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arXiv · 2605.17161

Modular constructive Lyndon interpolation for nondistributive logics

Andrea De Domenico·Giuseppe Greco·Alessandra Palmigiano·Apostolos Tzimoulis
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Abstract

We establish the Lyndon interpolation property for basic lattice expansion logics (LE-logics) in arbitrary signatures using display calculi. Our approach is constructive, yielding interpolants algorithmically from derivations, and modular, in the sense that interpolation for axiomatic extensions can be obtained by verifying a local interpolation property for the analytic structural rules corresponding to the additional axioms. To this end, we identify a class of interpolation-safe structural rules preserving local Lyndon interpolation. As applications of the general framework, we show that the tense version of Holliday's fundamental modal logic enjoys the Lyndon interpolation property.

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Andrea De Domenico, Giuseppe Greco, Alessandra Palmigiano, Apostolos Tzimoulis. 2026-05-16. Modular constructive Lyndon interpolation for nondistributive logics. https://arxiv.org/abs/2605.17161

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