Duality and universal models for the meet-implication fragment of IPC
arXiv:1403.0710 · doi:10.1007/978-3-662-46906-4_7
Abstract
In this paper we investigate the fragment of intuitionistic logic which only uses conjunction (meet) and implication, using finite duality for distributive lattices and universal models. We give a description of the finitely generated universal models of this fragment and give a complete characterization of the up-sets of Kripke models of intuitionistic logic which can be defined 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.
21 pages. To appear in the proceedings of the conference TbiLLC 2013