TY - GEN

T1 - Human reasoning with proportional quantifiers and its support by diagrams

AU - Sato, Yuri

AU - Mineshima, Koji

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

KW - Euler diagrams

KW - Logic and cognition

KW - Proportional quantifiers

KW - Reasoning

UR - http://www.scopus.com/inward/record.url?scp=84979573563&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84979573563&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-42333-3_10

DO - 10.1007/978-3-319-42333-3_10

M3 - Conference contribution

AN - SCOPUS:84979573563

SN - 9783319423326

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 123

EP - 138

BT - Diagrammatic Representation and Inference - 9th International Conference, Diagrams 2016, Proceedings

A2 - Jamnik, Mateja

A2 - Uesaka, Yuri

A2 - Schwartz, Stephanie Elzer

PB - Springer Verlag

T2 - 9th International Conference on the Theory and Applications of Diagrams, Diagrams 2016

Y2 - 7 August 2016 through 10 August 2016

ER -