Logical Geometries and Information in the Square of Oppositions

Journal of Logic, Language and Information 23 (4):527-565 (2014)
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The Aristotelian square of oppositions is a well-known diagram in logic and linguistics. In recent years, several extensions of the square have been discovered. However, these extensions have failed to become as widely known as the square. In this paper we argue that there is indeed a fundamental difference between the square and its extensions, viz., a difference in informativity. To do this, we distinguish between concrete Aristotelian diagrams and, on a more abstract level, the Aristotelian geometry. We then introduce two new logical geometries, and develop a formal, well-motivated account of their informativity. This enables us to show that the square is strictly more informative than many of the more complex diagrams



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Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.
A Natural History of Negation.Laurence R. Horn - 1989 - University of Chicago Press.
Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.
Logical Dynamics of Information and Interaction.Johan van Benthem - 2011 - New York: Cambridge University Press.

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