Abstract
The fuzzy modality probably is interpreted over
probabilistic type spaces by taking expected truth
values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is non-expansive wrt.
a suitable notion of behavioural distance. In the
present paper, we provide a characterization of the
expressive power of this logic based on this observation: We prove a probabilistic analogue of the
classical van Benthem theorem, which states that
modal logic is precisely the bisimulation-invariant
fragment of first-order logic. Specifically, we show
that every formula in probabilistic fuzzy first-order
logic that is non-expansive wrt. behavioural distance can be approximated by concepts of bounded
rank in probabilistic fuzzy description logic