An agent needs to determine a belief over potential outcomes for a new problem based on past observations gathered in her database (memory). There is a rich literature in cognitive science showing that human minds process and order information in categories, rather than piece by piece. We assume that agents are naturally equipped (by evolution) with a efficient heuristic intuition how to categorize. Depending on how available categorized information is activated and processed, we axiomatize two different versions of belief formation relying on categorizations. In one approach an agent relies only on the estimates induced by the single pieces of information contained in so called target categories that are activated by the problem for which a belief is asked for. Another approach forms a prototype based belief by averaging over all category-based estimates (so called prototypical estimates) corresponding to each category in the database. In both belief formations the involved estimates are weighted according to their similarity or relevance to the new problem. We impose normatively desirable and natural properties on the categorization of databases. On the stage of belief formation our axioms specify the relationship between different categorized databases and their corresponding induced (category or prototype based) beliefs. The axiomatization of a belief formation in Billot et al. (Econometrica, 2005) is covered for the situation of a (trivial) categorization of a database that consists only of singleton categories and agents basically do not process information categorical.
