The Modal Logics of Kripke-Feferman Truth


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 *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 *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.

To appear in the Journal of Symbolic Logic.