标题： 一个函数集框架：一般性质及其在模态逻辑中的应用 显示英文标题

标题： A Function-Set Framework: General Properties and Applications to Modal Logic

摘要： 表示方法对于数学建模现象是必不可少的，但有多种选择可用。 虽然这些选项中的每一个都提供了有用的特点，用于解决与研究现象相关的问题，但在这些表示方法之间比较结果可能并不简单，因为不同的框架被用于不同的上下文。 我们提出了一种基于集合论概念的通用结构，可以容纳与逻辑和语义框架相关的许多情况。 我们通过展示模态逻辑的替代构造来说明这种方法的灵活性；特别是，所有模态逻辑都可以在这个框架内表示。 显示英文摘要

摘要： Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results between these representations can be non-trivial, as different frameworks are used for different contexts. We present a general structure based on set-theoretic concepts that accommodates many situations related to logical and semantic frameworks. We show the versatility of this approach by presenting alternative constructions of modal logic; in particular, all modal logics can be represented within the framework.