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2018 Actualism, Serious Actualism, and Quantified Modal Logic
William H. Hanson
Notre Dame J. Formal Logic 59(2): 233-284 (2018). DOI: 10.1215/00294527-2017-0022


This article studies seriously actualistic quantified modal logics. A key component of the language is an abstraction operator by means of which predicates can be created out of complex formulas. This facilitates proof of a uniform substitution theorem: if a sentence is logically true, then any sentence that results from substituting a (perhaps complex) predicate abstract for each occurrence of a simple predicate abstract is also logically true. This solves a problem identified by Kripke early in the modern semantic study of quantified modal logic. A tableau proof system is presented and proved sound and complete with respect to logical truth. The main focus is on seriously actualistic T (SAT), an extension of T, but the results established hold also for systems based on other propositional modal logics (e.g., K, B, S4, and S5). Following Menzel it is shown that the formal language studied also supports an actualistic account of truth simpliciter.


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William H. Hanson. "Actualism, Serious Actualism, and Quantified Modal Logic." Notre Dame J. Formal Logic 59 (2) 233 - 284, 2018.


Received: 11 November 2014; Accepted: 5 February 2015; Published: 2018
First available in Project Euclid: 17 November 2017

zbMATH: 06870291
MathSciNet: MR3778310
Digital Object Identifier: 10.1215/00294527-2017-0022

Primary: 03B45

Keywords: actualism , predicate abstraction , quantified modal logic , serious actualism , tableau proof system , uniform substitution

Rights: Copyright © 2018 University of Notre Dame


Vol.59 • No. 2 • 2018
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