English

Fischer-Servi logic does not have interpolation

Logic 2026-04-10 v2

Abstract

We prove that the Fischer-Servi logic IK\mathsf{IK} 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 IT\mathsf{IT}, IK4\mathsf{IK4}, IS4\mathsf{IS4}, and IGL\mathsf{IGL}.

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

R2 v1 2026-07-01T11:51:05.182Z