 One of the most important ancient sources for the development of theories of consequence by medieval authors is, unsurprisingly, Aristotle. The Prior Analytics and the theory of syllogistic provided the main model for the correctness/validity of arguments for centuries, and even though theories of consequences can be seen as a generalization of the rather narrow theory of validity presented in the Prior Analytics, it is clear that syllogistic remains one of the key elements in the background. Indeed, the famous definition of a valid deduction (syllogism) at the beginning of the Prior Analytics is already a formulation of the necessary truth-preservation criterion (TP):