Logic, Logical Argument and Proof

Is logic or a logical argument synonymous with a 'proof'?

Consider this piece of commonsense reasoning - one would immediately remark something like - what use is a horse for a Presidential address at the White House? What is meant here is that there is no use of something like a 'HORSE' - a real horse (the animal) - for a Presidential address at the White House (say, while the President is addressing the Press or the public). So if I ask you to think of a use of a horse for the same, you would, in all probability, say - Yes, what use could that be of? And this is "acceptable commonsense reasoning".

Now, examine this reasoning. You haven't 'PROVED' that a horse is useless for a Presidential address. This is more of the form "As far as I can see, there is no use of a horse...." You haven't deduced this. 

Also, how does this work cognitively? You try to think of some possible uses, by fitting in a horse for the said purpose/situation, and then after seeing/gauging the way your few attempts fail, you "infer" that there is no apparent use of a horse for a Presidential address. (Note - this relates to the straight line of boxes on the table example earlier).

The question then is this - can there be a logical proof, and if not, then how come a logical explanation, for the above 'inference' (that there is no apparent use, i.e. fitting into the commonsensical conventions of human affairs, of a horse for a Presidential address, at the White House)?

I agree there can be absurd, but logically possible uses like - make horse-beef and feed it to the people there. But that doesnt fit into something "acceptable".

How will you explain/represent this piece of commonsensically acceptable reasoning, in logic?