Positive modal logic beyond distributivity

Nick Bezhanishvili, Anna Dmitrieva, Jim de Groot, Tommaso Moraschini

Research output: Contribution to journalArticlepeer-review


We develop a duality for (modal) lattices that need not be distributive, and use it to study positive (modal) logic beyond distributivity, which we call weak positive (modal) logic. This duality builds on the Hofmann, Mislove and Stralka duality for meet-semilattices. We introduce the notion of Π1-persistence and show that every weak positive modal logic is Π1-persistent. This approach leads to a new relational semantics for weak positive modal logic, for which we prove an analogue of Sahlqvist’s correspondence result.
Original languageEnglish
Article number103374
JournalAnnals of Pure and Applied Logic
Issue number2
Early online date26 Sep 2023
Publication statusPublished - Feb 2024


  • Duality
  • Modal logic
  • Non-distributive positive logic
  • Sahlqvist correspondence
  • Weak positive logic

Cite this