The square of opposition in orthomodular logic

HECTOR FREYTES, C. DE RONDE Y G. DOMENECH

Around and Beyond the Square of Opposition

Springer

Lugar: Basel; Año: 2012; p. 193 - 200

In Aristotelian logic, categorical propositions are divided in Universal Affirmative,Universal Negative, Particular Affirmative and Particular Negative. Possible relationsbetween two of the mentioned type of propositions are encoded in the square ofopposition. The square expresses the essential properties of monadic first order quantificationwhich, in an algebraic approach, may be represented taking into account monadicBoolean algebras. More precisely, quantifiers are considered as modal operators acting ona Boolean algebra and the square of opposition is represented by relations between certainterms of the language in which the algebraic structure is formulated. This representation issometimes called the modal square of opposition. Several generalizations of the monadicfirst order logic can be obtained by changing the underlying Boolean structure by anotherone giving rise to new possible interpretations of the square.