Family of Extended Dynamic Description Logics

作为描述逻辑的扩展,动态描述逻辑为语义Web服务的建模和推理提供了一种有效途径.在将语义Web服务建模为动作之后,动态描述逻辑从动作执行结果的角度提供了丰富的推理机制,但对于动作的执行过程却不能加以处理.借鉴Pratt关于命题动态逻辑的相关研究,一方面,对动态描述逻辑中动作的语义重新进行定义,将每个动作解释为由关于可能世界的序列组成的集合;另一方面,在动态描述逻辑中引入动作过程断言,用来对动作的执行过程加以刻画.在此基础上提出一类扩展的动态描述逻辑EDDL(X),其中的X表示从ALC(attributive language with complements)到SHOIN(D)等具有不同描述能力的描述逻辑.以X为描述逻辑ALCQO(attributive language with complements,qualified number restrictions and nominals)的情况为例,给出了EDDL(ALCQO)的表判定算法,并证明了算法的可终止性、可靠性和完备性.EDDL(X)可以从动作执行过程和动作执行结果两个方面对动作进行全面的刻画和推理,为语义Web服务的建模和推理提供了进一步的逻辑支持.;As the extension of the description logic, many dynamic description logics are proposed for modeling and reasoning about Semantic Web Services. These dynamic description logics provide decidable reasoning mechanisms for the result of action execution. However, the procedure of action execution can not be described and reasoned about according to these logics. Inspired by an extended propositional dynamic logic studied by Pratt, this paper proposes two improvements to the dynamic description logic. One is that, semantics of actions in the dynamic description logic are redefined in such a way that each action is interpreted as a set of trajectories, where each trajectory is a sequence of possible worlds of the semantic model. The other is that, assertions on the procedure of action execution are introduced to the logic so that not only the result but also the procedure can be described for the execution of actions. As a result, a family of extended dynamic description logics named EDDL(X) is presented in this paper, where X represents well-studied description logics ranging from ALC (attributive language with complements) to SHOIN(D). Taking the description logic ALCQO (attributive language with complements, qualified number restrictions and nominals) as an example of the X of EDDL(X), this paper proposes a tableau decision algorithm for the logic EDDL(ALCQO) and proves that this algorithm is terminating, sound and complete. With EDDL(X), both the result and the procedure of action execution can be described and reasoned about. Therefore, compared with dynamic description logics, EDDL(X) provides further support for modeling and reasoning about semantic Web services.