Minimizing Clutter Using Absence in Venn-i e

James Burton, Mihir Chakraborty, Lopamudra Choudhury, Gem Stapleton

Research output: Chapter in Book/Conference proceeding with ISSN or ISBNConference contribution with ISSN or ISBN

Abstract

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.
Original languageEnglish
Title of host publicationInternational Conference on the Theory and Application of Diagrams
Place of PublicationGermany
PublisherSpringer
Pages107-122
Number of pages16
Volume9781
ISBN (Print)9783319423326
DOIs
Publication statusPublished - 26 Jul 2016
EventInternational Conference on the Theory and Application of Diagrams - Philadelphia, USA, 7-10, 2016
Duration: 26 Jul 2016 → …

Publication series

NameLecture Notes in Computer Science

Conference

ConferenceInternational Conference on the Theory and Application of Diagrams
Period26/07/16 → …

Bibliographical note

© The Author(s) 2016 M. Jamnik et al.

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    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