I believe, and this is a central aspect of development in the Human Intuition Project Framework, that there are three types of connotations: properties, relations, and chunks.
A property is anything that has a value. It could be a numerical value, a name, or anything else.
A chunk is a mental object, holding stuff together. Any mental object is a chunk.
Finally, a relation maps from a set of (properties, chunks, and relations) to create new properties, chunks, or relations. It is very much like the term used in mathematical relations. And this quote from Augustus DeMorgan, mixing psychology and mathematics, is just eerie to my ears:
"When two objects, qualities, classes, or attributes, viewed together by the mind, are seen under some connexion, that connexion is called a relation."