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Diagrams and Nonmonotonic Logic: What Is the Cognitive Relation? Read chapter Read first chapter

2018 | OriginalPaper | Chapter

The Observational Advantages of Euler Diagrams with Existential Import

Authors : Gem Stapleton, Atsushi Shimojima, Mateja Jamnik

Published in: Diagrammatic Representation and Inference

Publisher: Springer International Publishing

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Abstract

The ability of diagrams to convey information effectively in part comes from their ability to make facts explicit that would otherwise need to be inferred. This type of advantage has often been referred to as a free ride and was deemed to occur only when a diagram was obtained by translating a symbolic representation of information. Recent work generalised free rides to the idea of an observational advantage, where the existence of such a translation is not required. Roughly speaking, it has been shown that Euler diagrams without existential import are observationally complete as compared to symbolic set theory. In this paper, we explore to what extent Euler diagrams with existential import are observationally complete with respect to set-theoretic sentences. We show that existential import significantly limits the cases when observational completeness arises, due to the potential for overspecificity.

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previous chapter Operations on Single Feature Indicator Systems
next chapter Observational Advantages: A Philosophical Discussion
Footnotes
1
In Euler diagrams without existential import, zones can represent empty sets. By contrast, under existential import all zones in the diagram represent non-empty sets [7]. Peirce denotes non-emptiness of a set with \(\otimes \)-sequences [12] (also used by Shin [15] and further developed by Choudhury and Chakraborty [4]). Other notations use graphs to denote elements in sets [6, 8, 9].
 
2
It is possible to define observability for other types of diagrams and statements too.
 
3
It is straightforward, yet lengthy, to define a translation from regions to set-expressions; due to space constraints, we refer the reader to [16].
 
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Metadata
Title
The Observational Advantages of Euler Diagrams with Existential Import
Authors
Gem Stapleton
Atsushi Shimojima
Mateja Jamnik
Copyright Year
2018
Book
Diagrammatic Representation and Inference

Print ISBN: 978-3-319-91375-9

Electronic ISBN: 978-3-319-91376-6

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-91376-6_29