  We study systems of relations of the form $Ax\,\sigma\,b$, where $\sigma$ is
a vector of binary relations with the components "$=$", "$\geq$" and "$\leq$",
and the parameters (elements of the matrix $A$ and right-hand side vector $b$)
can take values from prescribed intervals. What is considered to be the set of
its solutions depends on which logical quantifier is associated with each
interval-valued parameter and what is the order of the quantifier prefixes for
certain parameters. For solution sets that correspond to the quantifier prefix
of a general form, we present equivalent quantifier-free descriptions in the
classical interval arithmetic, in Kaucher complete interval arithmetic and in
the usual real arithmetic.
