An algebraic approach to intuitionistic modal logics in connection with intermediate predicate logics

Studia Logica ◽  
1989 ◽  
Vol 48 (2) ◽  
pp. 141-155 ◽  
Author(s):  
Nobu-Yuki Suzuki
Keyword(s):  
Algebraic Approach ◽  
Modal Logics ◽  
Intermediate Predicate Logics ◽  
Intuitionistic Modal Logics

scholarly journals Canonical formulas via locally finite reducts and generalized dualities

10.29007/hgbj ◽  
2018 ◽  
Author(s):  
Nick Bezhanishvili
Keyword(s):  
Modal Logic ◽  
Intuitionistic Logic ◽  
Algebraic Approach ◽  
Modal Logics ◽  
Substructural Logic ◽  
Locally Finite ◽  
Canonical Formulas

The method of canonical formulas is a powerful tool for investigating intuitionistic and modal logics. In this talk I will discuss an algebraic approach to this method. I will mostly concentrate on the case of intuitionistic logic. But I will also review the case of modal logic and possible generalizations to substructural logic.

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.

An application of Rieger-Nishimura formulas to the intuitionistic modal logics

Studia Logica ◽  
1985 ◽  
Vol 44 (1) ◽  
pp. 79-85 ◽  
Author(s):  
Dimiter Vakarelov
Keyword(s):  
Modal Logics ◽  
Intuitionistic Modal Logics
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