Geodesic
Table admissible inference rules
Algebra i logika, Tome 48 (2009) no. 3, pp. 400-414.

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A recursive basis of inference rules is described which are instantaneously admissible in all table (residually finite) logics extending one of the logics $\mathrm{Int}$ and $Grz$. A rather simple semantic criterion is derived to determine whether a given inference rule is admissible in all table superintuitionistic logics, and the relationship is established between admissibility of a rule in all table (residually finite) superintuitionistic logics and its truth values in $\mathrm{Int}$.
Keywords: inference rules, table logic, superintuitionistic logic. 
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V. V. Rimatskii. Table admissible inference rules. Algebra i logika, Tome 48 (2009) no. 3, pp. 400-414. http://geodesic.mathdoc.fr/item/AL_2009_48_3_a4/

[1] V. V. Rybakov, Admissibility of logical inference rules, Stud. Log. Found. Math., 136, Elsevier Sci. Publ. B. V., Amsterdam, 1997 | MR | Zbl

[2] V. V. Rybakov, “Bazisy dopustimykh pravil logik $S4$ i $Int$”, Algebra i logika, 24:1 (1985), 87–107 | MR | Zbl

[3] V. V. Rybakov, “Bazisy dopustimykh pravil modalnoi sistemy Grz i intuitsionistskoi logiki”, Matem. sb., 128(170):3(11) (1985), 321–338 | MR | Zbl

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

[5] V. V. Rimatskiy, “Finite bases of admissible inference rules for modal logics of width 2”, Bull. Sect. Log. Univ. Łódź Dep. Log., 26:3 (1997), 126–134 | MR | Zbl

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

[7] A. Chagrov, M. Zakharyaschev, Modal logics, Oxford Logic Guides, 35, Clarendon Press, Oxford, 1997 | MR | Zbl