A Knowledge Discovery (KD) process is a complex inter-disciplinary task, where different types of techniques coexist and cooperate for the purpose of extracting useful knowledge from large amounts of data. So, it is desirable having a unifying environment, built on a formal basis, where to design and perform the overall process. In this paper we propose a general framework which formalizes a KD process as an algebraic expression, that is, as a composition of operators representing elementary operations on two worlds: the data and the model worlds. Then, we describe a KD platform, named Rialto, based on such a framework. In particular, we provide the design principles of the underlying architecture, highlight the basic features, and provide a number of experimental results aimed at assessing the effectiveness of the design choices.