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arXiv · 1403.0710

Duality and universal models for the meet-implication fragment of IPC

Nick Bezhanishvili·Dion Coumans·Samuel J. van Gool·Dick de Jongh
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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.

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Nick Bezhanishvili, Dion Coumans, Samuel J. van Gool, Dick de Jongh. 2014-11-22. Duality and universal models for the meet-implication fragment of IPC. https://doi.org/10.1007/978-3-662-46906-4_7

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