Topological Semantics and Bisimulations for Intuitionistic Modal Logics and Their Classical Companion Logics

2007 ◽  
pp. 162-179 ◽  
Author(s):  
J. M. Davoren
Keyword(s):  
Modal Logics ◽  
Topological Semantics ◽  
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.

scholarly journals STRONG COMPLETENESS OF MODAL LOGICS OVER 0-DIMENSIONAL METRIC SPACES

2019 ◽  
Vol 13 (3) ◽  
pp. 611-632
Author(s):  
ROBERT GOLDBLATT ◽  
IAN HODKINSON
Keyword(s):  
Metric Spaces ◽  
Deductive System ◽  
Modal Logics ◽  
Topological Semantics ◽  
Strong Completeness

AbstractWe prove strong completeness results for some modal logics with the universal modality, with respect to their topological semantics over 0-dimensional dense-in-themselves metric spaces. We also use failure of compactness to show that, for some languages and spaces, no standard modal deductive system is strongly complete.

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