Knowledge space theory [1–3] offers a rigorous and efficient formal framework for the construction, validation, and application of e-assessment and e-learning adaptive systems. This theory is the basis for some existing e-learning and e-assessment adaptive systems in the U.S. and in Europe. Such systems are based on a fixed and local domain of knowledge, where fixed means that the domain does not change in time, and local refers to the fact that the items are stored and available locally. In this paper we present some theoretical notes on the efficient construction and application of knowledge spaces for knowledge domains that are both dynamic and distributed in space. This goes in the direction of an exploitation of new technologies like the GRID for building the next generation of learning environments.
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