A Tableau Decision Algorithm for Dynamic Description Logic

Abstract

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.