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arXiv · 2308.07789

Infinitary Cut-Elimination for Non-Wellfounded Parsimonious Linear Logic

Matteo Acclavio·Gianluca Curzi·Giulio Guerrieri
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Abstract

We investigate non-wellfounded proof systems based on parsimonious logic, a weaker variant of linear logic where the exponential modality ! is interpreted as a constructor for streams over finite data. Logical consistency is maintained at a global level by adapting a standard progressing criterion. We present an infinitary version of cut-elimination based on finite approximations, and we prove that, in presence of the progressing criterion, it returns well-defined non-wellfounded proofs at its limit. Furthermore, we show that cut-elimination preserves the progressive criterion and various regularity conditions internalizing degrees of proof-theoretical uniformity. Finally, we provide a denotational semantics for our systems based on the relational model.

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Matteo Acclavio, Gianluca Curzi, Giulio Guerrieri. 2023-08-15. Infinitary Cut-Elimination for Non-Wellfounded Parsimonious Linear Logic. https://arxiv.org/abs/2308.07789

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