Extension of sectional pseudocomplementation in posets

arXiv2207.02642MaRDI QIDQ6404157

Jānis Cīrulis

Publication date: 5 July 2022

Abstract: Sectional pseudocomplementation (sp-complementation) on a poset is a partial operation $*$ which associates with every pair $(x,y)$ of elements, where $xgey$, the pseudocomplement $x*y$ of $x$ in the upper section $[y)$. Any total extension $o$ of $*$ is said to be an extended sp-complementation and is considered as an implication-like operation. Extended sp-complementations have already be studied on semilattices and lattices. We describe several naturally arising classes of general posets with extended sp-complementation, present respective elementary properties of this operation, demonstrate that two other known attempts to isolate particular such classes are in fact not quite correct, and suggest suitable improvements.

Mathematics Subject Classification ID

Other algebras related to logic (03G25) Ordered sets (06A99) Algebraic structures (08A99)

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