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Problem cognition is often the first step to problem solving. Complex problem solving is often promoted by cooperative cognition. Our research work presented in this paper is initialed by a motivated example. Then meta-cognition and cooperative cognition are explored by defining their Cognition Logic Context and Cognition Resource Context. Cognition evolution is discussed from the transformation of problem state space. Moreover, the knowledge flow principle engaged in cooperative cognition is explored from the perspective of learning and cognition evolution. To promote cooperative cognition under Web environment, a context application paradigm is proposed based on P2P scenarios. The conclusions and our future works are presented at last.