Natural deduction (English Wikipedia)

Magnus et al. 2023, p. 142, CHAPTER 20, Proof-theoretic concepts. Magnus, P.D.; Button, Tim; Trueman, Robert; Zach, Richard (2023). forall x: An Introduction to Formal Logic (Fall 2023 ed.). Open Logic Project. Retrieved 4 May 2025.
Magnus et al. 2023, p. 82, 12.5 The double turnstile. Magnus, P.D.; Button, Tim; Trueman, Robert; Zach, Richard (2023). forall x: An Introduction to Formal Logic (Fall 2023 ed.). Open Logic Project. Retrieved 4 May 2025.

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Gentzen 1935a, Gentzen 1935b. Gentzen, Gerhard Karl Erich (1935a). "Untersuchungen über das logische Schließen. I". Mathematische Zeitschrift. 39 (2): 176–210. doi:10.1007/bf01201353. S2CID 121546341. Archived from the original on 24 December 2015. Gentzen, Gerhard Karl Erich (1935b). "Untersuchungen über das logische Schließen. II". Mathematische Zeitschrift. 39 (3): 405–431. doi:10.1007/bf01201363. S2CID 186239837. Archived from the original on 9 July 2012.
Gentzen 1935a, p. 176. Gentzen, Gerhard Karl Erich (1935a). "Untersuchungen über das logische Schließen. I". Mathematische Zeitschrift. 39 (2): 176–210. doi:10.1007/bf01201353. S2CID 121546341. Archived from the original on 24 December 2015.

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Pelletier & Hazen 2024. Pelletier, Francis Jeffry; Hazen, Allen (2024), "Natural Deduction Systems in Logic", in Zalta, Edward N.; Nodelman, Uri (eds.), The Stanford Encyclopedia of Philosophy (Spring 2024 ed.), Metaphysics Research Lab, Stanford University, retrieved 22 March 2024
Restall 2018. Restall, Greg (2018), "Substructural Logics", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Spring 2018 ed.), Metaphysics Research Lab, Stanford University, retrieved 22 March 2024
Paseau & Pregel 2023. Paseau, Alexander; Pregel, Fabian (2023), "Deductivism in the Philosophy of Mathematics", in Zalta, Edward N.; Nodelman, Uri (eds.), The Stanford Encyclopedia of Philosophy (Fall 2023 ed.), Metaphysics Research Lab, Stanford University, retrieved 22 March 2024

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Gentzen 1935a, Gentzen 1935b. Gentzen, Gerhard Karl Erich (1935a). "Untersuchungen über das logische Schließen. I". Mathematische Zeitschrift. 39 (2): 176–210. doi:10.1007/bf01201353. S2CID 121546341. Archived from the original on 24 December 2015. Gentzen, Gerhard Karl Erich (1935b). "Untersuchungen über das logische Schließen. II". Mathematische Zeitschrift. 39 (3): 405–431. doi:10.1007/bf01201363. S2CID 186239837. Archived from the original on 9 July 2012.
Gentzen 1935a, p. 176. Gentzen, Gerhard Karl Erich (1935a). "Untersuchungen über das logische Schließen. I". Mathematische Zeitschrift. 39 (2): 176–210. doi:10.1007/bf01201353. S2CID 121546341. Archived from the original on 24 December 2015.

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Martin-Löf 1996. Martin-Löf, Per (1996). "On the meanings of the logical constants and the justifications of the logical laws" (PDF). Nordic Journal of Philosophical Logic. 1 (1): 11–60. Archived from the original (PDF) on 8 December 2023. Retrieved 2 July 2010. Lecture notes to a short course at Università degli Studi di Siena, April 1983.

utm.edu (Global: 1,379^th place; English: 1,175^th place)

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Indrzejczak. Indrzejczak, Andrzej. "Natural Deduction". Internet Encyclopedia of Philosophy. Retrieved 4 May 2025.
Paseau & Leek. Paseau, A. C.; Leek, Robert. "The Compactness Theorem". Internet Encyclopedia of Philosophy. Retrieved 22 March 2024.

web.archive.org (Global: 1^st place; English: 1^st place)

Gentzen 1935a, Gentzen 1935b. Gentzen, Gerhard Karl Erich (1935a). "Untersuchungen über das logische Schließen. I". Mathematische Zeitschrift. 39 (2): 176–210. doi:10.1007/bf01201353. S2CID 121546341. Archived from the original on 24 December 2015. Gentzen, Gerhard Karl Erich (1935b). "Untersuchungen über das logische Schließen. II". Mathematische Zeitschrift. 39 (3): 405–431. doi:10.1007/bf01201363. S2CID 186239837. Archived from the original on 9 July 2012.
Gentzen 1935a, p. 176. Gentzen, Gerhard Karl Erich (1935a). "Untersuchungen über das logische Schließen. I". Mathematische Zeitschrift. 39 (2): 176–210. doi:10.1007/bf01201353. S2CID 121546341. Archived from the original on 24 December 2015.
Martin-Löf 1996. Martin-Löf, Per (1996). "On the meanings of the logical constants and the justifications of the logical laws" (PDF). Nordic Journal of Philosophical Logic. 1 (1): 11–60. Archived from the original (PDF) on 8 December 2023. Retrieved 2 July 2010. Lecture notes to a short course at Università degli Studi di Siena, April 1983.

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Weisstein. Weisstein, Eric W. "Connective". mathworld.wolfram.com. Retrieved 22 March 2024.

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Prawitz 1965, Prawitz 2006. Prawitz, Dag (1965). Natural Deduction: A Proof-Theoretic Study. Acta Universitatis Stockholmiensis; Stockholm Studies in Philosophy, 3. Stockholm, Göteborg, Uppsala: Almqvist & Wiksell. OCLC 912927896. Prawitz, Dag (2006). Natural Deduction: A Proof-Theoretic Study. Mineola, New York: Dover Publications. ISBN 9780486446554. OCLC 61296001.
Prawitz 1965. Prawitz, Dag (1965). Natural Deduction: A Proof-Theoretic Study. Acta Universitatis Stockholmiensis; Stockholm Studies in Philosophy, 3. Stockholm, Göteborg, Uppsala: Almqvist & Wiksell. OCLC 912927896.
Prawitz 1965, p. 20. Prawitz, Dag (1965). Natural Deduction: A Proof-Theoretic Study. Acta Universitatis Stockholmiensis; Stockholm Studies in Philosophy, 3. Stockholm, Göteborg, Uppsala: Almqvist & Wiksell. OCLC 912927896.
Prawitz 1965, p. 21. Prawitz, Dag (1965). Natural Deduction: A Proof-Theoretic Study. Acta Universitatis Stockholmiensis; Stockholm Studies in Philosophy, 3. Stockholm, Göteborg, Uppsala: Almqvist & Wiksell. OCLC 912927896.
Arthur 2017. Arthur, Richard T. W. (2017). An Introduction to Logic: Using Natural Deduction, Real Arguments, a Little History, and Some Humour (2nd ed.). Peterborough, Ontario: Broadview Press. ISBN 978-1-55481-332-2. OCLC 962129086.
See also his book Prawitz 1965, Prawitz 2006. Prawitz, Dag (1965). Natural Deduction: A Proof-Theoretic Study. Acta Universitatis Stockholmiensis; Stockholm Studies in Philosophy, 3. Stockholm, Göteborg, Uppsala: Almqvist & Wiksell. OCLC 912927896. Prawitz, Dag (2006). Natural Deduction: A Proof-Theoretic Study. Mineola, New York: Dover Publications. ISBN 9780486446554. OCLC 61296001.

worldcat.org

Arthur 2017. Arthur, Richard T. W. (2017). An Introduction to Logic: Using Natural Deduction, Real Arguments, a Little History, and Some Humour (2nd ed.). Peterborough, Ontario: Broadview Press. ISBN 978-1-55481-332-2. OCLC 962129086.

Natural deduction (English Wikipedia)

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