"Can I bum a cigarette?" - "I’m an athlete"

A: Can I bum a cigarette?

B: I'm an athlete.

I would like to know what the term for this type of answer is. To be honest, I came across it while reading an article online the other day, but it has completely fallen out of my head. The implication is that a person who asks a question, does not receive a yes or no answer for their question.

Here are some examples:

A: Can I bum a cigarette?
B: I’m an athlete (meaning—since I am an athlete, I'm watching my health, so do not smoke and consequently I do not have any cigarettes)

A: Do you want me to buy you an ice cream?
B: I'm lactose intolerant (ice cream has milk which might give B some GI distress)

A: Are you coming with us to the pool?
B: I cannot swim (I am not coming with you guys because I cannot swim)

As you can see from the examples above, all the answers are formulated in a different way. It is more like providing additional information regarding the question that is being asked.

Solution 1:

This is called an implicature.

It was coined by H. P. Grice to refer to what is suggested in an utterance, even though neither expressed nor strictly implied (that is, entailed) by the utterance.

I knew someone who only ever answered in implicatures. Someone would ask him who did he think was going to win the Super Bowl between the Giants and the Patriots and he'd say: "Well, I'm from New York, so ..."

Solution 2:

The response itself, which seems to not answer the question literally, is called an:

indirect speech act.

In your instances, a yes/no question is asked, but the response doesn't say yes or no directly but instead says something which allows the asker to infer the answer, indirectly.

In general, an exchange like this, where context would allow one to infer the answer or the next, the inference is a kind of:

implicature

This is in contrast to an entailment (or logical inference that is possible without context). These are a technical terms coined by Grice (of Grice's maxims) in the field of pragmatics.