In this paper, we present a general inference system for reasoning with if-then rules. They are defined using general lattice-theoretic notions and their semantics is defined using particular closure operators parameterized by systems of isotone Galois connections. In this general setting, we introduce a simplification logic, show its sound and complete axiomatization, and deal with related issues. The presented results can be seen as forming parameterized framework for dealing with if-then rules that allows to focus on particular dependencies obtained by choices of parameterizations.

中文翻译：

---

参数化简化逻辑 I：推理与闭包运算符的含义和类

在本文中，我们提出了一个通用推理系统，用于使用 if-then 规则进行推理。它们是使用一般格论概念定义的，它们的语义是使用由等音伽罗瓦连接系统参数化的特定闭包算子定义的。在这个一般设置中，我们引入了一个简化逻辑，展示了它的健全和完整的公理化，并处理了相关问题。所呈现的结果可以被视为形成用于处理 if-then 规则的参数化框架，该框架允许关注通过参数化选择获得的特定依赖关系。