Constructive canonicity in non-classical logics

DOI10.1016/S0168-0072(96)00048-6zbMath0949.03019OpenAlexW2017093277MaRDI QIDQ1361246

Silvio Ghilardi, Giancarlo Meloni

Publication date: 6 December 2000

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

Full work available at URL: https://doi.org/10.1016/s0168-0072(96)00048-6

zbMATH Keywords

modal logicintermediate logiccanonicitySahlqvist theoremconstructive analogue of Stone's representation theoremdifference connectiveintuitionistic modalities

Mathematics Subject Classification ID

Modal logic (including the logic of norms) (03B45) Heyting algebras (lattice-theoretic aspects) (06D20) Intermediate logics (03B55)

Related Items (19)

Power and Limits of Structural Display Rules ⋮ The distributivity on bi-approximation semantics ⋮ Algebraic modal correspondence: Sahlqvist and beyond ⋮ Algorithmic correspondence and canonicity for distributive modal logic ⋮ Topological duality and algebraic completions ⋮ Duality and canonical extensions for stably compact spaces ⋮ On canonicity of poset expansions ⋮ Canonical extensions of posets. ⋮ CANONICITY RESULTS OF SUBSTRUCTURAL AND LATTICE-BASED LOGICS ⋮ Canonical extensions and relational completeness of some substructural logics ⋮ Bounded lattice expansions ⋮ A SAHLQVIST THEOREM FOR SUBSTRUCTURAL LOGIC ⋮ A Sahlqvist theorem for distributive modal logic ⋮ Algorithmic correspondence and canonicity for non-distributive logics ⋮ Elementary canonical formulae: extending Sahlqvist's theorem ⋮ Unnamed Item ⋮ KRIPKE COMPLETENESS OF STRICTLY POSITIVE MODAL LOGICS OVER MEET-SEMILATTICES WITH OPERATORS ⋮ COMPLETE ADDITIVITY AND MODAL INCOMPLETENESS ⋮ Canonical Extensions, Esakia Spaces, and Universal Models

Cites Work

• The McKinsey axiom is not canonical
• A new proof of Sahlqvist's theorem on modal definability and completeness
• An incomplete logic containing S4
• An incompleteness theorem in modal logic
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