Repairing Description Logic Ontologies

描述逻辑（dl）是一系列基于逻辑的知识表示语言，用于形式化生物和医学等应用领域的本体。随着基于dl的本体规模的增长，用于提高其质量的工具变得更加重要。深度学习推理器可以检测不一致并推断其他隐含的结果。然而，对于本体的开发人员来说，通常很难理解为什么推理器计算出的结果会出现，以及如果不希望出现这种结果，如何修复本体。修复基于dl的本体的经典算法方法是计算（一个或多个）本体的最大子集，这些子集不再具有意想不到的后果。在之前的工作中，我们引入了一种更“温和”的方法来修复本体，它允许我们保留比经典方法更多的结果：而不是完全删除公理，我们的温和修复用“较弱”的公理代替它们，即具有较少结果的公理。除了引入一般的框架外，我们还定义了公理上弱化关系的有用性质，并研究了DL - EL的两种特殊的弱化关系。这个项目的主要目的是更详细地研究这种温和的修复方法。一方面，我们将考虑一般框架的变体，例如，选择削弱哪些公理和多少公理。另一方面，我们将为轻量级的dl（如EL）和表达性的dl（如ALC）设计不同的弱化关系，并研究它们的性质。此外，我们将澄清与其他领域类似方法的关系，如信念修正和不一致容忍推理，并将我们的方法扩展到隐私保护本体发布的设置。关于信念修正，应该指出的是，我们的温和修复方法与该区域所谓的伪收缩有关。然而，信念修正的重点更多地放在生成满足某些假设的收缩的抽象方法上，而不是定义和研究具体的修复方法。我们将研究我们的方法满足哪些假设。不一致性容忍推理很有趣，因为它通常基于考虑从一些、所有或所有修复的交集中得出的结果。我们将研究修复的新概念如何影响这些不一致容忍推理方法。在保护隐私的本体发布中，删除要从本体中隐藏的结果是不够的，因为攻击者可能有额外的背景信息。在以前的工作中，我们在一个非常有限的环境中考虑了这个问题，其中要发布的信息和背景知识都使用EL概念表示。我们打算将其推广到更通用的知识库形式和更具表达性的dl。

Description Logics (DLs) are a family of logic-based knowledge representation languages, which are used to formalize ontologies for application domains such as biology and medicine. As the size of DL-based ontologies grows, tools for improving their quality become more important. DL reasoners can detect inconsistencies and infer other implicit consequences. However, for the developer of an ontology, it is often hard to understand why a consequence computed by the reasoner follows, and how to repair the ontology if this consequence is not intended. The classical algorithmic approach for repairing DL-based ontologies is to compute (one or more) maximal subsets of the ontology that no longer have the unintended consequence. In previous work we have introduced a more "gentle" approach for repairing ontologies that allows us to retain more consequences than the classical approach: instead of completely removing axioms, our gentle repair replaces them by "weaker" axioms, i.e., axioms that have less consequences. In addition to introducing the general framework, we have defined useful properties of weakening relations on axioms and investigated two particular such relations for the DL EL.The purpose of this project is foremost to investigate this gentle repair approach in more detail. On the one hand, we will consider variants of the general framework, e.g., w.r.t. which and how many axioms are chosen to be weakened. On the other hand, we will design different weakening relations, both for light-weight DLs such as EL and for expressive DLs such as ALC, and investigate their properties. In addition, we will clarify the relationship to similar approaches in other areas such as belief revision and inconsistency-tolerant reasoning, and extend our approach to the setting of privacy-preserving ontology publishing. Regarding belief revision, it should be noted that our gentle repair approach is related to what is called pseudo-contraction in that area. However, the emphasis in belief revision is more on abstract approaches for generating contractions that satisfy certain postulates than on defining and investigating concrete repair approaches. We will investigate which of these postulates are satisfied by our approaches. Inconsistency-tolerant reasoning is of interest since it is often based on considering what follows from some, all, or the intersection of all repairs. We will investigate how our new notion of repair influences these inconsistency-tolerant reasoning approaches. In privacy-preserving ontology publishing, removing consequences that are to be hidden from the ontology is not sufficient since an attacker might have additional background information. In previous work, we have considered this problem in a very restricted setting, where both the information to be published and the background knowledge are represented using EL concepts. We intend to generalize this to more general forms of knowledge bases and more expressive DLs.