Intuitionistic logic and modality via topology

DOI10.1016/J.APAL.2003.11.013zbMath1049.03018OpenAlexW2078421228MaRDI QIDQ598307

Leo Esakia

Publication date: 6 August 2004

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apal.2003.11.013

zbMATH Keywords

Heyting algebrasClosure algebraDerivative algebraModal systemsProvability logicScattered spaceTopological semantics

Mathematics Subject Classification ID

Modal logic (including the logic of norms) (03B45) Scattered spaces (54G12) Boolean algebras with additional operations (diagonalizable algebras, etc.) (06E25) Post algebras (lattice-theoretic aspects) (06D25) Provability logics and related algebras (e.g., diagonalizable algebras) (03F45)

Related Items (22)

Alternative Semantics for Visser’s Propositional Logics ⋮ Doctrines, modalities and comonads ⋮ A topological approach to full belief ⋮ Fixed point logics and definable topological properties ⋮ Modal logic of generalized separated topological spaces ⋮ Fixed point logics and definable topological properties ⋮ Dynamic Cantor Derivative Logic ⋮ Formalising basic topology for computational logic in simple type theory ⋮ The alternation hierarchy of the \(\mu \)-calculus over weakly transitive frames ⋮ The d-logic of the rational numbers: a fruitful construction ⋮ Finite model property in weakly transitive tense logics ⋮ Foreword to the special issue dedicated to the memory of Leo Esakia ⋮ Lattice logic as a fragment of (2-sorted) residuated modal logic ⋮ THE MODAL LOGIC OF STONE SPACES: DIAMOND AS DERIVATIVE ⋮ Spatial logic of tangled closure operators and modal mu-calculus ⋮ Additive derivative and multiplicative coderivative operators on MV-algebras ⋮ The power of a propositional constant ⋮ Modal translation of substructural logics ⋮ The modalized Heyting calculus: a conservative modal extension of the Intuitionistic Logic ★ ⋮ Around provability logic ⋮ Modal Logics of Some Hereditarily Irresolvable Spaces ⋮ MONADIC INTUITIONISTIC AND MODAL LOGICS ADMITTING PROVABILITY INTERPRETATIONS

Cites Work

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• Intuitionism. An introduction
• Topological duality for diagonalizable algebras
• Provability interpretations of modal logic
• Scattered, Hausdorff-reducible, and hereditarily irresolvable spaces.
• Scattered toposes
• The algebra of topology
• On closed elements in closure algebras
• Infinitary combinatorics and modal logic
• Provability in arithmetic and a schema of Grzegorczyk
• The modal logic of inequality
• Arithmetical necessity, provability and intuitionistic logic
• Some relational systems and the associated topological spaces
• Some theorems about the sentential calculi of Lewis and Heyting
• On the syntactical construction of systems of modal logic

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