Reasoning and Query Answering Using Concept Similarity Measures and Graded Membership Functions

描述逻辑(DLS)是一类经过充分研究的基于逻辑的知识表示语言，例如，经常被用于形式化诸如生物和医学等应用领域的本体。为了将这种应用领域的重要概念定义为形式概念，DLS规定了个人属于某个概念的必要条件和充分条件。一旦以这种方式形式化了应用程序域的相关概念，就可以在查询中使用它们，以便从数据中检索新信息。由于传统的描述逻辑是基于经典一阶逻辑的，所以它们的语义是严格的，即一个人要属于一个概念，所有陈述的性质都需要满足，对查询的回答也是如此。在很难得到确切定义的应用中，放宽这一严格的要求并允许概念的近似定义将是有用的，其中大多数(但不是全部)所述属性被要求保持。类似地，如果查询没有确切的答案，满足查询所寻找的大多数特征的近似答案可能是有用的。为了允许概念的近似定义，我们引入了分级隶属函数的概念，它不是布尔隶属度值0或1，而是区间[0，1]的隶属度。例如，阈值概念可以要求一个人属于度至少为0.8的概念C。另一种基于对概念使用相似性度量的方法被用来放宽实例查询(即，由单个概念组成的查询)。给定查询概念C，我们正在寻找与C的相似度高于某一阈值的查询D的答案。虽然这两种方法是由两名申请者和博士生独立开发的，但事实证明，这两种方法是有密切联系的。相似性度量可用于定义分级隶属函数和阈值概念W.r.t.这些函数为松散的实例查询提供了更自然的语义。详细探索这两种方法之间的联系，并开发和研究一种组合方法；2.通过考虑a)比最初为其开发方法的DL EL更具表现力的DLS；b)更一般的术语形式；c)更一般的查询，如合取查询；d)更一般的推理问题，如确定适当的阈值，而不是要求用户提供它们，从而扩展该组合方法的适用性。

Description Logics (DLs) are a well-investigated family of logic-based knowledge representation languages, which are, e.g., frequently used to formalize ontologies for application domains such as biology and medicine. To define the important notions of such an application domain as formal concepts, DLs state necessary and sufficient conditions for an individual to belong to a concept. Once the relevant concepts of an application domain are formalized this way, they can be used in queries in order to retrieve new information from data. Since traditional DLs are based on classical first-order logic, their semantics is strict in the sense that all the stated properties need to be satisfied for an individual to belong to a concept, and the same is true for answers to queries. In applications where exact definitions are hard to come by, it would be useful to relax this strict requirement and allow for approximate definitions of concepts, where most, but not all, of the stated properties are required to hold. Similarly, if a query has no exact answer, approximate answers that satisfy most of the features the query is looking for could be useful.In order to allow for approximate definitions of concepts, we have introduced the notion of a graded membership function, which instead of a Boolean membership value 0 or 1 yields a membership degree from the interval [0,1]. Threshold concepts can then, for example, require that an individual belongs to a concept C with degree at least 0.8. A different approach, which is based on the use of similarity measures on concepts, was used to relax instance queries (i.e., queries that consist of a single concept). Given a query concept C, we are looking for answers to queries D whose similarity to C is higher than a certain threshold. While these two approaches were developed independently by the two applicants together with doctoral students, it has turned out that there are close connections. Similarity measures can be used to define graded membership functions, and threshold concepts w.r.t. these functions provide a more natural semantics for relaxed instance queries.The goals of this project are to1. explore the connection between the two approaches in detail, and develop and investigate a combined approach; 2. extend the applicability of this combined approach by considering a) more expressive DLs than the DL EL for which the approaches were initially developed; b) more general terminological formalisms; c) more general queries such as conjunctive queries; d) more general inference problems such as determining appropriate threshold values rather than requiring the user to provide them.