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Multiplicative Linear Logic from Logic Programs and Tilings

Abstract : We present a non-deterministic model of computation related to Robinson’s first-order resolution. This model formalises and extends ideas sketched by Girard in his Transcendental Syntax programme. After establishing formal defini- tions and basic properties, we show its Turing-completeness by exhibiting how it naturally models logic programs as well as non-deterministic tiling constructions such as those defining the abstract tile assembly model, recently used in DNA computing. In a second part, we explain how this model of computation yields, using realisability techniques, a dynamic semantics of proofs in the multiplicative fragment of linear logic (MLL), for which we obtain full-completeness results for both MLL and MLL extended with the so-called MIX rule.
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https://hal.archives-ouvertes.fr/hal-02895111
Contributor : Thomas Seiller Connect in order to contact the contributor
Submitted on : Tuesday, January 26, 2021 - 11:16:34 PM
Last modification on : Saturday, June 25, 2022 - 9:03:38 PM

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  • HAL Id : hal-02895111, version 3
  • ARXIV : 2007.16077

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Boris Eng, Thomas Seiller. Multiplicative Linear Logic from Logic Programs and Tilings. 2021. ⟨hal-02895111v3⟩

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