嵌套条件的结构态射——完整版
Structural Morphisms for Nested Conditions - Full Version
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中文总结 AI 辅助
本文针对用于约束图变换规则适用性的嵌套条件，引入模拟逻辑联结词的算子，提出结构态射概念并研究其与条件蕴含的一致性，在范畴论语境下证明相关操作的函子性与泛性质。
中文摘要 AI 辅助
嵌套条件除其他用途外，还被用作表达一阶公式的图形化方式，这些公式用于约束图变换规则对给定匹配的适用性。本文首先介绍条件上模拟逻辑联结词的若干算子，接着提出嵌套条件间结构态射的原创概念，确定态射与对应条件蕴含关系一致的情形，最后将结果置于范畴论语境中，证明各类操作的函子性与泛性质。
英文摘要
Nested conditions are used, among other things, as a graphical way to express first order formulas ruling the applicability of a graph transformation rule to a given match. In this paper, we first introduce several operators on conditions mimicking logical connectives. Next we propose an original notion of structural morphism among nested conditions, and we identify circumstances under which morphisms are consistent with the entailment of the corresponding conditions. Finally we frame the results in a categorical context, proving functoriality and universality properties of the various operations.
