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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
Formal Language Recognition by Hard Attention Transformers: Perspectives from Circuit Complexity ...
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3
Ordering Regular Languages and Automata: Complexity ...
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4
Multiplicative Linear Logic from Logic Programs and Tilings
In: https://hal.archives-ouvertes.fr/hal-02895111 ; 2021 (2021)
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5
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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6
Stellar Resolution: Multiplicatives - for the linear logician, through examples
In: https://hal.archives-ouvertes.fr/hal-02977750 ; 2021 (2021)
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7
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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8
Stellar Resolution: Multiplicatives - for the linear logician, through examples
In: https://hal.archives-ouvertes.fr/hal-02977750 ; 2021 (2021)
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9
Parametric updates in parametric timed automata
In: EISSN: 1860-5974 ; Logical Methods in Computer Science ; https://hal.archives-ouvertes.fr/hal-03340905 ; Logical Methods in Computer Science, Logical Methods in Computer Science Association, 2021, 17 (2), pp.13:1-13:67. ⟨10.23638/LMCS-17(2:13)2021⟩ ; https://lmcs.episciences.org/7470 (2021)
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10
Symbolic Model-based Design and Generation of Logical Scenarios for Autonomous Vehicles Validation
In: 2021 IEEE Intelligent Vehicles Symposium (IV) ; https://hal.archives-ouvertes.fr/hal-03540190 ; 2021 IEEE Intelligent Vehicles Symposium (IV), Jul 2021, Nagoya, Japan. pp.215-222, ⟨10.1109/IV48863.2021.9575528⟩ (2021)
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11
"By the way, do you like Spider Man?" -Towards A Social Planning Model for Rapport
In: SemDial 2021 - 25th Workshop on the Semantics and Pragmatics of Dialogue ; https://hal.inria.fr/hal-03536332 ; SemDial 2021 - 25th Workshop on the Semantics and Pragmatics of Dialogue, Sep 2021, Potsdam / Virtual, Germany (2021)
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12
Improving Automation for Higher-Order Proof Steps
In: Lecture Notes ; FroCos 2021 - 13th International Symposium on Frontiers of Combining Systems ; https://hal.archives-ouvertes.fr/hal-03528009 ; FroCos 2021 - 13th International Symposium on Frontiers of Combining Systems, Sep 2021, Birmingham, United Kingdom. pp.139-153, ⟨10.1007/978-3-030-86205-3_8⟩ (2021)
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13
Identification et gestion des données personnelles dans les textes ; Identification et gestion des données personnelles dans les textes: modèle sémantique et applications
In: CiDE.22 : 22éme édition du Colloque International sur le Document Electronique Données Documents Connaissances : Perspectives de recherche et d’enseignement ; https://hal.archives-ouvertes.fr/hal-03506075 ; CiDE.22 : 22éme édition du Colloque International sur le Document Electronique Données Documents Connaissances : Perspectives de recherche et d’enseignement, Dec 2021, Paris, France (2021)
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14
Data Papers et dissémination des données de la recherche : quelles pratiques en SHS ?
In: Colloque DHNord2021 : Publier, partager, réutiliser les données de la recherche : les data papers et leurs enjeux ; https://hal.archives-ouvertes.fr/hal-03506077 ; Colloque DHNord2021 : Publier, partager, réutiliser les données de la recherche : les data papers et leurs enjeux, Nov 2021, virtuelle, France (2021)
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15
MIC ...
Kurthy, Miklos. - : Open Science Framework, 2021
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16
A Logical Programming Language as an Instrument for Specifying and Verifying Dynamic Memory ...
Haberland, René. - : arXiv, 2021
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17
Polynomial Graph Parsing with Non-Structural Reentrancies ...
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Advances in formal Slavic linguistics 2018 ...
Unkn Unknown. - : Freie Universität Berlin, 2021
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19
Efficiently Testing Simon’s Congruence ...
Gawrychowski, Paweł; Kosche, Maria; Koß, Tore. - : Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021
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20
The Edit Distance to k-Subsequence Universality ...
Day, Joel D.; Fleischmann, Pamela; Kosche, Maria. - : Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021
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