Finite approximability of forest superintuitionistic logics

Ya. M. Drugush

doi:10.1007/bf01139937

Finite approximability of forest superintuitionistic logics

Mathematical Notes ◽

10.1007/bf01139937 ◽

1984 ◽

Vol 36 (5) ◽

pp. 878-882

Author(s):

Ya. M. Drugush

Keyword(s):

Superintuitionistic Logics ◽

Finite Approximability

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ON FINITE APPROXIMABILITY OF SUPERINTUITIONISTIC LOGICS

Mathematics of the USSR-Sbornik ◽

10.1070/sm1977v031n02abeh003624 ◽

1977 ◽

Vol 31 (2) ◽

pp. 257-268 ◽

Cited By ~ 5

Author(s):

S K Sobolev

Keyword(s):

Superintuitionistic Logics ◽

Finite Approximability

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A. V. Kuznécov and V. Á. Gérčiu. O supérintuicionistskih logikah i finitnoj approksimiruémosti. Doklady Akadémii Nauk SSSR, vol. 195 (1970), pp. 1029–1032. - A. V. Kuznecov and V. A. Gerčiu. Superintuitionistic logics and finite approximability. English translation of the preceding by E. Mendelson. Soviet mathematics, vol. 11 no. 6 (for 1970, pub. 1971), pp. 1614–1619.

Journal of Symbolic Logic ◽

10.2307/2272439 ◽

1972 ◽

Vol 37 (4) ◽

pp. 757-757

Author(s):

Ann Yasuhara

Keyword(s):

English Translation ◽

Nauk Sssr ◽

Akademii Nauk Sssr ◽

Doklady Akademii Nauk Sssr ◽

Superintuitionistic Logics ◽

Finite Approximability

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Canonical rules

Journal of Symbolic Logic ◽

10.2178/jsl/1254748686 ◽

2009 ◽

Vol 74 (4) ◽

pp. 1171-1205 ◽

Cited By ~ 16

Author(s):

Emil Jeřábek

Keyword(s):

Alternative Proof ◽

Finite Model ◽

Consequence Relations ◽

Model Property ◽

Finite Model Property ◽

Admissible Rules ◽

Superintuitionistic Logics ◽

Canonical Formulas ◽

Global Consequence

AbstractWe develop canonical rules capable of axiomatizing all systems of multiple-conclusion rules over K4 or IPC, by extension of the method of canonical formulas by Zakharyaschev [37]. We use the framework to give an alternative proof of the known analysis of admissible rules in basic transitive logics, which additionally yields the following dichotomy: any canonical rule is either admissible in the logic, or it is equivalent to an assumption-free rule. Other applications of canonical rules include a generalization of the Blok–Esakia theorem and the theory of modal companions to systems of multiple-conclusion rules or (unitary structural global) consequence relations, and a characterization of splittings in the lattices of consequence relations over monomodal or superintuitionistic logics with the finite model property.

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