Euler’s visual logic

Hammer, Eric; Shin, Sun-Joo

doi:10.1080/01445349808837293

Cited by 40 publications

(5 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Euler diagrams [10] are a simple, yet effective diagrammatic representation for reasoning about set relationships. We will use a colour-coded modification of the Gergonne's system of Euler diagrams [11] for its simplicity and visual clarity.…”

Section: Euler Diagramsmentioning

confidence: 99%

Investigating Diagrammatic Reasoning with Deep Neural Networks

Wang

Jamnik

Lió

2018

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Diagrams in mechanised reasoning systems are typically encoded into symbolic representations that can be easily processed with rule-based expert systems. This relies on human experts to define diagramto-symbol mapping and the set of rules to reason with the symbols. We present a new method of using Deep artificial Neural Networks (DNN) to learn continuous, vector-form representations of diagrams without any human input, and entirely from datasets of diagrammatic reasoning problems. Based on this DNN, we developed a novel reasoning system, Euler-Net, to solve syllogisms with Euler diagrams. Euler-Net takes two diagrams representing the premises in a syllogism as input, and outputs either a categorical (subset, intersection or disjoint) or diagrammatic conclusion (generating an Euler diagram representing the conclusion) to the syllogism. Euler-Net can achieve 99.5% accuracy for generating syllogism conclusions, and learns meaningful representations. We propose that our framework can be applied to other types of diagrams, especially the ones we are less sure how to formalise symbolically. Recently, DNNs have achieved human comparable performance in several tasks such as image recognition [6], natural language translation [7]. DNNs' success in

show abstract

Section: Euler Diagramsmentioning

confidence: 99%

Investigating Diagrammatic Reasoning with Deep Neural Networks

Wang

Jamnik

Lió

2018

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…The scientific community of mathematicians, and logicians in particular, became aware of the possibility of dealing rigorously with diagrammatic representations to-wards deductive logical reasoning near the end of last century, see [25,48,27,24], by introducing formal logical systems with diagrammatic primitive syntactic constituents.…”

Section: Contextualizationmentioning

confidence: 99%

“…On the other hand, EUL diagrams retain the clarity of the representations and inferences of Euler diagrams whereas Venn diagrams easily do not. See [27].…”

Section: Motivationmentioning

confidence: 99%

Syllogisms in Rudimentary Linear Logic, Diagrammatically

Pagnan

2013

J of Log Lang and Inf

View full text Add to dashboard Cite

We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a syllogism is provable in such a fragment if and only if it is diagrammatically provable. We extend this result to syllogistics with complemented termsà la De Morgan, with respect to a suitable extension of the diagrammatic reasoning system for the traditional case and a corresponding reading of such De Morgan style syllogistics in the previously referred to fragment of linear logic.

show abstract

“…In order to compare regions in different diagrams, Shin and Hammer developed counterpart relations [4,11]. This paper considers an alternative, but related, approach to these counterpart relations and generalizes it to comparing regions in Euler diagrams.…”

Section: Introductionmentioning

confidence: 99%

Corresponding Regions in Euler Diagrams

Howse

Stapleton

Flower

et al. 2002

Diagrammatic Representation and Inference

View full text Add to dashboard Cite

Abstract. Euler diagrams use topological properties to represent settheoretical concepts and thus are 'intuitive' to some people. When reasoning with Euler diagrams, it is essential to have a notion of correspondence among the regions in different diagrams. At the semantic level, two regions correspond when they represent the same set. However, we wish to construct a purely syntactic definition of corresponding regions, so that reasoning can take place entirely at the diagrammatic level. This task is interesting in Euler diagrams because some regions of one diagram may be missing from another. We construct the correspondence relation from 'zones' or minimal regions, introducing the concept of 'zonal regions' for the case in which labels may differ between diagrams. We show that the relation is an equivalence relation and that it is a generalization of the counterpart relations introduced by Shin and Hammer.

show abstract

Euler’s visual logic

Cited by 40 publications

References 2 publications

Investigating Diagrammatic Reasoning with Deep Neural Networks

Investigating Diagrammatic Reasoning with Deep Neural Networks

Syllogisms in Rudimentary Linear Logic, Diagrammatically

Corresponding Regions in Euler Diagrams

Contact Info

Product

Resources

About