TY - JOUR

T1 - Towards explaining the cognitive efficacy of Euler diagrams in syllogistic reasoning

T2 - A relational perspective

AU - Mineshima, Koji

AU - Sato, Yuri

AU - Takemura, Ryo

AU - Okada, Mitsuhiro

N1 - Funding Information:
We would like to express gratitude to the anonymous reviewers and the editors of this special issue for many helpful comments and suggestions. The fourth author is partially supported by Grant-in-Aid for Scientific Research (MEXT-JSPS) #23120002 and #30224025 .

PY - 2014/6

Y1 - 2014/6

N2 - Although diagrams have been widely used as methods for introducing students to elementary logical reasoning, it is still open to debate in cognitive psychology whether logic diagrams can aid untrained people to successfully conduct deductive reasoning. In our previous work, some empirical evidence was provided for the effectiveness of Euler diagrams in the process of solving categorical syllogisms. In this paper, we discuss the question of why Euler diagrams have such inferential efficacy in the light of a logical and proof-theoretical analysis of categorical syllogisms and diagrammatic reasoning. As a step towards an explanatory theory of reasoning with Euler diagrams, we argue that the effectiveness of Euler diagrams in supporting syllogistic reasoning derives from the fact that they are effective ways of representing and reasoning about relational structures that are implicit in categorical sentences. A special attention is paid to how Euler diagrams can facilitate the task of checking the invalidity of an inference, a task that is known to be particularly difficult for untrained reasoners. The distinctive features of our conception of diagrammatic reasoning are made clear by comparing it with the model-theoretic conception of ordinary reasoning developed in the mental model theory.

AB - Although diagrams have been widely used as methods for introducing students to elementary logical reasoning, it is still open to debate in cognitive psychology whether logic diagrams can aid untrained people to successfully conduct deductive reasoning. In our previous work, some empirical evidence was provided for the effectiveness of Euler diagrams in the process of solving categorical syllogisms. In this paper, we discuss the question of why Euler diagrams have such inferential efficacy in the light of a logical and proof-theoretical analysis of categorical syllogisms and diagrammatic reasoning. As a step towards an explanatory theory of reasoning with Euler diagrams, we argue that the effectiveness of Euler diagrams in supporting syllogistic reasoning derives from the fact that they are effective ways of representing and reasoning about relational structures that are implicit in categorical sentences. A special attention is paid to how Euler diagrams can facilitate the task of checking the invalidity of an inference, a task that is known to be particularly difficult for untrained reasoners. The distinctive features of our conception of diagrammatic reasoning are made clear by comparing it with the model-theoretic conception of ordinary reasoning developed in the mental model theory.

KW - Categorical syllogisms

KW - Diagrammatic reasoning

KW - Efficacy

KW - Euler diagram

KW - Mental model theory

KW - Relational inferences

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U2 - 10.1016/j.jvlc.2013.08.007

DO - 10.1016/j.jvlc.2013.08.007

M3 - Article

AN - SCOPUS:84885059842

SN - 1045-926X

VL - 25

SP - 156

EP - 169

JO - Journal of Visual Languages and Computing

JF - Journal of Visual Languages and Computing

IS - 3

ER -