  Conformance checking is a key process mining task for comparing the expected
behavior captured in a process model and the actual behavior recorded in a log.
While this problem has been extensively studied for pure control-flow
processes, conformance checking with multi-perspective processes is still at
its infancy. In this paper, we attack this challenging problem by considering
processes that combine the data and control-flow dimensions. In particular, we
adopt data Petri nets (DPNs) as the underlying reference formalism, and show
how solid, well-established automated reasoning techniques can be effectively
employed for computing conformance metrics and data-aware alignments. We do so
by introducing the CoCoMoT (Computing Conformance Modulo Theories) framework,
with a fourfold contribution. First, we show how SAT-based encodings studied in
the pure control-flow setting can be lifted to our data-aware case, using SMT
as the underlying formal and algorithmic framework. Second, we introduce a
novel preprocessing technique based on a notion of property-preserving
clustering, to speed up the computation of conformance checking outputs. Third,
we provide a proof-of-concept implementation that uses a state-of-the-art SMT
solver and report on preliminary experiments. Finally, we discuss how CoCoMoT
directly lends itself to a number of further tasks, like multi- and
anti-alignments, log analysis by clustering, and model repair.
