Towards More Effective Tableaux Reasoning for CKR

Representation of context dependent knowledge in the Semantic Web is a recently emergent issue. A number of logical formalisms with this aim have been proposed [3, 11, 14]. Among them is the DL based Contextualized Knowledge Repository (CKR) [13]. One of the mostly advocated advantages of context based knowledge representation is that reasoning procedures can be constructed by composing local reasoners running inside each context, with the obvious divide-and-conquer advantage. We recently proposed a tableaux decision algorithm [5, 9] for the case of CKR framework based on ALC DL. The algorithm extends the well known ALC tableaux algorithm [6, 12] and it is based on a combination of local reasoning inside each context with a set of novel rules that propagate knowledge across the neighboring contexts. To our best knowledge, it is the only direct tableaux reasoning algorithm for contextualized DL knowledge to date: by direct we mean not based on some reduction to a single DL knowledge base, which neglects the divide-and-conquer advantage. In this paper, we review this algorithm and we describe our initial ideas on possible optimization, including dimensional coverage caching and parallelization. In order to maximize the divide-and-conquer advantage, it is important to propagate only those symbols between local tableaux which are really needed to assure completeness. We propose a (correctness preserving) modification of three propagation rules that decreases the amount of propagation and also of related non-deterministic branching. Proofs of all theorems can be found in the accompanying technical report [9].