Closing the Gap between Neural Networks for Approximate and Rigorous Logical Reasoning

Tiansi Dong, Duo Wang, Mateja Jamnik, Pietro Lio

Keywords: neural reasoning, syllogistic reasoning, Euler diagram, composition tables, rigorous reasoning

TL;DR: this paper analyses features of neural networks for rigorous reasoning should and should not have.

Abstract:

Despite the historical successes of neural networks, the rigour of logical reasoning is still beyond their reach. Taking syllogistic reasoning as a subset of logical reasoning, we show supervised neural networks cannot reach the rigour of syllogistic reasoning, mainly because they use composition tables, which are coarse to distinguish each valid type of syllogistic reasoning and because end-to-end supervised learning may change the premises. As Transformer's Key-Query-Value structure is a combination table, we conclude that neural networks built upon Transformers cannot reach the rigour of syllogistic reasoning and, thus, cannot reach the rigour of logical reasoning. We logically prove that oversmoothing, in the setting of part-whole relations, can be avoided, if neural networks use region embeddings, and propose the method of reasoning through explicit constructing and inspecting region configurations, to achieve the rigour of logical reasoning.

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

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Submission Number: 1442