{'fraction_non_alphanumeric': 0.041666666666666664, 'fraction_numerical': 0.01425438596491228, 'mean_word_length': 4.601226993865031, '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}}
Classical Negation and Game-Theoretical Semantics

Typical applications of Hintikka’s game-theoretical semantics (GTS) give rise to semantic attributes—truth, falsity—expressible in the † 11 -fragment of second-order logic. Actually a much more general notion of semantic attribute is motivated by strategic considerations. When identifying such a generalization, the notion of classical negation plays a crucial role. We study two languages, L 1 and L 2 , in both of which two negation signs are available: + and (cid:24) . The latter is the usual GTS negation which transposes the players’ roles, while the former will be interpreted via the notion of mode . Logic L 1 extends independence-friendly (IF) logic; + behaves as classical negation in L 1 . Logic L 2 extends L 1 , and it is shown to capture the † 21 -fragment of third-order logic. Consequently the classical negation remains inexpressible in L 2 .