Khudairi, Hasen (2019) Modal Ω-Logic. Matteo Vincenzo D'Alfonso and Don Berkich (eds.), \textit{On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence}. pp. 65-82.

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Abstract

This essay examines the philosophical significance of $\Omega$-logic in Zermelo-Fraenkel set theory with choice (ZFC). The categorical duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of $\Omega$-logical validity can then be countenanced within a coalgebraic logic, and $\Omega$-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of $\Omega$-logical validity correspond to those of second-order logical consequence, $\Omega$-logical validity is genuinely logical. Second, the foregoing provides a modal account of the interpretation of mathematical vocabulary.

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Item Type:	Published Article or Volume
Creators:	Creators Email ORCID Khudairi, Hasen hasen.khudairi@gmail.com 0000-0003-1726-6123
Additional Information:	In Matteo Vincenzo D'Alfonso & Don Berkich (eds.), On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence, Springer. pp. 65-82. 2019
Keywords:	Ω-Logic; Modal Logic; Logical Consequence; Large Cardinals; Coalgebra; Automata; Set-theoretic Realism
Subjects:	Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Computation/Information
Depositing User:	Hasen Khudairi
Date Deposited:	25 Nov 2022 17:02
Last Modified:	25 Nov 2022 17:02
Item ID:	21460
Journal or Publication Title:	Matteo Vincenzo D'Alfonso and Don Berkich (eds.), \textit{On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence}
Publisher:	Springer
Subjects:	Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Computation/Information
Date:	2019
Page Range:	pp. 65-82
URI:	http://philsci-archive.pitt.edu/id/eprint/21460

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• Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 09 Aug 2018 22:54)
  • Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 17 May 2021 16:43)
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          • Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 29 Jun 2021 19:34)
            • Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 09 May 2022 22:47)
            • Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 22 Jul 2021 16:35)
              • Modal Ω-Logic. (deposited 25 Nov 2022 17:02) [Currently Displayed]
              • Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 22 Nov 2022 16:03)
                • Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 20 Dec 2022 18:42)

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