{'fraction_non_alphanumeric': 0.014285714285714285, 'fraction_numerical': 0.0, 'mean_word_length': 5.315315315315315, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Interpolation for Intermediate Logics via Hyper- and Linear Nested Sequents

The goal of this paper is extending to intermediate logics the constructive prooftheoretic method of proving Craig and Lyndon interpolation via hypersequents and nested sequents developed earlier for classical modal logics. While both Jankov and Gödel logics possess hypersequent systems, we show that our method can only be applied to the former. To tackle the latter, we switch to linear nested sequents, demonstrate syntactic cut elimination for them, and use it to prove interpolation for Gödel logic. Thereby, we answer in the positive the open question of whether Gödel logic enjoys the Lyndon interpolation property.