This would suggest that the formance of tableauxbased

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treatment of Abox and “terminological” constraints. This would suggest that the per-formance of tableaux–based algorithms, such as the one implemented in Race, can beimproved by using an evaluation strategy more similar to the precompletion strategy(e.g. work on individual first).
Chapter 9ConclusionsThis chapter summarise the results presented in this thesis, and suggests some direc-tions for future work.9.1Thesis contributionsThe aim of our work is to study basic reasoning techniques for DL knowledge baseswith Abox, and to determine whether they can lead to practical tractability. This thesisinvestigates two reasoning problems, namely KB satisfiability and query answering.9.1.1KB satisfiabilityDifferent techniques have been considered, and we chose to investigate the possibilityof extending the precompletion technique in order to provide an algorithm for the DLf.By exploiting the tree–like model property off, it has been proved that the tech-nique leads to a correct and complete algorithm for KB satisfiability. An experimentalDL reasoner based on the studied algorithm has been developed, and some experimentshave been performed to evaluate the behaviour of the system.The experiments provided evidence of the fact that, even with an optimised termi-nological reasoner, different optimisation techniques must be used in the precomple-tion phase in order to obtain acceptable performance. Although we have not providedformal proofs of correctness and completeness of the optimisations used, we have pro-vided arguments supporting the fact that their use does not affect the correctness andcompleteness of the underlying algorithm.190
9.2. FUTURE WORK191The system developed, although experimental, exhibits good performance com-pared to a state of the art DL system. As pointed out in Chapter 8, we think that theideas behind the precompletion technique may be used to improve the performance oftableaux based systems like Race.9.1.2Query answeringThe language for querying KBs has always been one of the weakest points of DLsystems; recently, there have been some attempts to find a solution to this inadequacy.In this thesis we develop a technique for answering conjunctive queries overfKBs.Again, the technique relies on a careful use of the model–theoretic properties off. A class of interpretations has been identified which is complete w.r.t. the prob-lem of conjunctive query answering inf. The properties of this class have beenused to devise an algorithm for query answering, and for proving its correctness andcompleteness.Although the results which have been presented here are specific to the DLf,the technique is general enough to provide query answering algorithms for a widerange of DLs. In addition, since the problem is reduced to KB satisfiability, the algo-rithm described can easily be implemented on top of most of the available DL systems.

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