The goal of this talk is twofold. One the one hand, we report on a hybrid knowledge representation and reasoning system called MANTRA. The system provides four different knowledge representation methods - first-order logic, terminological language, semantic networks, and production rules - distributed into a three levels architecture. Specifications of mathematical domains of computation and their inherently related type inference mechanisms can be transformed into knowledge bases.
On the other hand, we argue that a main requirement when designing future environments is the capability to cooperate and to integrate by communicating mathematical knowledge among/through mathematical services based upon restart-able computation and reasoning. Therefore, structures representing intermediate results in any kind of mathematical computation must also be considered.
