English

The Syllogistic with Unity

Logic in Computer Science 2024-04-24 v1 Logic

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.

Keywords

Cite

@article{arxiv.1110.2317,
  title  = {The Syllogistic with Unity},
  author = {Ian Pratt-Hartmann},
  journal= {arXiv preprint arXiv:1110.2317},
  year   = {2024}
}
R2 v1 2026-06-21T19:18:26.632Z