They can be the subject of properties, new classes of concrete objects can be defined, etc., etc. This view has untenable computational problems, both theoretical and practical. On the theoretical side, reasoning become undecidable. On the practial side, mechanisms have to be provided to give concrete objects properties, etc., etc. Concrete objects cannot participate in abstract properties at all.
Concrete objects can only participate as the target of concrete properties.
Concrete properties cannot have inverses, and cannot be unambiguous. This view has the easiest implementation. There is a single domain for concrete and abstract objects, with two subdomains. Some semantic mappings map to this domain. However, most semantic mappings map to one of the subdomains.