Prior Analytics describes a natural deduction system as part of an underlying logic. It is a proof-theoretic treatise concerned principally to establish and to perfect a deduction system for science. Aristotle knew that deductions about matters pertaining to a given subject matter are content specific and that they employ a topic neutral deduction system; such a system makes evident that given sentences logically follow from other given sentences. One process of deduction is accomplished through taking pairs of given categorical sentences to generate immediate inferences according to prescribed rules, which categorical inferences are then added to the given sentences and then again taken in pairs, to wit, syllogistically, until a final conclusion is obtained (see esp. A25). This process is treated in Prior Analytics in an exactly analogous fashion as chaining immediate inferences by using rules of propositional logic.
Boger, George, "Prior Analytics and Aristotle's Commitment to Logos" (1996). The Society for Ancient Greek Philosophy Newsletter. 178.