Approximate knowledge modeling and classification in a frame-based language: The system CAIN. We present an extension of the frame-based language Objlog+, called CAIN, which allows the homogeneous representation of approximate knowledge (fuzzy, uncertain, and default knowledge) by means of new facets. We developed elements to manage approximate knowledge: fuzzy operators, extension of the inheritance mechanisms, and weighting of structural links. Contrary to other works in the domain, our system is strongly based on a theoretical approach inspired from Zadeh’s and Dubois’ works. We also defined an original instance classification mechanism, which has the ability to take into account the notions of typicality and similarity as they are presented in the psychological literature. Our model proposes consideration of a particular semantics of default values to estimate the typicality between a class and the Instance To Classify (ITC). In that way, the possibilities of the typicality representation proposed by frame-based languages are exploited. To find the most appropriate solution we do not systematically choose the most specific class that matches the ITC but we retain the most typical solution. Approximate knowledge is used to make the matching used during the classification process more flexible. Taking into account additional knowledge concerning heuristics and elements of cognitive psychology leads to the enrichment of the classification mechanism.