Models for stronger normal intuitionistic modal logics

Studia Logica ◽  
1985 ◽  
Vol 44 (1) ◽  
pp. 39-70 ◽  
Author(s):  
Kosta Došen
Keyword(s):  
Modal Logics ◽  
Intuitionistic Modal Logics

Gentzen sequent calculi for some intuitionistic modal logics

2019 ◽  
Vol 27 (4) ◽  
pp. 596-623
Author(s):  
Zhe Lin ◽  
Minghui Ma
Keyword(s):  
Propositional Logic ◽  
Sequent Calculus ◽  
Modal Logics ◽  
Cut Elimination ◽  
Sequent Calculi ◽  
Intuitionistic Propositional Logic ◽  
Propositional Language ◽  
Intuitionistic Modal Logics ◽  
Subformula Property ◽  
Gentzen Sequent Calculus

Abstract Intuitionistic modal logics are extensions of intuitionistic propositional logic with modal axioms. We treat with two modal languages ${\mathscr{L}}_\Diamond $ and $\mathscr{L}_{\Diamond ,\Box }$ which extend the intuitionistic propositional language with $\Diamond $ and $\Diamond ,\Box $, respectively. Gentzen sequent calculi are established for several intuitionistic modal logics. In particular, we introduce a Gentzen sequent calculus for the well-known intuitionistic modal logic $\textsf{MIPC}$. These sequent calculi admit cut elimination and subformula property. They are decidable.

A Framework for Intuitionistic Modal Logics.

1988 ◽  
Vol 53 (2) ◽  
pp. 669
Author(s):  
William J. Rapaport ◽  
Gordon Plotkin ◽  
Colin Stirling
Keyword(s):  
Modal Logics ◽  
Intuitionistic Modal Logics
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