Border Algorithms for Computing Hasse Diagrams of Arbitrary Lattices

TL;DR

This paper generalizes the Border and iPred algorithms for computing Hasse diagrams from FCA lattices to arbitrary lattices, requiring a join-semilattice homomorphism into a distributive lattice for iPred.

Contribution

It extends existing algorithms to arbitrary lattices, broadening their applicability beyond FCA lattices.

Findings

Border and iPred algorithms can be generalized to arbitrary lattices.

iPred requires a join-semilattice homomorphism into a distributive lattice.

The generalization enables new applications in lattice theory.

Abstract

The Border algorithm and the iPred algorithm find the Hasse diagrams of FCA lattices. We show that they can be generalized to arbitrary lattices. In the case of iPred, this requires the identification of a join-semilattice homomorphism into a distributive lattice.