  Natural language contexts display logical regularities with respect to
substitutions of related concepts: these are captured in a functional
order-theoretic property called monotonicity. For a certain class of NLI
problems where the resulting entailment label depends only on the context
monotonicity and the relation between the substituted concepts, we build on
previous techniques that aim to improve the performance of NLI models for these
problems, as consistent performance across both upward and downward monotone
contexts still seems difficult to attain even for state-of-the-art models. To
this end, we reframe the problem of context monotonicity classification to make
it compatible with transformer-based pre-trained NLI models and add this task
to the training pipeline. Furthermore, we introduce a sound and complete
simplified monotonicity logic formalism which describes our treatment of
contexts as abstract units. Using the notions in our formalism, we adapt
targeted challenge sets to investigate whether an intermediate context
monotonicity classification task can aid NLI models' performance on examples
exhibiting monotonicity reasoning.
