Human reasoning with proportional quantifiers and its support by diagrams

Yuri Sato, Koji Mineshima

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)


In this paper, we study the cognitive effectiveness of diagrammatic reasoning with proportional quantifiers such as most. We first examine how Euler-style diagrams can represent syllogistic reasoning with proportional quantifiers, building on previous work on diagrams for the so-called plurative syllogism (Rescher and Gallagher, 1965). We then conduct an experiment to compare performances on syllogistic reasoning tasks of two groups: those who use only linguistic material (two sentential premises and one conclusion) and those who are also given Euler diagrams corresponding to the two premises. Our experiment showed that (a) in both groups, the speed and accuracy of syllogistic reasoning tasks with proportional quantifiers like most were worse than those with standard first-order quantifiers such as all and no, and (b) in both standard and non-standard (proportional) syllogisms, speed and accuracy for the group provided with diagrams were significantly better than the group provided only with sentential premises. These results suggest that syllogistic reasoning with proportional quantifiers like most is cognitively complex, yet can be effectively supported by Euler diagrams that represent the proportionality relationships between sets in a suitable way.

Original languageEnglish
Title of host publicationDiagrammatic Representation and Inference - 9th International Conference, Diagrams 2016, Proceedings
EditorsMateja Jamnik, Yuri Uesaka, Stephanie Elzer Schwartz
PublisherSpringer Verlag
Number of pages16
ISBN (Print)9783319423326
Publication statusPublished - 2016 Jan 1
Externally publishedYes
Event9th International Conference on the Theory and Applications of Diagrams, Diagrams 2016 - Philadelphia, United States
Duration: 2016 Aug 72016 Aug 10

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th International Conference on the Theory and Applications of Diagrams, Diagrams 2016
Country/TerritoryUnited States


  • Euler diagrams
  • Logic and cognition
  • Proportional quantifiers
  • Reasoning

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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