论文标题
单词和图表上的积极的一阶逻辑
Positive First-order Logic on Words and Graphs
论文作者
论文摘要
我们研究有限单词上的一阶逻辑片段，其中单元谓词只能呈积极形式。我们表明，有一种可定义的语言是单声谓词中的单调，但在fo+中不能定义。这提供了一个简单的证据，表明林登的保存定理在有限的结构上失败。我们将此示例语言提升为有限的图表，从而为FO可确定图类别独立兴趣提供了新的结果：即使在添加边缘下关闭课程时，也可能需要否定。我们最终表明，在fo+中是否可以定义给定的常规语言是否不可确定。
We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is an FO-definable language that is monotone in monadic predicates but not definable in FO+. This provides a simple proof that Lyndon's preservation theorem fails on finite structures. We lift this example language to finite graphs, thereby providing a new result of independent interest for FO-definable graph classes: negation might be needed even when the class is closed under addition of edges. We finally show that the problem of whether a given regular language of finite words is definable in FO+ is undecidable.
