Finite Lattices Do Not Make Reasoning in ALCI Harder
We consider the fuzzy logic ALCI with semantics based on a finite residuated lattice. We show that the problems of satisfiability and subsumption of concepts in this logic are ExpTime-complete w.r.t. general TBoxes and PSpace-complete w.r.t. acyclic TBoxes. This matches the known complexity bounds for reasoning in crisp ALCI.