Abstract: Concentrating on the history of the researches in pretabular logics of NExtK4, gets a conclusion: From the fact found by Scroggs that S5 is pretabular, to the result independently proved by Maksimova, Esakia and Meskhi that there are precisely five pretabular extensions of S4, and to the fact that Blok establishes two famous theorems, the problem of the pretabularity criterion isn’t resolved. Though Blok’s substitution-trick and copy-trick may be the closest way to resolve the problem, his method beginning from those “non-pretabular patterns” prevents him from resolving the problem. To improve his method, a more severe reduction is required in the depth of the first frame-pattern of a “quasi-Scroggs-chain”.

Key words: five-parameters method, Blok’s substitution-trick and copy-trick, quasi-Scroggs-chain

摘要： 对NExtK4中的濒表格逻辑的发展史进行了详细研究, 从中得到结论：从Scroggs发现S5是濒表格的, 到Maksimova、Esakia和Meskhi独立证明S4正好有5个濒表格扩充, 再到Blok建立的两个著名定理, 濒表格逻辑的判据问题始终没有得到解决。尽管Blok的替换术与复制术是最接近的解决判据问题的方法, 但由于其做法是从非“濒表格模式”的框架入手, 阻碍了看清问题的实质从而不能完全解决判据问题; 为改进Blok的方法, 必须在“拟Scroggs-链”的起始框架模式的深度上作更苛刻的归约。

关键词: 5参数法, Blok的替换术与复制术, 拟Scroggs-链