Abstract
Logic-based approaches to AI have the advantage that their behavior can in principle be explained with the help of proofs of the computed consequences. For ontologies based on Description Logic (DL), we have put this advantage into practice by showing how proofs for consequences derived by DL reasoners can be computed and displayed in a user-friendly way. However, these methods are insufficient in applications where also numerical reasoning is relevant. The present paper considers proofs for DLs extended with concrete domains (CDs) based on the rational numbers, which leave reasoning tractable if integrated into the lightweight DL \(\mathcal {E}\mathcal {L} _\bot \). Since no implemented DL reasoner supports these CDs, we first develop reasoning procedures for them, and show how they can be combined with reasoning approaches for pure DLs, both for \(\mathcal {E}\mathcal {L} _\bot \) and the more expressive DL \(\mathcal {ALC}\). These procedures are designed such that it is easy to extract proofs from them. We show how the extracted CD proofs can be combined with proofs on the DL side into integrated proofs that explain both the DL and the CD reasoning.
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Notes
- 1.
- 2.
- 3.
Often, the classification is done only for concept names in \(\mathcal {O}\), but we use a variant that considers all subconcepts, as it is done by the \(\mathcal {E}\mathcal {L} _\bot \) reasoner Elk.
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The index \(\textit{diff}\) in its name is motivated by the fact that such a predicate fixes the difference between the values of two variables.
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See [23] for syntax and semantics of concepts using role paths.
- 6.
The result in [23] applies to p-admissible CDs \(\mathcal {D}\) since it is easy to show that the extension of \(\mathcal {D}\) with the negation of its predicates satisfies the required conditions.
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This work was supported by the DFG grant 389792660 as part of TRR 248 (https://perspicuous-computing.science).
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Alrabbaa, C., Baader, F., Borgwardt, S., Koopmann, P., Kovtunova, A. (2023). Combining Proofs for Description Logic and Concrete Domain Reasoning. In: Fensel, A., Ozaki, A., Roman, D., Soylu, A. (eds) Rules and Reasoning. RuleML+RR 2023. Lecture Notes in Computer Science, vol 14244. Springer, Cham. https://doi.org/10.1007/978-3-031-45072-3_4
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