Scholarlink

<p>We give a definition of representability for distributive quasi relation algebras (DqRAs). These algebras are a generalisation of relation algebras and were first described by Galatos and Jipsen&#xa0;(Algebra Univers 69:1–21, 2013). Our definition uses a construction that starts with a poset. The algebra is concretely constructed as the lattice of upsets of a partially ordered equivalence relation. The key to defining the three negation-like unary operations is to impose certain symmetry requirements on the partial order. Our definition of representable distributive quasi relation algebras is easily seen to be a generalisation of the definition of representable relations algebras by Jónsson and Tarski (AMS 54:89, 1948). We give examples of representable DqRAs and give a necessary condition for an algebra to be finitely representable. We leave open the questions of whether every DqRA is representable, and also whether the class of representable DqRAs forms a variety. Moreover, our definition provides many other opportunities for investigations in the spirit of those carried out for representable relation algebras.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Representable distributive quasi relation algebras

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年4月3日

查看全文
  • Andrew Craig,
  • Claudette Robinson

摘要

We give a definition of representability for distributive quasi relation algebras (DqRAs). These algebras are a generalisation of relation algebras and were first described by Galatos and Jipsen (Algebra Univers 69:1–21, 2013). Our definition uses a construction that starts with a poset. The algebra is concretely constructed as the lattice of upsets of a partially ordered equivalence relation. The key to defining the three negation-like unary operations is to impose certain symmetry requirements on the partial order. Our definition of representable distributive quasi relation algebras is easily seen to be a generalisation of the definition of representable relations algebras by Jónsson and Tarski (AMS 54:89, 1948). We give examples of representable DqRAs and give a necessary condition for an algebra to be finitely representable. We leave open the questions of whether every DqRA is representable, and also whether the class of representable DqRAs forms a variety. Moreover, our definition provides many other opportunities for investigations in the spirit of those carried out for representable relation algebras.