Short story incorporating conclusions of cogent argument well (6)
I believe the answer is:
little
'short' is the definition.
(I know that short can be written as little)
'story incorporating conclusions of cogent argument well' is the wordplay.
'story' becomes 'lie' (story can mean a fabrication).
'incorporating' is an insertion indicator.
'conclusions of' suggests the final letters.
The last letters of 'cogent argument well' are 'ttl'.
'lie' enclosing 'ttl' is 'LITTLE'.
(Other definitions for little that I've seen before include "Fairies and leprechauns?" , "Tiny" , "Small in quantity or degree" , "petty" , "(Heroine of) Dickens novel" .)