Actions and Programs over Description Logic Ontologies

We aim at representing and reasoning about actions and (high level) programs over ontologies expressed in Description Logics. This is a critical issue that has resisted good solutions for a long time. In particular, while welldeveloped theories of actions and high-level programs exist in AI, e.g., the ones based on SitCalc, these theories do not apply smoothly to Description Logic ontologies, due to the profoundly non-definitorial nature of such ontologies (cf. cyclic TBoxes). Here we propose a radical solution: we assume a functional view of ontologies and see them as systems that allow for two kinds of operations: ASK, which returns the (certain) answer to a query, and TELL, which produces a new ontology as a result of the application of an atomic action. We base atomic actions on instance level update and instance level erasure on the ontology. Building on this functional view, we introduce Golog/ConGolog-like high-level programs on ontologies. This paper demonstrates the effectiveness of the approach in general, and presents the following specific results: we characterize the notion of single-step executability of such programs, devise methods for reasoning about sequences of actions, and present (nice) complexity results in the case where the ontology is expressed in DL-Lite.

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