关键词: 5参数法, Blok的替换术与复制术, 拟Scroggs-链

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