A Tool for Analysing Logics

Veloso, Sheila R. M.; Veloso, Paulo A. S.; Veloso, Paula M.

doi:10.1016/j.entcs.2011.03.010

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2014

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“…This geometry is concerned with (the interplay of) internal and external negations on an operator (e.g. ♦ = ¬ ¬), and is well-known in linguistics (van Benthem 1991;Löbner 1989;Löbner 1990;Westerståhl 2012) and logic (Demey 2012a;Libert 2012;Veloso et al 2011). Although the duality geometry is sometimes confused with the Aristotelian geometry (D'Alfonso 2012;Mélès 2012), they are conceptually independent of each other (Löbner 1990;Smessaert 2012b;Westerståhl 2012).…”

Section: Resultsmentioning

confidence: 99%

Logical Geometries and Information in the Square of Oppositions

Smessaert

Demey

2014

J of Log Lang and Inf

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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 (such as the square) and, on a more abstract level, the Aristotelian geometry (a set of logical relations). We then introduce two new logical geometries (and their corresponding diagrams), 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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