The Modal Logics of Kripke-Feferman Truth

TY - JOUR

T1 - The Modal Logics of Kripke-Feferman Truth

AU - Nicolai, Carlo

AU - Stern, Johannes

PY - 2020/10/27

Y1 - 2020/10/27

N2 - 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 nonclassical with respect to this semantics.

AB - 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 nonclassical with respect to this semantics.

U2 - 10.1017/jsl.2020.66

DO - 10.1017/jsl.2020.66

M3 - Article

SN - 0022-4812

VL - 85

SP - 1

EP - 31

JO - JOURNAL OF SYMBOLIC LOGIC

JF - JOURNAL OF SYMBOLIC LOGIC

IS - 3

ER -