Probabilistic Description Logics Based on the Aggregating Semantics and the Principle of Maximum Entropy

描述逻辑（DL）是一个基于逻辑的知识表示语言，专门用于表示术语知识。这种术语知识在TBox中使用一般概念包含（GCI）表示，而关于个人的知识（断言知识）则在ABBox中陈述。在许多应用领域中，知识并不总是确定的，这一事实激发了DL的可能扩展。在这样的扩展中，有必要将断言知识与术语知识区别对待。原则上，概率术语知识具有统计的味道，而概率断言知识具有主观的味道。然而，为了对包含这两种知识的知识库进行推理，需要一个涵盖这两个方面的公共语义框架。以前在这方面的工作还没有解决这个双重需要在一个完全令人满意的方式。该项目的主要思想是适应和扩展最近开发的聚合语义从一个限制的一阶情况下DL分别概括ABox断言和GCI封闭和开放的概率条件。这种语义在可能世界语义的基础上将主观概率与基于人口的陈述相结合，从而为主观概率和统计概率提供了一个共同的语义框架。作为第二个主要特征，我们在聚合语义之上应用最大熵原则。这克服了获得推断概率的大的和无信息的区间的陷阱，这是许多关于概率分布集合的推理方法的共同特征。 而语义属性的方法已经调查了一些细节的一阶逻辑的片段，只有初步的工作已经做了算法和计算性能。为了在实践中有用，通过应用这种方法获得的概率DL需要配备有效的推理程序。因此，该项目的主要重点将是调查的概率逻辑的计算特性（可判定性和复杂性），通过实例化的方法，特别是与DL的不同的表达能力。除了显示可判定性和复杂性的结果，我们将开发实用的算法，一些调查的DL和提供原型实现。另一个主要的挑战将是扩展的方法从宇宙的固定有限大小的无限的情况下，无论是考虑有限的宇宙增长的大小或考虑一个可数无限的宇宙的概率。此外，除了基本方法，我们还将研究扩展，例如在概念中使用概率，允许知识库中的额外约束和独立性假设。

Description Logics (DLs) are a well-investigated family of logic-based knowledge representation languages which are tailored towards representing terminological knowledge. This terminological knowledge is represented in the TBox using general concept inclusions (GCIs), whereas knowledge about individuals (assertional knowledge) is stated in the ABox. Probabilistic extensions of DLs are motivated by the fact that, in many application domains, knowledge is not always certain. In such extensions, there is a need for treating assertional knowledge differently from terminological knowledge. In principle, probabilistic terminological knowledge has a statistical flavour whereas probabilistic assertional knowledge has a subjective flavour. However, in order to reason with respect to a knowledge base containing both kinds of knowledge, one needs a common semantic framework covering both aspects. Previous work in this area has not addressed this dual need in a completely satisfactory way.The main idea underlying this project is to adapt and extend the recently developed aggregating semantics from a restricted first-order case to DLs by respectively generalizing ABox assertions and GCIs to closed and open probabilistic conditionals. This semantics combines subjective probabilities with population-based statements on the basis of a possible-worlds semantics, thus providing a common semantic framework for both subjective and statistical probabilities. As a second main feature, we apply the principle of maximum entropy on top of aggregating semantics. This overcomes the pitfall of obtaining large and uninformative intervals for inferred probabilities which is a common feature of many of the approaches that reason with respect to sets of probability distributions. Whereas the semantic properties of the approach have been investigated in some detail for a fragment of first-order logic, only preliminary work has been done on algorithmic and computational properties. To be useful in practice, the probabilistic DL obtained by applying this approach need to be equipped with effective reasoning procedures. Thus, the main emphasis of this project will be on investigating computational properties (decidability and complexity) of the probabilistic logics obtained by instantiating the approach in particular with DLs of different expressive power. In addition to showing decidability and complexity results, we will develop practical algorithms for some of the investigated DLs and provide prototypical implementations. Another major challenge will be to extend the approach from universes of fixed finite size to the infinite case by either considering limit probabilities for universes of growing size or considering a countably infinite universe. Furthermore, in addition to the basic approach, we will also investigate extensions, such as using probabilities also within concepts, allowing for additional constraints in the knowledge base and for independence assumptions.