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The square of opposition in orthomodular logic

Freytes, Hector and de Ronde, Christian and Domenech, Graciela (2012) The square of opposition in orthomodular logic. Around and beyond the square of opposition. pp. 193-201.

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Abstract

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


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Freytes, Hectorhfreytes@gmail.com
de Ronde, Christiancderonde@gmail.com
Domenech, Gracielagradomenech@gmail.com
Keywords: square of opposition, modal orthomodular logic, classical consequences
Subjects: Specific Sciences > Mathematics
Specific Sciences > Physics > Quantum Mechanics
Depositing User: Graciela Domenech
Date Deposited: 24 Apr 2014 16:36
Last Modified: 24 Apr 2014 16:36
Item ID: 10622
Journal or Publication Title: Around and beyond the square of opposition
Publisher: Jean-Yves Beziau and Dale Jacquette (eds), Springer
Subjects: Specific Sciences > Mathematics
Specific Sciences > Physics > Quantum Mechanics
Date: 2012
Page Range: pp. 193-201
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/10622

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