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The paper investigates the influence of Aristotelian metaphysics, especially of the concepts of form and matter, in the development of Latin medieval logical theories, in particular theories of consequence and theories of supposition. More specifically, it presents the main lines in the development of the concepts of formal/material consequence and formal/material supposition in the 13th and 14th centuries. It is suggested that the growing influence of Aristotelian metaphysics in the 13th century is an important element in the development of these logical theories; nevertheless, the early stages of these theories pre-date the rediscovery of Aristotle's metaphysics in the 13th century. Indeed, other relevant channels of transmission of the metaphysical concepts of form and matter to logical contexts are discussed: the Prior Analytics commentaries of the ancient commentators, Arabic texts, and the neo-Platonic metaphysics of the grammarian tradition stemming from Priscian.