A Modification of Visser’s Formal Logic and Its Connection with Solovay’s Modal Logic

Abstract

We present a new logic called SPL, embedded into Solovay’s provability logic S, using a translation that embeds Visser’s formal logic FPL into Gödel–Löb’s provability logic GL. SPL is formulated as sequent and natural deduction calculi, and a the Kripke semantics is proposed for SPL.