The application of Natural Language Inference (NLI) methods over large textual corpora can facilitate scientific discovery, reducing the gap between current research and the available large-scale scientific knowledge. However, contemporary NLI models are still limited in interpreting mathematical knowledge written in Natural Language, even though mathematics is an integral part of scientific argumentation for many disciplines. One of the fundamental requirements towards mathematical language understanding, is the creation of models able to meaningfully represent variables. This problem is particularly challenging since the meaning of a variable should be assigned exclusively from its defining type, i.e., the representation of a variable should come from its context. Recent research has formalised the variable typing task, a benchmark for the understanding of abstract mathematical types and variables in a sentence. In this work, we propose VarSlot, a Variable Slot-based approach, which not only delivers state-of-the-art results in the task of variable typing, but is also able to create context-based representations for variables.

This paper presents Diff-Explainer, the first hybrid framework for explainable multi-hop inference that integrates explicit constraints with neural architectures through differentiable convex optimization. Specifically, Diff- Explainer allows for the fine-tuning of neural representations within a constrained optimization framework to answer and explain multi-hop questions in natural language. To demonstrate the efficacy of the hybrid framework, we combine existing ILP-based solvers for multi-hop Question Answering (QA) with Transformer-based representations. An extensive empirical evaluation on scientific and commonsense QA tasks demonstrates that the integration of explicit constraints in a end-to-end differentiable framework can significantly improve the performance of non- differentiable ILP solvers (8.91%–13.3%). Moreover, additional analysis reveals that Diff-Explainer is able to achieve strong performance when compared to standalone Transformers and previous multi-hop approaches while still providing structured explanations in support of its predictions.

The Shared Task on Natural Language Premise Selection (NLPS) asks participants to retrieve the set of premises that are most likely to be useful for proving a given mathematical statement from a supporting knowledge base. While previous editions of the TextGraphs shared tasks series targeted multi-hop inference for explanation regeneration in the context of science questions (Thayaparan et al., 2021; Jansen and Ustalov, 2020, 2019), NLPS aims to assess the ability of state-of-the-art approaches to operate on a mixture of natural and mathematical language and model complex multi-hop reasoning dependencies between statements. To this end, this edition of the shared task makes use of a large set of approximately 21k mathematical statements extracted from the PS-ProofWiki dataset (Ferreira and Freitas, 2020a). In this summary paper, we present the results of the 1st edition of the NLPS task, providing a description of the evaluation data, and the participating systems. Additionally, we perform a detailed analysis of the results, evaluating various aspects involved in mathematical language processing and multi-hop inference. The best-performing system achieved a MAP of 15.39, improving the performance of a TF-IDF baseline by approximately 3.0 MAP.

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.

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.

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.

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.

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.