We ask whether contemporary LLMs are able to perform natural language inference (NLI) tasks on mathematical texts. We call this the Math NLI problem. We construct a corpus of Math NLI pairs whose premises are from extant mathematical text and whose hypotheses and gold labels were provided by people with experience in both research-level mathematics and also in the NLI field. We also investigate the quality of corpora using the same premises but whose hypotheses are provided by LLMs themselves. We not only investigate the performance but also the inter-group consistency of the diverse group of LLMs. We have both positive and negative findings. Among our positive findings: in some settings, using a majority vote of LLMs is approximately equivalent to using human-labeled data in the Math NLI area. On the negative side: LLMs still struggle with mathematical language. They occasionally fail at even basic inferences. Current models are not as prone to hypothesis-only “inference” in our data the way the previous generation had been. In addition to our findings, we also provide our corpora as data to support future work on Math NLI.

Against the backdrop of the ever-improving Natural Language Inference (NLI) models, recent efforts have focused on the suitability of the current NLI datasets and on the feasibility of the NLI task as it is currently approached. Many of the recent studies have exposed the inherent human disagreements of the inference task and have proposed a shift from categorical labels to human subjective probability assessments, capturing human uncertainty. In this work, we show how neither the current task formulation nor the proposed uncertainty gradient are entirely suitable for solving the NLI challenges. Instead, we propose an ordered sense space annotation, which distinguishes between logical and common-sense inference. One end of the space captures non-sensical inferences, while the other end represents strictly logical scenarios. In the middle of the space, we find a continuum of common-sense, namely, the subjective and graded opinion of a “person on the street.” To arrive at the proposed annotation scheme, we perform a careful investigation of the SICK corpus and we create a taxonomy of annotation issues and guidelines. We re-annotate the corpus with the proposed annotation scheme, utilizing four symbolic inference systems, and then perform a thorough evaluation of the scheme by fine-tuning and testing commonly used pre-trained language models on the re-annotated SICK within various settings. We also pioneer a crowd annotation of a small portion of the MultiNLI corpus, showcasing that it is possible to adapt our scheme for annotation by non-experts on another NLI corpus. Our work shows the efficiency and benefits of the proposed mechanism and opens the way for a careful NLI task refinement.

Deep learning (DL) based language models achieve high performance on various benchmarks for Natural Language Inference (NLI). And at this time, symbolic approaches to NLI are receiving less attention. Both approaches (symbolic and DL) have their advantages and weaknesses. However, currently, no method combines them in a system to solve the task of NLI. To merge symbolic and deep learning methods, we propose an inference framework called NeuralLog, which utilizes both a monotonicity-based logical inference engine and a neural network language model for phrase alignment. Our framework models the NLI task as a classic search problem and uses the beam search algorithm to search for optimal inference paths. Experiments show that our joint logic and neural inference system improves accuracy on the NLI task and can achieve state-of-art accuracy on the SICK and MED datasets.

Despite the tremendous recent progress on natural language inference (NLI), driven largely by large-scale investment in new datasets (e.g.,SNLI, MNLI) and advances in modeling, most progress has been limited to English due to a lack of reliable datasets for most of the world’s languages. In this paper, we present the first large-scale NLI dataset (consisting of ~56,000 annotated sentence pairs) for Chinese called the Original Chinese Natural Language Inference dataset (OCNLI). Unlike recent attempts at extending NLI to other languages, our dataset does not rely on any automatic translation or non-expert annotation. Instead, we elicit annotations from native speakers specializing in linguistics. We follow closely the annotation protocol used for MNLI, but create new strategies for eliciting diverse hypotheses. We establish several baseline results on our dataset using state-of-the-art pre-trained models for Chinese, and find even the best performing models to be far outpaced by human performance (~12% absolute performance gap), making it a challenging new resource that we hope will help to accelerate progress in Chinese NLU. To the best of our knowledge, this is the first human-elicited MNLI-style corpus for a non-English language.

This paper serves two purposes. It is a summary of much work concerning formal treatments of monotonicity and polarity in natural language, and it also discusses connections to related work on exclusion relations, and connections to psycholinguistics and computational linguistics. The second part of the paper presents a summary of some new work on a formal Monotonicity Calculus.