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In Aristotelian logic, categorical propositions are divided in UniversalAffirmative, Universal Negative, Particular Affirmative and ParticularNegative. Possible relations between two of the mentioned type of propositionsare encoded in the square of opposition. The square expresses the essentialproperties of monadic first order quantification which, in an algebraicapproach, may be represented taking into account monadic Boolean algebras. Moreprecisely, quantifiers are considered as modal operators acting on a Booleanalgebra and the square of opposition is represented by relations betweencertain terms of the language in which the algebraic structure is formulated.This representation is sometimes called the modal square of opposition. Severalgeneralizations of the monadic first order logic can be obtained by changingthe underlying Boolean structure by another one giving rise to new possibleinterpretations of the square.

The square of opposition in orthomodular logic