Fundamentals of Finitary Proofs

Taneli Huuskonen

doi:10.2478/forma-2024-0018

.blurhash-client-img { display: none !important; }

Fundamentals of Finitary Proofs

Formalized Mathematics

Volume 32 (2024): Issue 1 (August 2024)

By: Taneli Huuskonen

Open Access

|Dec 2024

Abstract

An abstract, generic textbook notion of a finitary proof and some of its basic properties are presented, using the Mizar system. A general form of Lindenbaum’s lemma is included.

References

Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.
Open DOI Search in Google Scholar Back to article
Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.
Open DOI Search in Google Scholar Back to article
Heinz-Dieter Ebbinghaus, Jörg Flum, and Wolfgang Thomas. Mathematical Logic. Springer, 1994.
Search in Google Scholar Back to article
Joanna Golińska-Pilarek and Taneli Huuskonen. Logic of descriptions. A new approach to the foundations of mathematics and science. Studies in Logic, Grammar and Rhetoric, 40(27), 2012.
Search in Google Scholar Back to article
Joanna Golińska-Pilarek and Taneli Huuskonen. Grzegorczyk’s non-Fregean logics. In Rafał Urbaniak and Gillman Payette, editors, Applications of Formal Philosophy: The Road Less Travelled, Logic, Reasoning and Argumentation. Springer, 2015.
Search in Google Scholar Back to article
Adam Grabowski. On fuzzy negations and laws of contraposition. Lattice of fuzzy negations. Formalized Mathematics, 31(1):151–159, 2023. doi:10.2478/forma-2023-0014.
Open DOI Search in Google Scholar Back to article
Adam Grabowski and Christoph Schwarzweller. Revisions as an essential tool to maintain mathematical repositories. In M. Kauers, M. Kerber, R. Miner, and W. Windsteiger, editors, Towards Mechanized Mathematical Assistants. Lecture Notes in Computer Science, volume 4573, pages 235–249. Springer: Berlin, Heidelberg, 2007.
Search in Google Scholar Back to article
Andrzej Grzegorczyk. Filozofia logiki i formalna logika niesymplifikacyjna. Zagadnienia Naukoznawstwa, XLVII(4), 2012. In Polish.
Search in Google Scholar Back to article
Taneli Huuskonen. Grzegorczyk’s logics. Part I. Formalized Mathematics, 23(3):177–187, 2015. doi:10.1515/forma-2015-0015.
Open DOI Search in Google Scholar Back to article
Takao Inoué and Riku Hanaoka. Intuitionistic Propositional Calculus in the extended framework with modal operator. Part II. Formalized Mathematics, 30(1):1–12, 2022. doi:10.2478/forma-2022-0001.
Open DOI Search in Google Scholar Back to article
Elliott Mendelson. Introduction to Mathematical Logic. Chapman Hall/CRC, 1997. http://books.google.pl/books?id=ZO1p4QGspoYC.
Search in Google Scholar Back to article
Roman Suszko. Non-Fregean logic and theories. Analele Universitatii Bucuresti. Acta Logica, 9:105–125, 1968.
Search in Google Scholar Back to article
Roman Suszko. Semantics for the sentential calculus with identity. Studia Logica, 28: 77–81, 1971.
Search in Google Scholar Back to article
Roman Suszko. Abolition of the Fregean axiom. In R. Parikh, editor, Logic Colloquium: Symposium on Logic held at Boston, 1972–73, volume 453 of Lecture Notes in Mathematics, pages 169–239, Heidelberg, 1975. Springer.
Search in Google Scholar Back to article