On 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 G¨odel-L¨ob’s provability GL. SPL is formulated in the form of sequent and natural deduction calculi, a relational semantics is proposed.