Introduction

Most DLs without role constructors are decidable Rogers (1987), Soare (1987), and with role constructors are not. We consider two sets \(\{\circ ,*\}\) of role constructors: one is \(\circ ,*\) being taken as binary-valued constructors, which are used in binary DL, and anther is \(\circ ,*\) being taken as unary constructors, which are used in Post \(\textbf{L}_3\) -valued, \(\textbf{B}_2^2\) -valued, and Post \(\textbf{L}_4\) -valued DLs with role constructors. In the latter case, \(R^*\) is the transitive closure of role R.