Lattices freely generated by posets within a variety. Part I: Four easy varieties

TL;DR

This paper presents an algorithm for computing closure systems from implications and applies it to generate lattices from posets within four specific varieties, advancing lattice theory methods.

Contribution

It introduces a new algorithm for closure systems and demonstrates its application to construct lattices in four simple varieties from posets.

Findings

Algorithm efficiently computes closure systems from implications.

Lattices in four varieties are generated from posets using the algorithm.

Provides a framework for lattice construction within specific varieties.

Abstract

We introduce an algorithm for computing closure systems derived from a family of implications on a set. Semilattices presentations are explored and used in conjunction with the algorithm to compute various types of lattices freely generated by partially ordered sets within four easy varieties.