Description of modal logics which enjoy co-cover property
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 316-325.

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

Here we use admissible rules to determine whenever modal logic satisfies weak co-cover property. We prove that logic $\lambda$ over $S4$ satisfies such property iff the given set of rules are admissible in $\lambda$.
Keywords: modal logic, inference rule, Kripke frame and model
Mots-clés : admissible rule.
@article{SEMR_2022_19_1_a12,
     author = {V. V. Rimatskiy},
     title = {Description of modal logics which enjoy co-cover property},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {316--325},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a12/}
}
TY  - JOUR
AU  - V. V. Rimatskiy
TI  - Description of modal logics which enjoy co-cover property
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2022
SP  - 316
EP  - 325
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a12/
LA  - en
ID  - SEMR_2022_19_1_a12
ER  - 
%0 Journal Article
%A V. V. Rimatskiy
%T Description of modal logics which enjoy co-cover property
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2022
%P 316-325
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a12/
%G en
%F SEMR_2022_19_1_a12
V. V. Rimatskiy. Description of modal logics which enjoy co-cover property. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 316-325. http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a12/

[1] V.V. Rybakov, Admissibility of logical inference rules, Studies in Logic and the Foundations of Mathematics, 136, Elsevier, Amsterdam, 1997 | MR | Zbl

[2] R. Harrop, “Concerning formulas of the types $A \to B \vee C, A \to (\exists x) B(x)$ in intuitionistic formal systems”, J. Symb. Log., 25:1 (1960), 27–32 | DOI | MR | Zbl

[3] G.E. Mints, “Derivability of admissible rules”, J. Sov. Math., 6:4 (1976), 417–421 | DOI | Zbl

[4] J. Porte, “The deducibilities of S5”, J. Phylos. Logic, 10:1 (1981), 409–422 | DOI | MR | Zbl

[5] P. Lorenzen, Einfüng in die operative Logik und Mathematik, Springer-Verlag, Berlin–Göttingen–Heidelberg, 1955 | MR | Zbl

[6] H. Friedman, “One hundred and two problems in mathematical logic”, J. Symb. Log., 40:3 (1975), 113–130 | DOI | MR | Zbl

[7] V.V. Rybakov, “A criterion for admissibility of rules in the modal system S4 and intuitionistic logic”, Algebra Logic, 23:5 (1984), 369–384 | DOI | MR | Zbl

[8] R. Iemhoff, “A(nother) characterization of intuitionistic propositional logic”, Ann. Pure Appl. Logic, 113:1-3 (2002), 161–173 | DOI | MR | Zbl

[9] V.V. Rybakov, “An explicit basis for rules admissible in modal system S4”, Bull. Sect. Log., Univ. Łódź, Dep. Log., 28:3 (1999), 135–143 | MR | Zbl