One Modal Logic to Rule Them All?
Holliday W, Litak TM (2018)
Publication Language: English
Publication Type: Conference contribution, Conference Contribution
Publication year: 2018
Publisher: College Publications
City/Town: London, UK
Pages Range: 367-386
Conference Proceedings Title: Advances in Modal Logic 2018
Event location: Bern
ISBN: 978-1-84890-255-8
Open Access Link: https://escholarship.org/uc/item/07v9360j
Abstract
In this paper, we introduce an extension of the modal language with what we call the global quantificational modality [∀p]. In essence, this modality combines the propositional quantifier ∀p with the global modality A: [∀p] plays the same role as the compound modality ∀pA. Unlike the propositional quantifier by itself, the global quantificational modality can be straightforwardly interpreted in any Boolean Algebra Expansion (BAE). We present a logic GQM for this language and prove that it is complete with respect to the intended algebraic semantics. This logic enables a conceptual shift, as what have traditionally been called different “modal logics” now become [∀p]-universal theories over the base logic GQM: instead of defining a new logic with an axiom schema such as Pφ → PPφ, one reasons in GQM about what follows from the globally quantified formula [∀p](Pp → PPp).
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APA:
Holliday, W., & Litak, T.M. (2018). One Modal Logic to Rule Them All? In Guram Bezhanishvili, Giovanna D'Agostino, George Metcalfe, Thomas Studer (Eds.), Advances in Modal Logic 2018 (pp. 367-386). Bern, CH: London, UK: College Publications.
MLA:
Holliday, Wesley, and Tadeusz Michal Litak. "One Modal Logic to Rule Them All?" Proceedings of the Advances in Modal Logic 2018, Bern Ed. Guram Bezhanishvili, Giovanna D'Agostino, George Metcalfe, Thomas Studer, London, UK: College Publications, 2018. 367-386.
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