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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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2
Learning and controlling the source-filter representation of speech with a variational autoencoder
In: https://hal.archives-ouvertes.fr/hal-03650569 ; 2022 (2022)
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3
A Collection of Classroom Instruction ... : A Collection of Classroom Instruction ...
Thobias Sarbunan. - : Science Data Bank, 2022
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4
Money Change_experiment -10000-FULL.rar ...
Tzouvelekas, Emmanuel. - : figshare, 2022
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Money Change_experiment -10000-FULL.rar ...
Tzouvelekas, Emmanuel. - : figshare, 2022
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6
On the Transferability of Pre-trained Language Models for Low-Resource Programming Languages ...
Chen, Fuxiang. - : Federated Research Data Repository / dépôt fédéré de données de recherche, 2022
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7
МОДЕЛИ ПРОСТОГО ПРЕДЛОЖЕНИЯ И ИХ СИНОНИМИЯ В ТУВИНСКОМ ЯЗЫКЕ ... : MODELS OF A SIMPLE SENTENCE AND THEIR SYNONYMY IN THE TUVAN LANGUAGE ...
Н.Ч. Серээдар. - : Мир науки, культуры, образования, 2022
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8
LEXICAL AND SEMANTIC CHARACTERISTICS OF HYPONOMIC RELATIONS AND DEEPLY ANALYZING ITS FEATURES IN ENGLISH LINGUISTUCS ...
Jumaeva, Nasiba Komil Qizi. - : Academic research in educational sciences, 2022
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9
Constrained control of gene-flow models
In: https://hal.archives-ouvertes.fr/hal-02373668 ; 2021 (2021)
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10
Linguistic Resources Linguistic Resources for the automatic for the automatic annotation of speech annotation of speech (version 6)
In: https://hal.archives-ouvertes.fr/hal-03468442 ; 2021 (2021)
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11
Multiplicative Linear Logic from Logic Programs and Tilings
In: https://hal.archives-ouvertes.fr/hal-02895111 ; 2021 (2021)
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12
A gentle introduction to Girard's Transcendental Syntax for the linear logician
In: https://hal.archives-ouvertes.fr/hal-02977750 ; 2021 (2021)
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13
Stellar Resolution: Multiplicatives - for the linear logician, through examples
In: https://hal.archives-ouvertes.fr/hal-02977750 ; 2021 (2021)
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14
A gentle introduction to Girard's Transcendental Syntax for the linear logician
In: https://hal.archives-ouvertes.fr/hal-02977750 ; 2021 (2021)
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15
Stellar Resolution: Multiplicatives - for the linear logician, through examples
In: https://hal.archives-ouvertes.fr/hal-02977750 ; 2021 (2021)
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16
A mathematical model of the vowel space
In: https://hal.archives-ouvertes.fr/hal-03384303 ; 2021 (2021)
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17
A mathematical model of the vowel space
In: https://hal.archives-ouvertes.fr/hal-03384303 ; 2021 (2021)
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18
Training RNN Language Models on Uncertain ASR Hypotheses in Limited Data Scenarios
In: https://hal.inria.fr/hal-03327306 ; 2021 (2021)
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19
Beyond Facts - a Survey and Conceptualisation of Claims in Online Discourse Analysis
In: https://hal.mines-ales.fr/hal-03185097 ; 2021 (2021)
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20
НЕЙРОДИДАКТИЧЕСКИЙ ПОДХОД В МЕТОДОЛОГИИ ПЕДАГОГИКИ ... : NEURODIDACTIC APPROACH IN THE METHODOLOGY OF PEDAGOGY ...
Е.А. Местоева; М.Х. Мальсагова. - : Мир науки, культуры, образования, 2021
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