A Diagrammatic Calculus of Syllogisms

  • Ruggero Pagnan
Part of the Studies in Universal Logic book series (SUL)


A diagrammatic calculus of syllogisms is introduced and discussed, so that a syllogism is valid if and only if its conclusion follows from its premises by calculation. The calculus at issue allows the easy retrieving of the traditional rules of the syllogism and of the laws of the square of opposition. Moreover, it extends to n-term syllogisms and to syllogisms with complemented terms. In this respect, a comparison with De Morgan’s spicular notation is treated.


Syllogism Syllogistic diagram Syllogistic inference 

Mathematics Subject Classification



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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.DISIUniversity of GenoaGenoaItaly

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