基于OBDD的描述逻辑εL循环术语集推理  

OBDD-Based Reasoning for Terminological Cycles of the Description Logic εL

作　　者：古天龙[1] 吕思菁 常亮[1] 徐周波[1] 

机构地区：[1]广西可信软件重点实验室(桂林电子科技大学),广西桂林541004

出　　处：《软件学报》2014年第1期64-77,共14页Journal of Software

基　　金：国家自然科学基金(60963010;60903079;61100025;61262030;61363030);广西自然科学基金(2012GXNSFBA 053169)

摘　　要：循环术语集推理是描述逻辑研究中面临的难点问题,尚未得到很好的解决.有序二叉决策图(ordered binary decision diagram,简称OBDD)是一种对布尔函数进行紧凑表示和高效操作的数据结构,适用于表示和处理大规模问题.将OBDD应用于描述逻辑循环术语集的推理.首先,针对描述逻辑εL中的循环术语集,给出了描述图上关于最大模拟关系的重要性质,并借助集合表示和集合运算对该性质进行了表述和证明.在此基础上,应用布尔函数对描述图进行编码,给出了基于OBDD求解最大模拟关系的方法,进而给出了最大不动点语义下基于OBDD对概念包含关系进行判定的算法;接下来,基于OBDD给出了求解描述图中可以到达循环路径的所有结点的方法,进而给出了最小不动点语义下基于OBDD对概念包含关系进行判定的算法;最后,对算法的正确性、复杂度等进行了分析和证明,并对算法进行了编程实现,给出了关于计算性能的实验结果.该工作为循环术语集的推理提供了一条有效途径,也为OBDD在逻辑推理中的应用提供了新的案例.Reasoning about terminological cycles of description logics is a hard problem that needs to be solved. Ordered binary decision diagram （OBDD） is a data structure suitable for dealing with large-scale problems since through the diagram Boolean functions can be represented compactly and computed efficiently. In this paper, OBDD is adopted to reason about terminological cycles of description logics. First, for terminological cycles of the description logic sL, with the help of set representation and operation, a property about the greatest simulation relationship on description graphs of terminological cycles is specified and proved. Second, by encoding description graphs of terminological cycles as Boolean functions, an OBDD-based procedure for computing the greatest simulation relationship is proposed, and based on this procedure an algorithm is presented for deciding the subsumption relationship between concepts under the greatest fix-point semantics. Third, based on OBDD, a procedure for calculating all the nodes which can reach cycle paths in a description graph is proposed, and based on this procedure an algorithm for deciding the subsumption relationship under the least fix-point semantics is also presented. Finally, the correctness and time complexity of both algorithms are proved; the computing performance of both algorithms are also demonstrated by a set of experiments. This work provides an effective approach for reasoning about terminological cycles of description logics; it also provides a new case for applying OBDD in the fields of logical reasoning.

关 键 词：描述逻辑εL 循环术语集 有序二叉决策图 概念包含关系 不动点语义 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]