论文标题
用示例表征模态公式
Characterising Modal Formulas with Examples
论文作者
论文摘要
我们启动对模态语言的有限特征和精确可学习性的研究。模态公式W.R.T.的有限表征一组公式是一组有限的有限模型（标记为正或负），将该公式与其他公式与该集合区分开。如果每个L形式都有有限的特征W.R.T. L.此定义不仅可以应用于基本的模态逻辑K，还可以应用于任意的正常模态逻辑。我们表明，普通的模态逻辑可以接受有限的特征（对于完整的模态语言），如果是局部表格。这表明，关于完整的模态语言的有限特征很少，因此激发了对完整模态语言片段的有限特征的研究。我们的主要结果是，没有真相稳定$ \ top $和$ \ bot $的积极模态语言允许有限的特征。此外，我们表明该结果本质上是最佳的：当语言随着真实的commant consance $ \ bot $或除了非常有限的否定形式而言，有限特征不再存在。
We initiate the study of finite characterizations and exact learnability of modal languages. A finite characterization of a modal formula w.r.t. a set of formulas is a finite set of finite models (labelled either positive or negative) which distinguishes this formula from every other formula from that set. A modal language L admits finite characterisations if every L-formula has a finite characterization w.r.t. L. This definition can be applied not only to the basic modal logic K, but to arbitrary normal modal logics. We show that a normal modal logic admits finite characterisations (for the full modal language) iff it is locally tabular. This shows that finite characterizations with respect to the full modal language are rare, and hence motivates the study of finite characterizations for fragments of the full modal language. Our main result is that the positive modal language without the truth-constants $\top$ and $\bot$ admits finite characterisations. Moreover, we show that this result is essentially optimal: finite characterizations no longer exist when the language is extended with the truth constant $\bot$ or with all but very limited forms of negation.
