Explicit basis for admissible rules in $K$-saturated tabular logics
Diskretnaya Matematika, Tome 34 (2022) no. 1, pp. 126-140.

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

We construct an explicit finite basis for admissible rules in $K$-saturated tabular logics that extend the logic $Grz$.
Keywords: Kripke frame (model), admissible inference rule, basis admissible rules.
@article{DM_2022_34_1_a8,
     author = {V. V. Rimatskii},
     title = {Explicit basis for admissible rules in $K$-saturated tabular logics},
     journal = {Diskretnaya Matematika},
     pages = {126--140},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2022_34_1_a8/}
}
TY  - JOUR
AU  - V. V. Rimatskii
TI  - Explicit basis for admissible rules in $K$-saturated tabular logics
JO  - Diskretnaya Matematika
PY  - 2022
SP  - 126
EP  - 140
VL  - 34
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2022_34_1_a8/
LA  - ru
ID  - DM_2022_34_1_a8
ER  - 
%0 Journal Article
%A V. V. Rimatskii
%T Explicit basis for admissible rules in $K$-saturated tabular logics
%J Diskretnaya Matematika
%D 2022
%P 126-140
%V 34
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2022_34_1_a8/
%G ru
%F DM_2022_34_1_a8
V. V. Rimatskii. Explicit basis for admissible rules in $K$-saturated tabular logics. Diskretnaya Matematika, Tome 34 (2022) no. 1, pp. 126-140. http://geodesic.mathdoc.fr/item/DM_2022_34_1_a8/

[1] Lorenzen P., Einfung in Operative Logik und Mathematik, Berlin–Göttingen–Heidelberg, 1955, 816 pp. | MR

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

[3] Rybakov V.V., “Kriterii dopustimosti pravil vyvoda v modalnoi sisteme $S4$ i intuitsionistskoi logike $H$”, Algebra i logika, 23:5 (1984), 369–384 | MR | Zbl

[4] Rybakov V.V., Admissibility of Logical Inference Rules, Studies in Logic and Found. of Math., 136, Elsevier Sci. Publ., New-York–Amsterdam, 1997, 616 pp. | MR | Zbl

[5] Rimatskii V.V., “Bazisy dopustimykh pravil vyvoda tablichnykh modalnykh logik glubiny 2”, Algebra i logika, 35:5 (1996), 612–622 | MR

[6] Rimatskii V.V., “Bazisy dopustimykh pravil $K$-nasyschennykh logik”, Algebra i logika, 47:6 (2008), 750–761 | MR | Zbl

[7] Rimatskii V.V., Lukina O. V., “Yavnyi bazis dopustimykh pravil vyvoda tablichnoi logiki”, Vestnik Krasnoyarsk. gos. un-ta, 2006, no. 1, 68–71

[8] Rimatskii V.V., “O konechnoi baziruemosti po dopustimosti modalnykh logik shiriny 2”, Algebra i logika, 38:4 (1999), 436–455 | MR

[9] Rimatskii V.V., Kiyatkin V.R., “Nezavisimyi bazis dopustimykh pravil vyvoda predtablichnykh logik i ikh rasshirenii”, Sib. elektron. matem. izv., 10 (2003), 79–89 | MR

[10] Rybakov V.V., Terziler M., Rimatskiy V.V., “Basis in semi-redused form for the admissible rules of the intuitionistic logic IPC”, Math. Logic Quarterly, 46:2 (2000), 207–218 | 3.0.CO;2-E class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[11] Iemhoff R., “On the admissible rules of intuitionistic propositional logic”, J. Symb. Logic, 66:2 (2001), 281–294 | DOI | MR | Zbl

[12] Rybakov V.V., “Construction of an explicit basis for rules admissible in modal system S4”, Math. Logic Quarterly, 47:4 (2001), 441–451 | 3.0.CO;2-J class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR

[13] Rimatskii V.V., “Yavnyi bazis dopustimykh pravil vyvoda logik konechnoi shiriny”, Zhurnal SFU, Ser. matem. i fizika, 2008, no. 1, 85–93

[14] Rybakov V.V., Terziler M., Genzer C., “An essay on unification and inference rules for modal logic”, Bull. Sect. Log., 28:3 (1999), 145–157 | MR | Zbl