文章基本信息

标题：Revisiting the proof theory of Classical S4
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作者：Bruno Lopes ; Cecília Englander ; Fernanda Lobo 等
期刊名称：O Que Nos Faz Pensar
印刷版ISSN：0104-6675
出版年度：2016
卷号：25
期号：39
页码：71-86
出版社：Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio)
摘要：In 1965 Dag Prawitz presented an extension of Gentzen-type systems of Natural Deduction to modal concepts of S4. Maria da Paz Medeiros showed in 2006 that the proof of normalisation for classical S4 does not hold and proposed a new proof of normalisation for a logically equivalent system, the system NS4. However two problems in the proof of the critical lemma used by Medeiros in her proof were pointed out by Yuuki Andou in 2009. This paper presents a proof of the critical lemma, resulting in a proof of normalisation for NS4.
关键词：modal logic; proof theory; normalisation.