Actualism, Serious Actualism, and Quantified Modal Logic

Notre Dame Journal of Formal Logic 59 (2):233-284 (2018)
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 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, an extension of T, but the results established hold also for systems based on other propositional modal logics. Following Menzel it is shown that the formal language studied also supports an actualistic account of truth simpliciter.
Keywords actualism   predicate abstraction   serious actualism   tableau proof system   uniform substitution  quantified modal logic
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DOI 10.1215/00294527-2017-0022
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