  Weighted knowledge bases for description logics with typicality have been
recently considered under a "concept-wise" multipreference semantics (in both
the two-valued and fuzzy case), as the basis of a logical semantics of
MultiLayer Perceptrons (MLPs). In this paper we consider weighted conditional
ALC knowledge bases with typicality in the finitely many-valued case, through
three different semantic constructions. For the boolean fragment LC of ALC we
exploit ASP and "asprin" for reasoning with the concept-wise multipreference
entailment under a phi-coherent semantics, suitable to characterize the
stationary states of MLPs. As a proof of concept, we experiment the proposed
approach for checking properties of trained MLPs.
  The paper is under consideration for acceptance in TPLP.
