Fischer-Servi logic does not have interpolation
Logic
2026-04-10 v2
Abstract
We prove that the Fischer-Servi logic does not have the (Craig) interpolation property. This is obtained by showing that the corresponding class of modal Heyting algebras lacks the amalgamation property. We also generalize this result to some extensions of the Fischer-Servi logic such as , , , and .
Cite
@article{arxiv.2604.02082,
title = {Fischer-Servi logic does not have interpolation},
author = {Rodrigo Nicolau Almeida and Nick Bezhanishvili and Simon Lemal},
journal= {arXiv preprint arXiv:2604.02082},
year = {2026}
}
Comments
14 pages