In essence, simply the act of argument or reasoning. 

Immediate Inference.— Judging that the truth of one proposition directly entails the truth of a second proposition. Strictly speaking, this is not a genuine inference since all that can be inferred from a single proposition is a logically equivalent form of the same proposition. 

Mediate Inference.— Judging that the truth of one proposition, when related to a second true proposition, entails the truth of a third proposition. The second proposition, in this respect, mediates or connects the first and the third propositions.  Such mediate inference is divided: objectively inferential (or illative) demonstrations, in which the conclusion of an argument is a completely new truth, only virtually contained in the premises of the argument; and subjectively inferential (or illative) demonstrations, sometimes referred to as explanatory or explicative demonstrations, in which the conclusion of an argument states more clearly what is contained in the major premise of the argument.  Classical logic also recognizes an expository syllogism, by which a particular example is adduced, without however demonstrating any new truth.  Such expository syllogisms are not, strictly speaking, inferential.