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A gentle introduction to Girard's Transcendental Syntax for the linear logician
In: https://hal.archives-ouvertes.fr/hal-02977750 ; 2022 (2022)
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.
Keyword: [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO]; [MATH.MATH-LO]Mathematics [math]/Logic [math.LO]; ACM: F.: Theory of Computation/F.1: COMPUTATION BY ABSTRACT DEVICES/F.1.1: Models of Computation; ACM: F.: Theory of Computation/F.3: LOGICS AND MEANINGS OF PROGRAMS/F.3.2: Semantics of Programming Languages; ACM: F.: Theory of Computation/F.3: LOGICS AND MEANINGS OF PROGRAMS/F.3.2: Semantics of Programming Languages/F.3.2.1: Denotational semantics; ACM: F.: Theory of Computation/F.4: MATHEMATICAL LOGIC AND FORMAL LANGUAGES/F.4.1: Mathematical Logic/F.4.1.0: Computability theory; ACM: F.: Theory of Computation/F.4: MATHEMATICAL LOGIC AND FORMAL LANGUAGES/F.4.1: Mathematical Logic/F.4.1.2: Lambda calculus and related systems; ACM: F.: Theory of Computation/F.4: MATHEMATICAL LOGIC AND FORMAL LANGUAGES/F.4.1: Mathematical Logic/F.4.1.3: Logic and constraint programming; ACM: F.: Theory of Computation/F.4: MATHEMATICAL LOGIC AND FORMAL LANGUAGES/F.4.1: Mathematical Logic/F.4.1.7: Proof theory; Geometry of Interaction; Linear Logic; Models of Computation; Realizability semantics; Semantics
URL: https://hal.archives-ouvertes.fr/hal-02977750v7/file/main.pdf
https://hal.archives-ouvertes.fr/hal-02977750
https://hal.archives-ouvertes.fr/hal-02977750v7/document
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B2 eta C1 mailetako azterketen etiketatzea eta analisia ...
Mikel Osinalde Agirre, Mikel Iruskieta. - : https://b2share.eudat.eu, 2022
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Ludwig Wittgenstein: The Nature of Religion - Irfan Ajvazi ...
Ajvazi, Irfan. - : Humanities Commons, 2022
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FAIRsharing record for: Metadata Encoding and Transmission Standard ... : METS ...
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FAIRsharing record for: Corpus Encoding Standards ... : CES / XCES ...
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FAIRsharing record for: Computer applications in terminology -- Terminological markup framework ... : ISO 16642:2017 ...
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Replication data and results for the publication "The dirty work of boundary maintenance" ...
Meier-Vieracker, Simon. - : Technische Universität Dresden, 2022
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FAIRsharing record for: Systems to manage terminology, knowledge and content -- Design, implementation and maintenance of terminology management systems ... : ISO 26162:2012 ...
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