Inference, ratiocination denote the process of arriving at conclusions from data or premises.
Inference often connotes guesswork based on trivial or inadequate data or premises; in technical logical use it names the process of inferring (see INFER ) but does not in itself suggest care in reasoning or in deduction.
Ratiocination adds the implication of exactitude and of an extended process or the passing by steps from one inference to another. It often carries the connotation of tediousness or of hairsplitting. The same distinctions in implications are observable in the corresponding adjectives inferential and ratiocinative.