On implications in sectionally pseudocomplemented posets
Logic
2013-01-07 v2
Abstract
A sectionally pseudocomplemented poset P is one which has the top element and in which every principal order filter is a pseudocomplemented poset. The sectional pseudocomplements give rise to an implication-like operation on P which coincides with the relative pseudocomplementation if P is relatively psudocomplemented. We characterise this operation and study some elementary properties of upper semilattices, lower semilattices and lattices equipped with this kind of implication. We deal also with a few weaker versions of implication. Sectionally pseudocomplemented lattices have already been studied in the literature.
Cite
@article{arxiv.0705.3803,
title = {On implications in sectionally pseudocomplemented posets},
author = {J\{=}anis C\=ırulis},
journal= {arXiv preprint arXiv:0705.3803},
year = {2013}
}