Superamalgamation for modal lattices via non-distributive dualities

Rodrigo Nicolau Almeida; Nick Bezhanishvili; Simon Lemal

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arXiv · 2602.20380

Superamalgamation for modal lattices via non-distributive dualities

Rodrigo Nicolau Almeida·Nick Bezhanishvili·Simon Lemal

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Abstract

We show that the variety of modal lattices has the superamalgamation property. As a consequence, we obtain that the weak positive modal logic has the Craig interpolation property. Our proof employs the recent duality for modal lattices based on modal L-spaces. Moreover, we extend this result to a number of other weak positive modal logics axiomatized by modal axioms corresponding to universal Horn sentences.

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Rodrigo Nicolau Almeida, Nick Bezhanishvili, Simon Lemal. 2026-02-23. Superamalgamation for modal lattices via non-distributive dualities. https://arxiv.org/abs/2602.20380

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