and rationality from the saying of what is said.

The properties of conventional implicature include: no contribution to truth condition, associated with speaker/utterance (not sentence), conversational, conventional, derived from Grice’s co-operative principle and maxims, attached by convention to particular items and constructions, non-conventional, motivated, arbitrary, not calculable (given by convention), cancellable, detachable, non-universal.

The Horn's 4 properties of conventional implicature are: conventionality – part of conventional meaning of the linguist.