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]

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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

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