Complexity Sources in Fuzzy Description Logic

In recent years many Fuzzy Description Logics (FDLs) based on infinite $t$-norms have been proved to be undecidable. On the other hand, several FDLs based on finite $t$-norms, not only have been proved to be decidable, but they have been proved to belong to the same complexity classes as the corresponding crisp DLs. In light of such results, a question that naturally arises is whether the finite-valued fuzzy framework is no more complex than the crisp-valued formalism. The aim of this work is to analyze some of the complexity sources that are not present in the crisp framework. To this end, we will consider FDL languages with low expressivity that allow us to observe how the need for more complex deciding strategies, not required in the crisp framework, arises in many-valued FDLs.