We propose a theoretical framework for specification and analysis of a class of learning problems that arise in open-ended environments that contain multiple, distributed, dynamic data and knowledge sources. We introduce a family of learning operators for precise specification of some existing solutions and to facilitate the design and analysis of new algorithms for this class of problems. We state some properties of instance and hypothesis representations, and learning operators that make exact learning possible in some settings. We also explore some relationships between models of learning using different subsets of the proposed operators under certain assumptions. 1 Learning from Distributed Dynamic Data Many practical knowledge discovery tasks (e.g., learning the behavior of complex computer systems from observations, computer-aided scientific discovery in bioinformatics) present several new challenges in machine learning. The data repositories in such applications tend to be v...