For most of recorded history, logic was seen as an attempt to systematize the entailment patterns observed in natural---that is to say, human---languages. Only with the rise of quantification theory and the emergence of mathematical logic at the end of the nineteenth century did the syntactic structure of natural language lose its pre-eminence. 

Recently, however, there has been a resurgence of interest in natural language reasoning, as a result of two very different developments. The first is the discovery of a rich, complexity-theoretic landscape among fragments of natural languages defined by the syntactic devices they feature: quantifying determiners, relative clauses, ditransitive verb, passive constructions, anaphora, and so on. The second is the recent rise of transformer-based language models, which can be fine-tuned to solve a range of natural language inference tasks. 

In this talk I combine both these strands of research to direct the spotlight back on logical systems based on natural, rather than, formal, languages. As I shall argue, the study of such systems opens up new avenues of logical research.