We study the separation of positive and negative data examples in terms of description logic (DL) concepts and formulas of decidable FO fragments, in the presence of an ontology. In contrast to previous work, we add a signature that specifies a subset of the symbols from the data and ontology that can be used for separation. We consider weak and strong versions of the resulting problem that differ in how the negative examples are treated. Our main results are that (a projective form of) the weak version is decidable in $\mathcal{ALCI}$ while it is undecidable in the guarded fragment GF, the guarded negation fragment GNF, and the DL $\mathcal{ALCFIO}$, and that strong separability is decidable in $\mathcal{ALCI}$, GF, and GNF. We also provide (mostly tight) complexity bounds.

中文翻译：

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通过概念和公式分离正负数据示例：受限签名的情况

我们在存在本体的情况下，根据描述逻辑 (DL) 概念和可判定 FO 片段的公式研究正负数据示例的分离。与之前的工作相比，我们添加了一个签名，该签名指定了数据和本体中可用于分离的符号子集。我们考虑由此产生的问题的弱和强版本，它们在如何处理负面示例方面有所不同。我们的主要结果是弱版本（的投影形式）在 $\mathcal{ALCI}$ 中是不可判定的，而在受保护的片段 GF、受保护的否定片段 GNF 和 DL $\mathcal{ALCFIO}$ 中是不可判定的，并且这种强可分性在 $\mathcal{ALCI}$、GF 和 GNF 中是可判定的。我们还提供（主要是紧密的）复杂度界限。