Duality and universal models for the meet-implication fragment of IPC
Nick Bezhanishvili, Dion Coumans, Sam van Gool, Dick de Jongh

Abstract:
In this paper we investigate the fragment of intuitionistic
logic which only uses conjunction (meet) and implication, using nite
duality for distributive lattices and universal models. We give a description
of the nitely generated universal models of this fragment and give a
complete characterization of the up-sets of Kripke models of intuitionistic
logic which can be dened by meet-implication-formulas. We use these
results to derive a new version of subframe formulas for intuitionistic logic
and to show that the uniform interpolants of meet-implication-formulas
are not necessarily uniform interpolants in the full intuitionistic logic.