Finite fuzzy description logics: a crisp representation for finite fuzzy ALCH

Fuzzy Description Logics (DLs) are a formalism for the representation of structured knowledge affected by imprecision or vagueness. In the setting of fuzzy DLs, restricting to a finite set of degrees of truth has proved to be useful. In this paper, we propose finite fuzzy DLs as a generalization of existing approaches. We assume a finite totally ordered set of linguistic terms or labels, which is very useful in practice since expert knowledge is usually expressed using linguistic terms. Then, we consider any smooth t-norm defined over this set of degrees of truth. In particular, we focus on the finite fuzzy DL $mathcal{ALCH}$, studying some logical properties, and showing the decidability of the logic by presenting a reasoning preserving reduction to the non-fuzzy case.