An Extension of Connexive Logic C

Hitoshi Omori, Heinrich Wansing

研究成果: 書籍の章/レポート/Proceedings会議への寄与査読

30 被引用数 (Scopus)

抄録

In [38], one of the present authors introduced a system of connexive logic, called C, as a simple variant of Nelson's Logic N4, obtained by making a small change in the falsification clause for the conditional. This was an important step marked in the field of connexive logic since C can be seen as the first system of connexive logic with an intuitively plausible semantics. The aim of this article is to consider an extension of C obtained by adding the law of excluded middle with respect to the strong negation. The extension of C is motivated by three questions. The first question comes from a system CN devised by John Cantwell. The second question concerns how many more connexive theses, beside the basic theses of Aristotle and Boethius, can be captured within the framework suggested in the above paper. The third question addresses the relation between constructivity and the law of excluded middle. We will show that the quantified version of our extension of C satisfies the Existence Property and its dual, but fails to satisfy the Disjunction Property and its dual when the law of excluded middle is restricted to atomic formulas. We will also mention some open problems related to the new system introduced in this article.

本文言語英語
ホスト出版物のタイトルAdvances in Modal Logic, AiML 2020
編集者Nicola Olivetti, Rineke Verbrugge, Sara Negri, Sara Negri, Gabriel Sandu
出版社College Publications
ページ503-522
ページ数20
ISBN(印刷版)1904987206
出版ステータス出版済み - 2020
イベント13th Conference on Advances in Modal Logic, AiML 2020 - Virtual, Helsinki, フィンランド
継続期間: 2020 8月 242020 8月 28

出版物シリーズ

名前Advances in Modal Logic
13

会議

会議13th Conference on Advances in Modal Logic, AiML 2020
国/地域フィンランド
CityVirtual, Helsinki
Period20/8/2420/8/28

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