< Back to previous page

Publication

Generalizing Aristotelian Relations and Diagrams

Book Contribution - Book Chapter Conference Contribution

The square of opposition is a type of diagram that graphically represents the Aristotelian relations between sentences or formulas. It has been noted in the literature that certain extensions of the square have several Boolean subtypes. However, the traditional Aristotelian relations themselves cannot be used to distinguish these different subtypes. Furthermore, the traditional Aristotelian relations are relations between two individual formulas. In this paper I propose a very natural generalization, resting on elementary set-theoretical notions, of these relations to sets of formulas of arbitrary size. I show that this generalization can be used to construct new diagrams, viz. generalized squares of opposition, that can express information that could not be expressed by the traditional squares. Furthermore, I show that the generalized Aristotelian relations can be used to classify Boolean subtypes of extensions of the square that could not be distinguished by the traditional relations.
Book: Diagrammatic Representation and Inference
Pages: 329 - 337
ISBN:978-3-031-15145-3
Publication year:2022
Accessibility:Closed