Since cognition could be treated as problem-solving issues based on dynamical knowledge transferring and propagation, the meta-learning and group learning are put forward in conformance with meta-cognition and group cognition through New Product Development (NPD) analysis. To meet the globally distributed tendency of problem solving with cognitive intention based on Internet technology, a P2P-based Problem Solving Environment (PSE) is explored to facilitate Web-based knowledge transferring and propagation. By taking advantage of P2P-based PSE, an infrastructure of knowledge grid oriented toward cooperative cognition is structured to support E-Science.