  Neurosymbolic AI is a growing field of research aiming to combine neural
networks learning capabilities with the reasoning abilities of symbolic
systems. This hybridization can take many shapes. In this paper, we propose a
new formalism for supervised multi-label classification with propositional
background knowledge. We introduce a new neurosymbolic technique called
semantic conditioning at inference, which only constrains the system during
inference while leaving the training unaffected. We discuss its theoritical and
practical advantages over two other popular neurosymbolic techniques: semantic
conditioning and semantic regularization. We develop a new multi-scale
methodology to evaluate how the benefits of a neurosymbolic technique evolve
with the scale of the network. We then evaluate experimentally and compare the
benefits of all three techniques across model scales on several datasets. Our
results demonstrate that semantic conditioning at inference can be used to
build more accurate neural-based systems with fewer resources while
guaranteeing the semantic consistency of outputs.
