The Modal Logics of Kripke-Feferman Truth

Johannes Stern*, Carlo Nicolai

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

We determine the modal logic of fixed-point models of truth and their axiomatizations by Solomon Feferman via Solovay-style completeness results. Given a fixed-point model $\mc{M}$, or an axiomatization $S$ thereof, we find a modal logic $M$ such that a modal sentence $\vphi$ is a theorem of $M$ if and only if the sentence $\vphi^*$ obtained by translating the modal operator with the truth predicate is true in $\mc{M}$ or a theorem of $S$ under all such translations. To this end, we introduce a novel version of possible worlds semantics featuring both classical and nonclassical worlds and establish the completeness of a family of non-congruent modal logics whose internal logic is nonclassical with respect to this semantics.
Original languageEnglish
JournalJournal of Symbolic Logic
DOIs
Publication statusPublished - 27 Oct 2020

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