Lyndon interpolation theorem of instantial neighborhood logic – constructively via a sequent calculus

Abstract

Instantial neighborhood logic (INL) is classical propositional logic enriched by a two-sorted operator □. In a neighborhood model, a formula like □(α1,...,αj;α0) (for an arbitrary natural number j) means that, the current point has a neighborhood in which α0 universally holds and none of α1,...,αj universally fails. This paper offers to INL: (1) a cut-free sequent calculus, and (2) a constructive proof of its Lyndon interpolation theorem.