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Combining Higher-Order Logic with Set Theory Formalizations.

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Title: Combining Higher-Order Logic with Set Theory Formalizations.
Authors: Kaliszyk, Cezary1,2 (AUTHOR) cezary.kaliszyk@uibk.ac.at, Pąk, Karol3 (AUTHOR)
Source: Journal of Automated Reasoning. Jun2023, Vol. 67 Issue 2, p1-23. 23p.
Abstract: The Isabelle Higher-order Tarski–Grothendieck object logic includes in its foundations both higher-order logic and set theory, which allows importing the libraries of Isabelle/HOL and Isabelle/Mizar. The two libraries, however, define all the basic concepts independently, which means that the results in the two are disconnected. In this paper, we align significant parts of these two libraries, by defining isomorphisms between their concepts, including the real numbers and algebraic structures. The isomorphisms allow us to transport theorems between the foundations and use the results from the libraries simultaneously. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Automated Reasoning is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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PubType: Academic Journal
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  Data: Combining Higher-Order Logic with Set Theory Formalizations.
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  Data: The Isabelle Higher-order Tarski–Grothendieck object logic includes in its foundations both higher-order logic and set theory, which allows importing the libraries of Isabelle/HOL and Isabelle/Mizar. The two libraries, however, define all the basic concepts independently, which means that the results in the two are disconnected. In this paper, we align significant parts of these two libraries, by defining isomorphisms between their concepts, including the real numbers and algebraic structures. The isomorphisms allow us to transport theorems between the foundations and use the results from the libraries simultaneously. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Automated Reasoning is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10817-023-09663-5
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        Text: English
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      – TitleFull: Combining Higher-Order Logic with Set Theory Formalizations.
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              Text: Jun2023
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              Y: 2023
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