{'fraction_non_alphanumeric': 0.02577873254564984, 'fraction_numerical': 0.00322234156820623, 'mean_word_length': 4.914285714285715, '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}}
On the notion of negation in certain non-classical propositional logics

E.A. Nemesszeghy, ON THE NOTION OF NEGATION IN CERTAIN NON-CLASSICAL PROPOSITIONAL LOGICS. The purpose of this study is to investigate some aspects of how negation functions in certain non-classical prepositional logics. These include the intuitionistic system developed by Heyting^^^, the (2) minimal calculus proposed by Johansson , and various intermediate logics between the minimal and the classical systems. Part I contains the new results which can be grouped into two classes: extensioncriteria results and infinite chain results. In the first group criteria are given for answering the question: when do formulae added to the axioms of the minimal calculus as extra axioms extend the mini­ mal calculus to various known intermediate logics? One of the results in this group (THEOREM 1 in Chapter II, Section 1) is a generalization (3) of a result of Jankov . In the second group certain intermediate logics are defined which form infinite chains between well-known logical systems. One of the results here (THEOREM 1 in Chapter II, Section 2) is a generalization of a result of McKay^^^. In Part II the new results are discussed from the viewpoint of negation. It is rather difficult, however, to draw definite conclusions which are acceptable to all. For these depend on, and are closely bound up with, certain basic philosophical presuppositions which are neither provable, nor disprovable in a strict sense. Taking an essentially classical position, it is argued that the logics appearing in the defined infinite chains are such that they diverge only in the vicinity of negation, and the notions of negation in them are simply ordered in a sense which is specified during the discussion. In Appendix I a number of conjectures are formulated in connection with the new results.