Medieval logic consists of theories and practices clustered around a core of rules and axioms; the logic contains widely known principles which can be derived from the core. These are used by Aristotle to prove conversion principles, and reduce some syllogisms to others: Exposition (“existential instantiation”), Expository Syllogism (“existential generalization”) and Reductio. Medieval logicians expand on Aristotle’s notation, and this brings new logical principles, such as quantifier interchanges. Theorists use the flexible word order to Latin to let surface order of expressions determine semantic scope. They also make assumptions about existential import that need dealing with. More important, medieval logic is formulated within a natural language, Latin, so there is no logical form except for grammatical form. We look at what is most distinctive of late medieval logic, the useful theory of modes of personal supposition. We examine special terms used to accommodate sentences containing three or more main quantified phrases. Logicians theorize about the logical behavior of pronouns with antecedents; without such pronouns the system of logic is weak; with them added it is expressively as rich as contemporary predicate logic. Also touched on are tense and modality, and intentional contexts, and artificial signs used to alter scope.