Duality for Quasilattices and Galois Connections

被引：1

作者：

Romanowska, Anna B. ^{[1
]}

Smith, Jonathan D. H. ^{[2
]}

机构：

[1] Warsaw Univ Technol, Fac Math & Informat Sci, PL-00661 Warsaw, Poland

[2] Iowa State Univ, Dept Math, Ames, IA 50011 USA

来源：

FUNDAMENTA INFORMATICAE | 2017年 / 156卷 / 3-4期

关键词：

duality; Plonka sum; quasilattice; semilattice sum; Galois connection; VARIETIES;

D O I：

10.3233/FI-2017-1611

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

The primary goal of the paper is to establish a duality for quasilattices. The main ingredients are duality for semilattices and their representations, the structural analysis of quasilattices as Plonka sums of lattices, and the duality for lattices developed by Hartonas and Dunn. Lattice duality treats the identity function on a lattice as a Galois connection between its meet and join semilattice reducts, and then invokes a duality between Galois connections and polarities. A second goal of the paper is a further examination of this latter duality, using the concept of a pairing to provide an algebraic equivalent to the relational structure of a polarity.

引用

页码：331 / 359

页数：29