One Modal Logic to Rule Them All?
Holliday W, Litak T (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).
Authors with CRIS profile
Involved external institutions
United States (USA) (US)How to cite
APA:
Holliday, W., & Litak, T. (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 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.
BibTeX: Download