Can transformers learn to comprehend logical semantics in natural language? Although many strands of work on natural language inference have focussed on transformer models’ ability to perform reasoning on text, the above question has not been answered adequately. This is primarily because the logical problems that have been studied in the context of natural language inference have their computational complexity vary with the logical and grammatical constructs within the sentences. As such, it is difficult to access whether the difference in accuracy is due to logical semantics or the difference in computational complexity. A problem that is much suited to address this issue is that of the model-checking problem, whose computational complexity remains constant (for fragments derived from first-order logic). However, the model-checking problem remains untouched in natural language inference research. Thus, we investigated the problem of model-checking with natural language to adequately answer the question of how the logical semantics of natural language affects transformers’ performance. Our results imply that the language fragment has a significant impact on the performance of transformer models. Furthermore, we hypothesise that a transformer model can at least partially understand the logical semantics in natural language but can not completely learn the rules governing the model-checking algorithm.

State-of-the-art deep-learning-based approaches to Natural Language Processing (NLP) are credited with various capabilities that involve reasoning with natural language texts. %However, reasoning in this setting is often ill-defined and shallow. In this paper we carry out a large-scale empirical study investigating the detection of formally valid inferences in controlled fragments of natural language for which the satisfiability problem becomes increasingly complex. We find that, while transformer-based language models perform surprisingly well in these scenarios, a deeper analysis reveals that they appear to overfit to superficial patterns in the data rather than acquiring the logical principles governing the reasoning in these fragments.

An emerging line of research in Explainable NLP is the creation of datasets enriched with human-annotated explanations and rationales, used to build and evaluate models with step-wise inference and explanation generation capabilities. While human-annotated explanations are used as ground-truth for the inference, there is a lack of systematic assessment of their consistency and rigour. In an attempt to provide a critical quality assessment of Explanation Gold Standards (XGSs) for NLI, we propose a systematic annotation methodology, named Explanation Entailment Verification (EEV), to quantify the logical validity of human-annotated explanations. The application of EEV on three mainstream datasets reveals the surprising conclusion that a majority of the explanations, while appearing coherent on the surface, represent logically invalid arguments, ranging from being incomplete to containing clearly identifiable logical errors. This conclusion confirms that the inferential properties of explanations are still poorly formalised and understood, and that additional work on this line of research is necessary to improve the way Explanation Gold Standards are constructed.

The relational syllogistic is an extension of the language of Classical syllogisms in which predicates are allowed to feature transitive verbs with quantified objects. It is known that the relational syllogistic does not admit a finite set of syllogism-like rules whose associated (direct) derivation relation is sound and complete. We present a modest extension of this language which does.