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A gentle introduction to Girard's Transcendental Syntax for the linear logician

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Boris Eng

Abstract

Girard's Transcendental Syntax suggests a new framework for proof theory where logic (proofs, formulas, truth, ...) is no more primitive but computation is. Logic is grounded on a model of computation I call "stellar resolution" which is basically logic-free Robinson's first-order clausal resolution with a dynamics related to tiling models. This model naturally encodes the cut-elimination for proof-structures. By using realisability techniques for linear logic, it is possible to reconstruct formulas/types and logical correctness in order to obtain models of linear logic. Girard's philosophical justification of these works comes from Kantian inspirations: the Transcendental Syntax appears as a way to talk about the "conditions of possibility of logic", that is the conditions from which logical constructions emerge out of the meaningless (computation). We illustrate this foundational project with a reconstruction of Intuitionistic MELL(+MIX) and describe few other novelties such as the treatment of second order and Girard's logical constants "fu" and "wo".
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Dates and versions

hal-02977750 , version 1 (25-10-2020)
hal-02977750 , version 2 (04-12-2020)
hal-02977750 , version 3 (25-01-2021)
hal-02977750 , version 4 (23-03-2021)
hal-02977750 , version 5 (04-05-2021)
hal-02977750 , version 6 (29-11-2021)
hal-02977750 , version 7 (03-04-2022)

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Boris Eng. A gentle introduction to Girard's Transcendental Syntax for the linear logician. 2021. ⟨hal-02977750v5⟩
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