Construction of system of spheres-based transitively relational partial meet multiple contractions: An impossibility result

In this paper we show that, contrary to what is the case in what concerns contractions by a single sentence, there is not a system of spheres-based construction of multiple contractions which generates each and every transitively relational partial meet multiple contraction.Before proving the general result, we consider the class of system of spheres-based multiple contractions introduced in [17] and [5] and show that this class neither subsumes nor is subsumed by the class of transitively relational partial meet multiple contractions.Furthermore, we propose two system of spheres-based constructions of multiple contractions which generate (only) transitively relational partial meet multiple contractions. Therefore we can conclude that, although it is impossible to obtain a system of spheres-based definition of all the transitively relational partial meet multiple contractions, there are classes of system of spheres-based multiple contractions which are subsumed by the class of transitively relational partial meet multiple contractions.