According to the classical Indian school of logic (Nyaya), in the process of inference (anumana), the reasoning proceeds from

Nyaya inference moves from a particular to another particular by way of a universal rule.

One perceives a particular mark, such as smoke on the hill.

A universal invariable relation, vyapti, wherever there is smoke there is fire, is recalled.

Applying that universal to the present case yields a new particular, the hill has fire.

Thus reasoning runs particular to particular through the mediating universal.