A syllogistic inference is a form of inference investigated by Aristotle (384–322 bce) in Prior Analytics. There are two premisses of the form: Some [every, no] $A$ is [is not] $B$, and one conclusion of the same form. Aristotle theorized which inferences of this form are valid. An example of a valid inference (called Barbara by medieval logicians) is:

Aristotle also had a modal syllogistic in which premisses and conclusion are qualified by the modalities necessarily and possibly. Aristotle’s discussion of modal syllogistic is regarded as much less satisfactory.