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Modal Ω-Logic

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:
CreatorsEmailORCID
Khudairi, Hasenhasen.khudairi@gmail.com0000-0003-1726-6123
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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