This paper presents a conceptual system in which concepts are defined by binary associations between properties. Properties are measurable membership functions, defined on sets equipped with a measure that is the disjoint domains of representation. Instances of concepts (observations) are sets of points from these domains. Requiring properties to be measurable enables their overlap to be precisely described. Similarity between concepts, and between observations and concepts, is naturally defined using fuzzy subsethood, and similarity and overlap are used to set attention in categorization tasks. This formulation therefore follows Gardenfors in recognizing the importance of property associations and of similarity in conceptual systems