Definite descriptions are phrases of the form 'the $x$ such that $\varphi$', used to refer to single entities in a context. They are often more meaningful to users than individual names alone, in particular when modelling or querying data over ontologies. We investigate free description logics with both individual names and definite descriptions as terms of the language, while also accounting for their possible lack of denotation. We focus on the extensions of $\mathcal{ALC}$ and, respectively, $\mathcal{EL}$ with nominals, the universal role, and definite descriptions. We show that standard reasoning in these extensions is not harder than in the original languages, and we characterise the expressive power of concepts relative to first-order formulas using a suitable notion of bisimulation. Moreover, we lay the foundations for automated support for definite descriptions generation by studying the complexity of deciding the existence of definite descriptions for an individual under an ontology. Finally, we provide a polynomial-time reduction of reasoning in other free description logic languages based on dual-domain semantics to the case of partial interpretations.
翻译:直截了当的描述是“ $x$ ” 的短语, 用于在某种背景下指单个实体。 它们通常比单个名称对用户更有意义, 特别是当建模或查询关于本意的数据时。 我们用个人姓名和明确描述作为语言术语的自由描述逻辑进行调查, 同时也考虑到它们可能缺乏批注。 我们侧重于以名义、通用作用和明确描述分别提供$\mathcal{EL}美元和$\mathcal{EL}美元。 我们显示,这些扩展的标准推理对用户来说并不比原始语言更难, 我们用适当的推理概念来描述相对于一阶公式的表达力, 使用适当的推理概念来描述。 此外, 我们为自动支持确定描述的生成奠定了基础, 研究在本意下个人明确描述是否存在的复杂性。 最后, 我们提供了基于双义语系语义解释的其他自由描述逻辑语言中推理的多时减。