Description Logics are Hybrid Multi-Modal Logics
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Yuefei Sui,Meiying Sun. Description Logics are Hybrid Multi-Modal Logics. International Journal of Software and Informatics, 2014,8(1):133~142
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Abstract:There are several translations from description logics to multi-modal logics, and these different translations have different logical properties which have not been considered in these translations. To give a faithful and full translation from description logics to multi-modal logics, we need extend the multi-modal logics to the hybrid multi-modal logics and classify the formulas in the hybrid multi-modal logics into two levels, so that one level of formulas corresponds to concepts and another corresponds to statements in description logics. This paper will give a faithful translation from the description logic ALC to the hybrid multi-modal logic and a faithful translation from the hybrid multi-modal logic to ALC, so that there is a faithful and full translation from ACL to the hybrid multi-modal logic, which implies that ACL is sound and complete if and only if the hybrid multi-modal logic is sound and complete.
keywords:logical translation  description logic  hybrid multi-modal logic  faithfulness  completeness
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