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.

Mathematical statements written in natural language are usually composed of two different modalities: mathematical elements and natural language. These two modalities have several distinct linguistic and semantic properties. State-of-the-art representation techniques have demonstrated an inability in capturing such an entangled style of discourse. In this work, we propose STAR, a model that uses cross-modal attention to learn how to represent mathematical text for the task of Natural Language Premise Selection. This task uses conjectures written in both natural and mathematical language to recommend premises that most likely will be relevant to prove a particular statement. We found that STAR not only outperforms baselines that do not distinguish between natural language and mathematical elements, but it also achieves better performance than state-of-the-art models.

Probing (or diagnostic classification) has become a popular strategy for investigating whether a given set of intermediate features is present in the representations of neural models. Naive probing studies may have misleading results, but various recent works have suggested more reliable methodologies that compensate for the possible pitfalls of probing. However, these best practices are numerous and fast-evolving. To simplify the process of running a set of probing experiments in line with suggested methodologies, we introduce Probe-Ably: an extendable probing framework which supports and automates the application of probing methods to the user’s inputs.

Mathematical text is written using a combination of words and mathematical expressions. This combination, along with a specific way of structuring sentences makes it challenging for state-of-art NLP tools to understand and reason on top of mathematical discourse. In this work, we propose a new NLP task, the natural premise selection, which is used to retrieve supporting definitions and supporting propositions that are useful for generating an informal mathematical proof for a particular statement. We also make available a dataset, NL-PS, which can be used to evaluate different approaches for the natural premise selection task. Using different baselines, we demonstrate the underlying interpretation challenges associated with the task.

The discovery of supporting evidence for addressing complex mathematical problems is a semantically challenging task, which is still unexplored in the field of natural language processing for mathematical text. The natural language premise selection task consists in using conjectures written in both natural language and mathematical formulae to recommend premises that most likely will be useful to prove a particular statement. We propose an approach to solve this task as a link prediction problem, using Deep Convolutional Graph Neural Networks. This paper also analyses how different baselines perform in this task and shows that a graph structure can provide higher F1-score, especially when considering multi-hop premise selection.