PP-2014-02: Duality and universal models for the meet-implication fragment of IPC

PP-2014-02: Bezhanishvili, Nick and Coumans, Dion and van Gool, Sam and de Jongh, Dick (2014) Duality and universal models for the meet-implication fragment of IPC. [Report]

[img]
Preview
Text (Full Text)
PP-2014-02.text.pdf

Download (308kB) | Preview
[img] Text (Abstract)
PP-2014-02.abstract.txt

Download (910B)

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.

Item Type: Report
Report Nr: PP-2014-02
Series Name: Prepublication (PP) Series
Year: 2014
Uncontrolled Keywords: Duality; Universal models; Intuitionistic logic; Heyting algebras; Free algebras; Implicative semilattices
Subjects: Logic
Depositing User: Nick Bezhanishvili
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/490

Actions (login required)

View Item View Item