  Traditional conformance checking tasks assume that event data provide a
faithful and complete representation of the actual process executions. This
assumption has been recently questioned: more and more often events are not
traced explicitly, but are instead indirectly obtained as the result of event
recognition pipelines, and thus inherently come with uncertainty. In this work,
differently from the typical probabilistic interpretation of uncertainty, we
consider the relevant case where uncertainty refers to which activity is
actually conducted, under a fuzzy semantics. In this novel setting, we consider
the problem of checking whether fuzzy event data conform with declarative
temporal rules specified as Declare patterns or, more generally, as formulae of
linear temporal logic over finite traces (LTLf). This requires to relax the
assumption that at each instant only one activity is executed, and to
correspondingly redefine boolean operators of the logic with a fuzzy semantics.
Specifically, we provide a threefold contribution. First, we define a fuzzy
counterpart of LTLf tailored to our purpose. Second, we cast conformance
checking over fuzzy logs as a verification problem in this logic. Third, we
provide a proof-of-concept, efficient implementation based on the PyTorch
Python library, suited to check conformance of multiple fuzzy traces at once.
