Venn diagram system has been extended by introducing names of individuals and their absence. Absence gives a kind of negation of singular propositions. We have offered here a non-classical interpretation of this negation. Soundness and completeness of the present diagram system have been established with respect to this interpretation.

The development of diagrammatic logics is strongly motivated by the desire to make formal reasoning accessible to broad audiences. One major research problem, for which surprisingly little progress has been made, is to understand how to choose between semantically equivalent diagrams from the perspective of human cognition. The particular focus of this paper is on choosing between diagrams that represent either the presence or absence of individuals. To understand how to best make this choice, we conducted an empirical study. We (...) found that representing the presence of individuals supported task performance either significantly better than, or no worse than, representing the absence of individuals. The particularly striking feature of our results was that representing the absence of individuals in a way that makes the diagram highly cluttered is detrimental to human cognition. As a result, diagrams with this feature should be avoided, but diagrams using presence or low-cluttered absence can be used to support cognition in the context of the tasks performed in our study. (shrink)

In logic, Aristotelian diagrams are almost always assumed to be closed under negation, and are thus highly symmetric in nature. In linguistics, by contrast, these diagrams are used to study lexicalization, which is notoriously not closed under negation, thus yielding more asymmetric diagrams. This paper studies the interplay between logical symmetry and linguistic asymmetry in Aristotelian diagrams. I discuss two major symmetric Aristotelian diagrams, viz. the square and the hexagon of opposition, and show how linguistic considerations yield various asymmetric versions (...) of these diagrams. I then discuss a pentagon of opposition, which occupies an uneasy position between the square and the hexagon. Although this pentagon belongs neither to the symmetric realm of logic nor to the asymmetric realm of linguistics, it occurs several times in the literature. The oldest known occurrence can be found in the cosmological work of the 14th-century author Nicole Oresme. (shrink)