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

Abstract : Technically speaking, the transcendental syntax is about designing logics with a computational foundation. It suggests a new framework for proof theory where logic (proofs, formulas, truth, ...) is no more primitive but computation is. All the logical entities and activities will be presented as formatting/structuring on a given model of computation which should be as general, simple and natural as possible. The selected ground for logic in the transcendental syntax is a model of computation I call "stellar resolution" which is basically a logic-free reformulation of Robinson's first-order clausal resolution with a dynamics related to tile systems. An initial goal of the transcendental syntax is to retrieve linear logic from this new framework. In particular, this model naturally encodes cut-elimination for proof-structures. By using an idea of interactive typing'' reminiscent of realisability theory, it is possible to design formulas/types generalising the connectives of linear logic. Thanks to interactive typing, we are able to reach a semantic-free space where correctness criteria are seen as tests (as in unit testing or model checking) certifying logical correctness, thus allowing an effective use of logical entities.
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https://hal.archives-ouvertes.fr/hal-02977750
Contributor : Boris ENG Connect in order to contact the contributor
Submitted on : Sunday, April 3, 2022 - 10:52:41 PM
Last modification on : Wednesday, April 6, 2022 - 3:32:28 AM

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• HAL Id : hal-02977750, version 7
• ARXIV : 2012.04752

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Boris Eng. A gentle introduction to Girard's Transcendental Syntax for the linear logician. 2022. ⟨hal-02977750v7⟩

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