On Banach spaces of sequences and free linear logic exponential modality

Sergey Slavnov

doi:10.1017/s0960129517000251

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arXiv · 1509.03853

On Banach spaces of sequences and free linear logic exponential modality

Sergey Slavnov

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Abstract

We introduce a category of vector spaces modelling full propositional linear logic, similar to probabilistic coherence spaces and to Koethe sequences spaces. Its objects are {\it rigged sequences spaces}, Banach spaces of sequences, with norms defined from pairing with finite sequences, and morphisms are bounded linear maps, continuous in a suitable topology. The main interest of the work is that our model gives a realization of the free linear logic exponentials construction.

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Sergey Slavnov. 2016-11-23. On Banach spaces of sequences and free linear logic exponential modality. https://doi.org/10.1017/s0960129517000251

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