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In the early stage of artificial intelligence (AI), AI very closed to then modern cognitive psychology based on the recognition that both computer and human brain are information processing machines meeting the requirements to show intelligence. It seems that the similar trend appears again today between Web Intelligence (WI) and Brain Informatics (BI) based on the recognition that both World Wide Web (the Web) and the human brain are informational huge open systems meeting the requirements to deal with scalable, dynamically changing, distributed, incomplete and inconsistent information, and the advancement both in the Web (e.g., semantic Web and human-level wisdom-Web computing) and in BI (e.g., advanced information technologies for brain science and non-invasive neuroimaging technologies, such as functional magnetic resonance imaging (fMRI)). ACT-R is a theory and model of computational cognitive architecture, which consists of functional modules, such as declarative knowledge module, procedural knowledge module, goal module and input (visual, aural), output (motor, verbal) modules. Information can be proposed parallel inside and among the modules, but has to be sequentially if it needs procedural module to coordinate the behavior across modules. At the International WIC Institute (WICI), we are trying to introduce this kind of architecture and the mechanism of activation of the units in declarative knowledge module into our wisdom-Web computing system. Based on or related to ACT-R, theories and models that are with very close relation to WI have also been developed, such as threaded cognition for concurrent multitasking, cognitive agents, human-Web interaction (e.g., SNIT-ACT (Scent-based navigation and information foraging in the ACT cognitive architecture). At the WICI, we are also working on the user behavior and reasoning on the Web by eyetracker and fMRI. Human can perceive the real world under many levels of granularity (i.e., abstraction) and can also easi- ly switch among granularities. By focusing on different levels of granularity, one can obtain different levels of knowledge, as well as indepth understanding of the inherent knowledge structure. At the WICI, we are taking Granular Reasoning (GrR) as a human intelligence inspired methodology and developing specific methods for a reasoning process in a variable precision at Web scale. All of above will be discussed in my talk as examples of various levels from BI to WI to show the trend of close interacting between BI and WI, which will benefit both WI and BI researches.