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动态描述逻辑的Tableau判定算法

期刊名称：动态描述逻辑的Tableau判定算法. 计算机学报, 31(6): 896-909, 2008.
时间：0
分类：TP18[自动化与计算机技术—控制科学与工程;自动化与计算机技术—控制理论与控制工程]
作者机构：[1]中国科学院计算技术研究所智能信息处理重点实验室,北京100190, [2]中国科学院研究生院,北京100039
相关基金：本课题得到国家自然科学基金（90604017,60775035）、国家“八六三”高技术研究发展计划项目基金（2007AA01Z132）和国家＂九七三＂重点基础研究发展规划项目基金（2007CB311004）资助.
相关项目：基于感知学习和语言认知的智能计算模型

关键词：动态描述逻辑, 动作理论, 可满足性问题, TABLEAU算法, 可判定性, dynamic description logic, action theory, satisfiability, Tableau algorithm, decidability

中文摘要：

动态描述逻辑在描述逻辑的基础上引入了动态维，用于描述和推理动态领域的知识，但目前缺少有效的判定算法作为支撑。文中以描述逻辑ALCO的动态扩展为例，构建出动态描述逻辑D-ALCO。以D-ALCO的构建过程为基础，将ALCO的Tableau算法、命题动态逻辑的Tableau算法以及对可能模型途径的处理有机地结合起来，给出了D-ALCO的Tableau判定算法，证明了算法的可终止性、可靠性和完备性．应用该算法，可以在采用开世界假设的情况下对D-ALCO中公式的可满足性进行判定。对于D-ALCQO、D-ALCQIO等具有更强描述能力的动态描述逻辑，可以对该算法扩展后得到相应的Tableau判定算法。

英文摘要：

By introducing a dynamic dimension into the description logic, two kinds of dynamic description logics have been proposed in the literatures for representing and reasoning about knowledge of dynamic application domains. But both of them lack efficient decision algorithms. This paper presents a Tableau decision algorithm for the dynamic description logic D-ALCO. D-ALCO is a combination of the description logic ALCO, the dynamic logic, and an action theory based on the possible models approach. In D-ALCO, based on domain ontologies expressed in ALCO, atomic actions are described by specifying their preconditions and effects; With the help of standard action constructors of the dynamic logic, complex actions can be described also; Both atomic actions and complex actions are then used as modal operators in the construction of formulas. The Tableau decision algorithm for D-ALCO forms an elaborated combination of the Tableau algorithm for ALCO, the decision algorithm for propositional dynamic logic, and the embodiment of the possible models approach. The authors prove that the algorithm is terminating, sound and complete for deciding the satisfiability of D-ALCO formulas with the Open World Assumption. The algorithm is flexible and can be extended for more expressive dynamic description logics such as the D-ALCQO and the D-ALCQIO.

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