This paper is a contribution to formal ontology study. Some entities belong more or less to a class. In particular, some individual entities are attached to classes whereas they do not check all the properties of the class. To specify whether an individual entity belonging to a class is typical or not, we borrow the topological concepts of interior, border, closure, and exterior. We define a system of relations by adapting these topological operators. A scale of typicality, based on topology, is introduced. It enables to define levels of typicality where individual entities are more or less typical elements of a concept.

In thesauri, conceptual structures or semantic networks, relationships are too often vague. For instance, in terminology, the relationships between concepts are often reduced to the distinction established by standard (ISO 704, 1987) and (ISO 1087, 1990) between hierarchical relationships (genus-species relationships and part/whole relationships) and non-hierarchical relationships (“time, space, causal relationships, etc.”). The semantics of relationships are vague because the principal users of these relationships are industrial actors (translators of technical handbooks, terminologists, data-processing specialists, etc.). Nevertheless, the consistency of the models built must always be guaranteed... One possible approach to this problem consists in organizing the relationships in a typology based on logical properties. For instance, we typically use only the general relation “Is-a”. It is too vague. We assume that general relation “Is-a” is characterized by asymmetry. This asymmetry is specified in: (1) the belonging of one individualizable entity to a distributive class, (2) Inclusion among distributive classes and (3) relation part of (or “composition”).