English

Simple Laws about Nonprominent Properties of Binary Relations

Logic 2018-11-21 v2

Abstract

We checked each binary relation on a 5-element set for a given set of properties, including usual ones like asymmetry and less known ones like Euclideanness. Using a poor man's Quine-McCluskey algorithm, we computed prime implicants of non-occurring property combinations, like "not irreflexive, but asymmetric". We considered the non-trivial laws obtained this way, and manually proved them true for binary relations on arbitrary sets, thus contributing to the encyclopedic knowledge about less known properties.

Cite

@article{arxiv.1806.05036,
  title  = {Simple Laws about Nonprominent Properties of Binary Relations},
  author = {Jochen Burghardt},
  journal= {arXiv preprint arXiv:1806.05036},
  year   = {2018}
}

Comments

70 pages, 46 figures. Comparison to previous version: 9 more relation properties; found 274 prime implicants, each one manually proven or disproven; program improvements

R2 v1 2026-06-23T02:28:41.265Z