Ya. I. Petrukhin, “On a modification of Visser's formal logic and its connection with Solovay's modal logic”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, Number 11,Pages <nobr>15

On a modification of Visser's formal logic and its connection with Solovay's modal logic

Ya. I. Petrukhin

Institute for Information Transmission Problems of the Russian Academy of Sciences, 19 Bolshoy Karetny Lane, build 1, Moscow, 127051 Russia

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 GL. SPL is formulated in the form of sequent and natural deduction calculi, a relational semantics is proposed.

Keywords: modal logic, sequent calculus, Visser's logic, Solovay's logic, provability logic, embedding procedure.

UDC: 510.6

Received: 14.12.2022
Revised: 24.05.2023
Accepted: 29.05.2023

DOI: 10.26907/0021-3446-2023-11-15-25