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Studia Logica

, Volume 107, Issue 2, pp 247–282 | Cite as

Intermediate Logics Admitting a Structural Hypersequent Calculus

  • Frederik M. LauridsenEmail author
Open Access
Article

Abstract

We characterise the intermediate logics which admit a cut-free hypersequent calculus of the form \(\mathbf {HLJ} + \mathscr {R}\), where \(\mathbf {HLJ}\) is the hypersequent counterpart of the sequent calculus \(\mathbf {LJ}\) for propositional intuitionistic logic, and \(\mathscr {R}\) is a set of so-called structural hypersequent rules, i.e., rules not involving any logical connectives. The characterisation of this class of intermediate logics is presented both in terms of the algebraic and the relational semantics for intermediate logics. We discuss various—positive as well as negative—consequences of this characterisation.

Keywords

Intermediate logics Hypersequent calculi Algebraic proof theory Heyting algebras 

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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands

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