In term logic (a branch of philosophical logic), the square of opposition is a diagram representing the relations between the four basic categorical propositions. The origin of the square can be traced back to Aristotle's tractate On Interpretation and its distinction between two oppositions: contradiction and contrariety. However, Aristotle did not draw any diagram; this was done several centuries later by Apuleius and Boethius. Summary In traditional logic, a proposition (Latin: propositio) is a spoken assertion (oratio enunciativa), not the meaning of an assertion, as in modern philosophy of language and logic. A categorical proposition is a simple proposition containing two terms, subject () and predicate (), in which the predicate is either asserted or denied of the subject. Every categorical proposition can be reduced to one of four logical forms, named , , , and based on the Latin (I affirm), for the affirmative propositions and , and (I deny), for the negative propositions and . These are: The proposition, the universal affirmative (universalis affirmativa), whose form in Latin is 'omne est ', usually translated as 'every is a '. The proposition, the universal negative (universalis negativa), Latin form 'nullum est ', usually translated as 'no are '. The proposition, the particular affirmative (particularis affirmativa), Latin 'quoddam est ', usually translated as 'some are '. The proposition, the particular negative (particularis negativa), Latin 'quoddam nōn est ', usually translated as 'some are not '. In tabular form: *Proposition may be stated as "All is ." However, Proposition when stated correspondingly as "All is not ." is ambiguous because it can be either an or proposition, thus requiring a context to determine the form; the standard form "No is " is unambiguous, so it is preferred. Proposition also takes the forms "Sometimes is not ." and "A certain is not ." (literally the Latin 'Quoddam nōn est .') ** in the modern forms means that a statement applies on an object . It may be simply interpreted as " is " in many cases. can be also written as . Aristotle states (in chapters six and seven of the Peri hermēneias (Περὶ Ἑρμηνείας, Latin De Interpretatione, English 'On Interpretation')), that there are certain logical relationships between these four kinds of proposition. He says that to every affirmation there corresponds exactly one negation, and that every affirmation and its negation are 'opposed' such that always one of them must be true,