Abstract
In this chapter, we present some motivation for proofs explanations. For the tasks of providing proofs and explanations, we compare three deduction systems. In the sequel, we present an example of proof and possible explanation of this same proof in our system \({\mathrm{ SC} }_{\mathcal{ ALC} }\). Finally, in the last section of this chapter, we use examples of DL deductions from Berardi et al. (Artif Intell 168:84, 2005), using \({\mathrm{ ND} }_{\mathcal{ ALCQI} }\) to reason on the \(\mathcal{ ALCQI} \) KB. The idea is to exemplify how one can obtain from \({\mathrm{ ND} }_{\mathcal{ ALCQI} }\) proofs, a more precise and direct explanation.
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Notes
- 1.
Intuitionistic Logic and Minimal Logic have similar behavior concerning the relationship between their respective systems of ND and SC.
- 2.
Instead, we allow explicit inequality assertions of the form \(x\ne y\). Those assertions are assumed symmetric.
References
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Rademaker, A. (2012). Proofs and Explanations. In: A Proof Theory for Description Logics. SpringerBriefs in Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-4002-3_7
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DOI: https://doi.org/10.1007/978-1-4471-4002-3_7
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