The Syllogistic with Unity
arXiv:1110.2317 · doi:10.1007/s10992-012-9229-3
Abstract
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.