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. 

References

Tharindu Madusanka, Ian Pratt-Hartmann and Riza Batista-Navarro: Natural Language Satisfiability: Exploring the Problem Distribution and Evaluating Transformer-based Language Models, Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), 2024. pp. 15278--15294.

Ian Pratt-Hartmann and Lawrence S. Moss, Logics for the Relational Syllogistic, Review of Symbolic Logic, 2(4), 2009, pp. 647--683 .

Ian Pratt-Hartmann and Allan Third "More Fragments of Language: the Case of Ditransitive Verbs'', Notre Dame Journal of Formal Logic, 47(2), 2006, pp.151--177.

Viktor Schlegel, Kamen Pavlov and Ian Pratt-Hartmann: "Can Transformers Reason in Fragments of Natural Language?", Proceedsings of the 2022 Conference on Empirical Methods in Natural Language Processing (EMNLP), 2022, pp. 11184--11199.

Ian Pratt-Hartmann "On the Computational Complexity of the Numerically Definite Syllogistic and Related Logics'', Bulletin of Symbolic Logic, 14(1), 2008, pp. 1--28.