On the KLM Properties of a Fuzzy DL with Typicality

The paper investigates the properties of a fuzzy logic typicality. extension with typicality operator was proposed in recent work to define multipreference semantics for Multilayer Perceptrons, by regarding deep neural network as conditional knowledge base. In this paper, we study its properties. First, monotonic \(\mathcal {ALC}\) is considered (called {ALC}^{\mathbf{F}}\mathbf{T}\)) and reformulation KLM preferential consequence relation devised. Most are satisfied, depending on combination functions considered. We then strengthen {ALC}^{\mathbf{F}}\mathbf{T}\) closure construction introducing notion faithful model weighted base, which generalizes coherent base previously introduced,