This paper discusses relational operations in the first-order logical environment {FOLE}. Here we demonstrate how FOLE expresses the relational operations of database theory in a clear and implementable representation. An analysis of the representation of database tables/relations in FOLE reveals a principled way to express the relational operations. This representation is expressed in terms of a distinction between basic components versus composite relational operations. The 9 basic components fall into three categories: reflection (2), Booleans or basic operations (3), and adjoint flow (4). Adjoint flow is given for signatures (2) and for type domains (2), which are then combined into full adjoint flow. The basic components are used to express various composite operations, where we illustrate each of these with a flowchart. Implementation of the composite operations is then expressed in an input/output table containing four parts: constraint, construction, input, and output. We explain how limits and colimits are constructed from diagrams of tables, and then classify composite relational operations into three categories: limit-like, colimit-like and unorthodox.
翻译:本文讨论第一阶逻辑环境 {FOLE} 中的关联操作 。 这里我们演示FOLE如何以清晰和可执行的表示方式表达数据库理论的关联操作 。 对FOLE中数据库表格/关系表示的分析揭示了表达关联操作的原则性方法 。 该表示方式表现为基本组成部分与复合关联操作之间的区别 。 9个基本组成部分分为三类 : 反射(2) 布尔或基本操作(3) 和连接流(4) 。 给签名(2) 和类型域(2) 提供联合流程,然后将其合并为完全的连接流 。 基本组成部分用于表达各种组合操作, 我们用流程图来说明其中的每个组合操作 。 综合操作的实施随后以包含四个部分的投入/产出表表示 : 制约、 构建、 输入 和输出 。 我们解释图表中如何构建限制和共同关联操作的大小, 然后将复合关联操作分为三个类别 : 类似限制、 类似 和 非正统 。