Full Cut Elimination and Interpolation for Intuitionistic Logic with Existence Predicate

Bulletin of the Section of Logic 48 (2):137-158 (2019)

Authors
Paolo Maffezioli
University of Barcelona
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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Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.

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