Geodesic
On a modification of Visser's formal logic and its connection with Solovay's modal logic
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2023), pp. 15-25.

Voir la notice de l'article provenant de la source Math-Net.Ru

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, Solovay's logic, provability logic, embedding procedure.
Mots-clés : Visser's logic 
@article{IVM_2023_11_a1,
     author = {Ya. I. Petrukhin},
     title = {On a modification of {Visser's} formal logic and its connection with {Solovay's} modal logic},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {15--25},
     publisher = {mathdoc},
     number = {11},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_11_a1/}
}
TY  - JOUR
AU  - Ya. I. Petrukhin
TI  - On a modification of Visser's formal logic and its connection with Solovay's modal logic
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2023
SP  - 15
EP  - 25
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2023_11_a1/
LA  - ru
ID  - IVM_2023_11_a1
ER  - 
%0 Journal Article
%A Ya. I. Petrukhin
%T On a modification of Visser's formal logic and its connection with Solovay's modal logic
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2023
%P 15-25
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2023_11_a1/
%G ru
%F IVM_2023_11_a1
Ya. I. Petrukhin. On a modification of Visser's formal logic and its connection with Solovay's modal logic. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2023), pp. 15-25. http://geodesic.mathdoc.fr/item/IVM_2023_11_a1/

[1] Visser A., “A propositional logic with explicit fixed points”, Studia Logica, 40:2 (1981), 155–175 | DOI | MR | Zbl

[2] Solovay R.M., “Provability interpretations of modal logic”, Israel J. Math., 25:3–4 (1976), 287–304 | DOI | MR | Zbl

[3] Kushida H., “A Proof Theory for the Logic of Provability in True Arithmetic”, Studia Logica, 108:4 (2020), 857–875 | DOI | MR | Zbl

[4] Gödel K., “Eine interpretation des intuitionistischen Aussagenkalküls”, Ergebnisse Math. Colloq., 4 (1933), 39–40 | Zbl

[5] Ishii K., Kashima R., Kikuchi K., “Sequent Calculi for Visser's Propositional Logics”, Notre Dame J. Formal Logic, 42:1 (2001), 1–22 | DOI | MR | Zbl

[6] Yamasaki S., Sano K., “Proof-Theoretic Embedding from Visser's Basic Propositional Logic to Modal Logic K$4$ via Non-labelled Sequent Calculi”, Philosophical Logic: Current Trends in Asia. Logic in Asia: Studia Logica Library, Springer, Singapore, 2017, 233–257 | DOI | MR

[7] McKinsey J.C.C., Tarski A., “Some theorems about the sentential calculi of Lewis and Heyting”, J. Symbol. Logic, 13:1 (1948), 1–15 | DOI | MR | Zbl

[8] Visser A., “The provability logics of recursively enumerable theories extending Peano arithmetic at arbitrary theories extending Peano arithmetic”, J. Philosoph. Logic, 13:1 (1984), 97–113 | DOI | MR | Zbl