Journal of Philosophical Logic

, Volume 42, Issue 2, pp 391–407

The Syllogistic with Unity


DOI: 10.1007/s10992-012-9229-3

Cite this article as:
Pratt-Hartmann, I. J Philos Logic (2013) 42: 391. doi:10.1007/s10992-012-9229-3


We extend the language of the classical syllogisms with the sentence-forms “At most 1 p is a q” and “More than 1 p is a q”. We show that the resulting logic does not admit a finite set of syllogism-like rules whose associated derivation relation is sound and complete, even when reductio ad absurdum is allowed.


SyllogismsProof theoryLogic and natural languageComputational complexity

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.School of Computer ScienceManchester UniversityManchesterUK