Implication Algebras and Implication Semigroups of Binary Relations
Logic
2023-01-09 v1
Abstract
Representable implication algebras are known to be axiomatised by a finite number of equations (making the representation and finite representation problems decidable here). We show that this also holds in the context of unary (and binary) relations and present a Stone-style representation theorem. We then show that the (finite) representation decision problem is undecidable for implication semigroups, in stark contrast with implication algebras.
Cite
@article{arxiv.2301.02266,
title = {Implication Algebras and Implication Semigroups of Binary Relations},
author = {Andrew Lewis-Smith Jaš Šemrl},
journal= {arXiv preprint arXiv:2301.02266},
year = {2023}
}