Advances and Applications in Discrete Mathematics
Volume 22, Issue 2, Pages 161 - 193
(November 2019) http://dx.doi.org/10.17654/ |
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GRAPH THEORETICAL APPROACH TO THE TRADITIONAL SYLLOGISM AND ITS GENERALIZATION
Fumio Hazama
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Abstract: A graph-theoretical method which determines the validity of traditional syllogism is proposed. The graph introduced here also enables one to classify all of the valid syllogisms in a unified way. The method itself suggests a natural generalization, called extended syllogism, of traditional syllogism. The extension embeds the original graph into a larger and a highly symmetric graph. By employing the action of its automorphism group on the extended graph, one obtains a classification of all of the valid extended syllogisms. |
Keywords and phrases: syllogism, graph theory, three-dimensional cube.
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