Distributed skill functions and the meshing of knowledge structures

The scope of knowledge space theory was extended by bringing into the picture the underlying skills and capabilities that are relevant to solving the problems in a knowledge domain. A major challenge to this approach comes from the need to aggregate distributed information on (partially) overlapping domains and skill sets. The notion of a distributed skill function is introduced for formalizing the integration of several skill functions that represent the assignment of skills to problems. It is shown that their consistency is captured by the meshability of the delineated knowledge structures. This result draws upon a characterization of the meshing of finite or infinite collections of knowledge structures, which extends and generalizes previous results on the binary case. The discussion covers implications for knowledge assessment and for practical applications, such as integrating skill assignments coming from different experts or distributed resources in technology-enhanced learning.