  Combining logic and probability has been a long stand- ing goal of AI
research. Markov Logic Networks (MLNs) achieve this by attaching weights to
formulas in first-order logic, and can be seen as templates for constructing
features for ground Markov networks. Most techniques for learning weights of
MLNs are domain-size agnostic, i.e., the size of the domain is not explicitly
taken into account while learn- ing the parameters of the model. This often
results in ex- treme probabilities when testing on domain sizes different from
those seen during training. In this paper, we propose Domain Aware Markov logic
Networks (DA-MLNs) which present a principled solution to this problem. While
defin- ing the ground network distribution, DA-MLNs divide the ground feature
weight by a scaling factor which is a function of the number of connections the
ground atoms appearing in the feature are involved in. We show that standard
MLNs fall out as a special case of our formalism when this func- tion evaluates
to a constant equal to 1. Experiments on the benchmark Friends & Smokers domain
show that our ap- proach results in significantly higher accuracies compared to
existing methods when testing on domains whose sizes different from those seen
during training.
