Bulletin of the Section of Logic 48 (2):137-158 (2019)
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Abstract |
In previous work by Baaz and Iemhoff, a Gentzen calculus for intuitionistic logic with existence predicate is presented that satisfies partial cut elimination and Craig's interpolation property; it is also conjectured that interpolation fails for the implication-free fragment. In this paper an equivalent calculus is introduced that satisfies full cut elimination and allows a direct proof of interpolation via Maehara's lemma. In this way, it is possible to obtain much simpler interpolants and to better understand and overcome the failure of interpolation for the implication-free fragment.
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DOI | 10.18778/0138-0680.48.2.04 |
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References found in this work BETA
Contraction-Free Sequent Calculi for Geometric Theories with an Application to Barr's Theorem.Sara Negri - 2003 - Archive for Mathematical Logic 42 (4):389-401.
Gentzen Calculi for the Existence Predicate.Matthias Baaz & Rosalie Iemhoff - 2006 - Studia Logica 82 (1):7-23.
Citations of this work BETA
A More Unified Approach to Free Logics.Edi Pavlović & Norbert Gratzl - 2021 - Journal of Philosophical Logic 50 (1):117-148.
Free Definite Description Theory – Sequent Calculi and Cut Elimination.Andrzej Indrzejczak - forthcoming - Logic and Logical Philosophy:1.
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