Quality Implicature

A quality implicature is a conversational implicature based on the addressee's assumption as to whether or not the speaker is observing or flouting the conversational maxim of quality. 
If the speaker is assumed to be observing the maxim, then the addressee makes a standard implicature. If the speaker is assumed to be flouting the maxim, then the addressee makes a more nonstandard type of implicature. Examples (English) 

• The sentence John has two Ph.D.'s implicates both of the following:

"I believe John has two Ph.D.'s."
"I have adequate evidence that John has two Ph.D.'s." 
It may also cause an implicature derived from the addressee’s belief that the speaker is flouting the maxim quality. 

• In the following exchange, the obvious falsehood of B’s utterance implicates that B is saying that A is wildly incorrect:

A: Tehran’s in Turkey, isn’t it, teacher? 
B: And London’s in Armenia, I suppose.