TY - GEN

T1 - Minimizing Clutter Using Absence in Venn-i e

AU - Burton, James

AU - Chakraborty, Mihir

AU - Choudhury, Lopamudra

AU - Stapleton, Gem

N1 - © The Author(s) 2016 M. Jamnik et al.

PY - 2016/7/26

Y1 - 2016/7/26

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-319-42333-3_9

DO - 10.1007/978-3-319-42333-3_9

M3 - Conference contribution with ISSN or ISBN

SN - 9783319423326

VL - 9781

T3 - Lecture Notes in Computer Science

SP - 107

EP - 122

BT - International Conference on the Theory and Application of Diagrams

PB - Springer

CY - Germany

T2 - International Conference on the Theory and Application of Diagrams

Y2 - 26 July 2016

ER -