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arXiv · 2409.10418

Hyperformalism for Bunched Natural Deduction Systems

Shay Allen Logan·Blane Worley
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Abstract

Logics closed under classes of substitutions broader than class of uniform substitutions are known as hyperformal logics. This paper extends known results about hyperformal logics in two ways. First: we examine a very powerful form of hyperformalism that tracks, for bunched natural deduction systems, essentially all the intensional content that can possibly be tracked. We demonstrate that, after a few tweaks, the well-known relevant logic $\mathbf{B}$ exhibits this form of hyperformalism. Second: we demonstrate that not only can hyperformalism be extended along these lines, it can also be extended to accommodate not just what is proved in a given logic but the proofs themselves. Altogether, the paper demonstrates that the space of possibilities for the study of hyperformalism is much larger than might have been expected.

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Shay Allen Logan, Blane Worley. 2024-09-16. Hyperformalism for Bunched Natural Deduction Systems. https://doi.org/10.1007/s10992-025-09802-w

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