Over the last two decades substantial advances have beenmade in our understanding of diagrammatic logics. Many of these logics have the expressiveness of monadic first-order logic, sometimes with equality, and are equipped with sound and complete inference rules. Aparticular challenge is the representation of negated statements. This paper addresses the problem of how to represent negated statementsinvolving constants, thus asserting the absence of specific individuals, in the context of Euler-diagram-based logics. Our first contribution is to explore the potential benefits of explicitly representing absence using constants, in terms of clutter reduction, and to highlight ontological issues that arise. We go on to define a measure of clutter arising from constants. By defining a set of semantics-preserving inference rules, we are able to algorithmically minimize diagram clutter, in part made possible by the inclusion of absence. Consequently, information about individuals can be represented in a minimally cluttered way.
|Title of host publication||International Conference on the Theory and Application of Diagrams|
|Place of Publication||Germany|
|Number of pages||16|
|Publication status||Published - 26 Jul 2016|
|Event||International Conference on the Theory and Application of Diagrams - Philadelphia, USA, 7-10, 2016|
Duration: 26 Jul 2016 → …
|Name||Lecture Notes in Computer Science|
|Conference||International Conference on the Theory and Application of Diagrams|
|Period||26/07/16 → …|
Bibliographical note© The Author(s) 2016 M. Jamnik et al.
Burton, J., Chakraborty, M., Choudhury, L., & Stapleton, G. (2016). Minimizing Clutter Using Absence in Venn-i e. In International Conference on the Theory and Application of Diagrams (Vol. 9781, pp. 107-122). (Lecture Notes in Computer Science). Springer. https://doi.org/10.1007/978-3-319-42333-3_9