This paper introduces the MCML approach for empirically studying
the learnability of relational properties that can be
expressed in the well-known software design language Alloy. A
key novelty of MCML is quantification of the performance of and semantic
differences among trained machine learning (ML) models, specifically
decision trees, with respect to entire (bounded) input spaces,
and not just for given training and test
datasets (as is the common practice). MCML reduces the quantification
problems to the classic complexity theory problem of model counting, and employs state-of-the-art model
counters. The results show that relatively simple
ML models can achieve surprisingly high performance (accuracy and F1-score)
when evaluated in the common setting of using
training and test datasets – even when the training dataset is
much smaller than the test dataset – indicating the seeming
simplicity of learning relational properties. However, MCML
metrics based on model counting show that the performance can degrade
substantially when tested against the entire (bounded) input space,
indicating the high complexity of precisely learning these properties,
and the usefulness of model counting in quantifying the true performance.