License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2021.20
URN: urn:nbn:de:0030-drops-142581
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14258/
Blanqui, Frédéric ;
Dowek, Gilles ;
Grienenberger, Émilie ;
Hondet, Gabriel ;
Thiré, François
Some Axioms for Mathematics
Abstract
The λΠ-calculus modulo theory is a logical framework in which many logical systems can be expressed as theories. We present such a theory, the theory {U}, where proofs of several logical systems can be expressed. Moreover, we identify a sub-theory of {U} corresponding to each of these systems, and prove that, when a proof in {U} uses only symbols of a sub-theory, then it is a proof in that sub-theory.
BibTeX - Entry
@InProceedings{blanqui_et_al:LIPIcs.FSCD.2021.20,
author = {Blanqui, Fr\'{e}d\'{e}ric and Dowek, Gilles and Grienenberger, \'{E}milie and Hondet, Gabriel and Thir\'{e}, Fran\c{c}ois},
title = {{Some Axioms for Mathematics}},
booktitle = {6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
pages = {20:1--20:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-191-7},
ISSN = {1868-8969},
year = {2021},
volume = {195},
editor = {Kobayashi, Naoki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/14258},
URN = {urn:nbn:de:0030-drops-142581},
doi = {10.4230/LIPIcs.FSCD.2021.20},
annote = {Keywords: logical framework, axiomatic theory, dependent types, rewriting, interoperabilty}
}
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Keywords: |
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logical framework, axiomatic theory, dependent types, rewriting, interoperabilty |
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Collection: |
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6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021) |
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Issue Date: |
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2021 |
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Date of publication: |
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06.07.2021 |
