Port-Royal Logic, or Logique de Port-Royal, is the common name of La logique, ou l'art de penser, an important textbook on logic first published anonymously in 1662 by Antoine Arnauld and Pierre Nicole, two prominent members of the Jansenist movement, centered on Port-Royal. Blaise Pascal likely contributed considerable portions of the text. Its linguistic companion piece is the Port Royal Grammar (1660) by Arnauld and Lancelot.
Written in French, it became quite popular and was in use up to the twentieth century, introducing the reader to logic, and exhibiting strong Cartesian elements in its metaphysics and epistemology (Arnauld having been one of the main philosophers whose objections were published, with replies, in Descartes' Meditations on First Philosophy). The Port-Royal Logic is sometimes cited as a paradigmatic example of traditional term logic.
The philosopher Louis Marin particularly studied it in the 20th century (La Critique du discours, Éditions de Minuit, 1975), while Michel Foucault considered it, in The Order of Things, one of the bases of the classical épistémè.
Among the contributions of the Port-Royal Logic is the introduction of a distinction between comprehension and extension, which would later become a more refined distinction between intension and extension. Roughly speaking: a definition with more qualifications or features (the intension) denotes a class with fewer members (the extension), and vice versa. The main idea traces back through the scholastic philosophers to Aristotle's ideas about genus and species, and is fundamental in the philosophy of Leibniz. More recently, it has been related to mathematical lattice theory in Formal Concept Analysis, and independently formalized similarly by Yu. Schreider's group in Moscow,Jon Barwise & Jerry Seligman in Information Flow, and others.