Towards a crisp representation of fuzzy description logics under Lukasiewicz semantics

Classical ontologies are not suitable to represent imprecise nor uncertain pieces of information. Fuzzy Description Logics were born to represent the former type of knowledge, but they require an appropriate fuzzy language to be agreed and an important number of available resources to be adapted. An alternative is to use classical ontologies to represent fuzzy ontologies. To date, all of the work in this direction has restricted to the Zadeh family of fuzzy operators. In this paper, we generalize existing proposals and propose a reasoning preserving procedure to obtain a crisp representation for a fuzzy extension of the logic $mathcal{ALCHIO}$ under {L}ukasiewicz semantics. This reduction makes possible to reuse a crisp representation language as well as currently available reasoners under crisp semantics.