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All fields Title Creator / Publisher Keyword Year AND OR AND NOT All fields Title Creator / Publisher Keyword Year AND OR AND NOT All fields Title Creator / Publisher Keyword Year AND OR AND NOT All fields Title Creator / Publisher Keyword Year AND OR AND NOT All fields Title Creator / Publisher Keyword Year Sort by creator [A → Z]' creator [Z → A]' publishing year ↑ (asc)' publishing year ↓ (desc)' title [A → Z]' title [Z → A]' Simple Search Hits 1 – 6 of 6 1 A gentle introduction to Girard's Transcendental Syntax for the linear logician Eng, Boris In: https://hal.archives-ouvertes.fr/hal-02977750 ; 2022 (2022) BASE Show details 2 Multiplicative Linear Logic from Logic Programs and Tilings Eng, Boris; Seiller, Thomas In: https://hal.archives-ouvertes.fr/hal-02895111 ; 2021 (2021) BASE Show details 3 A gentle introduction to Girard's Transcendental Syntax for the linear logician Eng, Boris In: https://hal.archives-ouvertes.fr/hal-02977750 ; 2021 (2021) 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". 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; Semantics URL: https://hal.archives-ouvertes.fr/hal-02977750v5/document https://hal.archives-ouvertes.fr/hal-02977750 https://hal.archives-ouvertes.fr/hal-02977750v5/file/main.pdf BASE Hide details 4 Stellar Resolution: Multiplicatives - for the linear logician, through examples Eng, Boris In: https://hal.archives-ouvertes.fr/hal-02977750 ; 2021 (2021) BASE Show details 5 A gentle introduction to Girard's Transcendental Syntax for the linear logician Eng, Boris In: https://hal.archives-ouvertes.fr/hal-02977750 ; 2021 (2021) BASE Show details 6 Stellar Resolution: Multiplicatives - for the linear logician, through examples Eng, Boris In: https://hal.archives-ouvertes.fr/hal-02977750 ; 2021 (2021) BASE Show details

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