A topos over an ontology as a model of experts intuition

A formal representation of an expert's world model is described, which covers not only the domain ontology, but also the relationships of similarity between its entities. Similarities are formally treated in the framework of pretopological, topological and metric spaces, where an actually achievable grade of metricity of similarity relationships is determined experimentally. An automated inference under uncertainty in the proposed model is based on the internal logic of a (pre)sheaf where the base category is the formal domain ontology (a field of knowledge). The ordinary skeleton of entities and relationships is embedded into a (pre)topological structure, formed by the subjectively significant, for the expert, "regions of evidence", where the decision process is "intuitively obvious" and formalized with the lattice of conceptual similarities of the corresponding local neighbourhoods in his/her world model.