https://hal.science/hal-02977750v7Eng, BorisBorisEngLIPN - Laboratoire d'Informatique de Paris-Nord - CNRS - Centre National de la Recherche Scientifique - Université Sorbonne Paris NordA gentle introduction to Girard's Transcendental Syntax for the linear logicianHAL CCSD2022Models of ComputationLinear LogicSemanticsGeometry of InteractionRealizability semantics[INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO][MATH.MATH-LO] Mathematics [math]/Logic [math.LO]ENG, Boris2022-04-03 22:52:412023-02-02 17:00:082022-04-05 11:25:55enPreprints, Working Papers, ...https://hal.science/hal-02977750v7/documenthttps://hal.science/hal-02977750v6application/pdf7Technically 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.