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arXiv · 2004.07275

The Modal Logics of Kripke-Feferman Truth

Carlo Nicolai·Johannes Stern
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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 $\mathcal{M}$, or an axiomatization $S$ thereof, we find a modal logic $M$ such that a modal sentence $φ$ is a theorem of $M$ if and only if the sentence $φ^*$ obtained by translating the modal operator with the truth predicate is true in $\mathcal{M}$ 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 subclassical with respect to this semantics.

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Carlo Nicolai, Johannes Stern. 2020-05-06. The Modal Logics of Kripke-Feferman Truth. https://doi.org/10.1017/jsl.2020.66

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