Planning Problems for Graph Structured Data in Description Logics

Motivation The complex structure and increasing size of information that has to be managed in today’s applications calls for flexible mechanisms for storing such information, making it easily and efficiently accessible, and facilitating its change and evolution over time. The paradigm of graph structured data (GSD) [5] has gained popularity recently as an alternative to traditional relational databases that provides more flexibility and thus can overcome the limitations of an a priori imposed rigid structure on the data. Indeed, differently from relational data, GSD do not require a schema to be fixed a priori. This flexibility makes them well suited for many emerging application areas such as managing Web data, information integration, persistent storage in object-oriented software development, or management of scientific data. Concrete examples of models for GSD are RDFS [2], object-oriented data models, and XML. Here we build on recent work that advocates the use of Description Logics (DLs) for managing change in GSD that happens as the result of (agents or users) executing actions [4]. We consider GSD understood in a broad sense, as information represented by means of a node and edge labeled graph, in which the labels convey semantic information. We identify GSD with the finite structures over which DLs are interpreted, and use DL knowledge bases as descriptions of constraints and properties of the data. We express actions using a specially tailored action language in which actions are finite sequences of (possibly conditional) insertions and deletions performed on the extensions of labels. For this setting, the static verification problem, which consists on deciding whether the execution of a given action will preserve some given integrity constraints on any possible GSD, has been studied in [4]. Here we discuss further problems that can be considered as variants of planning, such as deciding whether there is a sequence of actions that leads a given structure into a state where some property (either desired or not) holds, or whether a given sequence of actions leads every structure into a state where some property necessarily holds. We develop algorithms for variations of these problems, and characterize their computational complexity. We refer the reader to [1] for the extended version of this paper, which also includes an extensive discussion of related work.