  We present a first result towards the use of entailment in- side relational
dual tableau-based decision procedures. To this end, we introduce a fragment of
RL(1) which admits a restricted form of composition, (R ; S) or (R ; 1), where
the left subterm R of (R ; S) is only allowed to be either the constant 1, or a
Boolean term neither containing the complement operator nor the constant 1,
while in the case of (R ; 1), R can only be a Boolean term involving relational
variables and the operators of intersection and of union. We prove the
decidability of the fragment by defining a dual tableau- based decision
procedure with a suitable blocking mechanism and where the rules to decompose
compositional formulae are modified so to deal with the constant 1 while
preserving termination. The fragment properly includes the logics presented in
previous work and, therefore, it allows one to express, among others, the
multi-modal logic K with union and intersection of accessibility relations, and
the description logic ALC with union and intersection of roles.
