  Lifted probabilistic inference exploits symmetries in a probabilistic model
to allow for tractable probabilistic inference with respect to domain sizes. To
apply lifted inference, a lifted representation has to be obtained, and to do
so, the so-called colour passing algorithm is the state of the art. The colour
passing algorithm, however, is bound to a specific inference algorithm and we
found that it ignores commutativity of factors while constructing a lifted
representation. We contribute a modified version of the colour passing
algorithm that uses logical variables to construct a lifted representation
independent of a specific inference algorithm while at the same time exploiting
commutativity of factors during an offline-step. Our proposed algorithm
efficiently detects more symmetries than the state of the art and thereby
drastically increases compression, yielding significantly faster online query
times for probabilistic inference when the resulting model is applied.
