On superintuitionistic logics as fragments of proof logic extensions

Studia Logica ◽  
1986 ◽  
Vol 45 (1) ◽  
pp. 77-99 ◽  
Author(s):  
A. V. Kuznetsov ◽  
A. Yu. Muravitsky
Keyword(s):  
Superintuitionistic Logics

Canonical rules

2009 ◽  
Vol 74 (4) ◽  
pp. 1171-1205 ◽  
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.

New constants in two pretabular superintuitionistic logics

2011 ◽  
Vol 50 (2) ◽  
pp. 171-186 ◽  
Author(s):  
A. D. Yashin
Keyword(s):  
Superintuitionistic Logics

scholarly journals STABLE MODAL LOGICS

2018 ◽  
Vol 11 (3) ◽  
pp. 436-469 ◽  
Author(s):  
GURAM BEZHANISHVILI ◽  
NICK BEZHANISHVILI ◽  
JULIA ILIN
Keyword(s):  
Modal Logic ◽  
General Concept ◽  
Modal Logics ◽  
Normal Modal Logic ◽  
Superintuitionistic Logics ◽  
Modal Systems

AbstractStable logics are modal logics characterized by a class of frames closed under relation preserving images. These logics admit all filtrations. Since many basic modal systems such as K4 and S4 are not stable, we introduce the more general concept of an M-stable logic, where M is an arbitrary normal modal logic that admits some filtration. Of course, M can be chosen to be K4 or S4. We give several characterizations of M-stable logics. We prove that there are continuum many S4-stable logics and continuum many K4-stable logics between K4 and S4. We axiomatize K4-stable and S4-stable logics by means of stable formulas and discuss the connection between S4-stable logics and stable superintuitionistic logics. We conclude the article with many examples (and nonexamples) of stable, K4-stable, and S4-stable logics and provide their axiomatization in terms of stable rules and formulas.

On variable separation in modal and superintuitionistic logics

Studia Logica ◽  
1995 ◽  
Vol 55 (1) ◽  
pp. 99-112 ◽  
Author(s):  
Larisa Maksimova
Keyword(s):  
Variable Separation ◽  
Superintuitionistic Logics
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