Notre Dame Journal of Formal Logic

Actualism, Serious Actualism, and Quantified Modal Logic

William H. Hanson

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Abstract

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.

Article information

Source
Notre Dame J. Formal Logic, Volume 59, Number 2 (2018), 233-284.

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

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1510888080

Digital Object Identifier
doi:10.1215/00294527-2017-0022

Mathematical Reviews number (MathSciNet)
MR3778310

Zentralblatt MATH identifier
06870291

Subjects
Primary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}

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

Citation

Hanson, William H. Actualism, Serious Actualism, and Quantified Modal Logic. Notre Dame J. Formal Logic 59 (2018), no. 2, 233--284. doi:10.1215/00294527-2017-0022. https://projecteuclid.org/euclid.ndjfl/1510888080


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