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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2023, Number 11, Pages 15–25
DOI: https://doi.org/10.26907/0021-3446-2023-11-15-25 (Mi ivm9914) 		 
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
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DOI: https://doi.org/10.26907/0021-3446-2023-11-15-25
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.
Funding agency Grant number
Russian Science Foundation 21-18-00195
Received: 14.12.2022
Revised: 24.05.2023
Accepted: 29.05.2023
Document Type: Article
UDC: 510.6
Language: Russian
Citation: 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, no. 11, 15–25
Citation in format AMSBIB
\Bibitem{Pet23}
\by Ya.~I.~Petrukhin
\paper On a modification of Visser's formal logic and its connection with Solovay's modal logic
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2023
\issue 11
\pages 15--25
\mathnet{http://mi.mathnet.ru/ivm9914}
\crossref{https://doi.org/10.26907/0021-3446-2023-11-15-25}
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