ABSTRACT: As the value of land in the urban regions of the world increases, there is a trend towards the subdivision of property rights in 3D. That is to say, rights to land may be replaced by rights to the space above and below the land. This increases the complexity of the descriptions that are needed to define the regions of space to which the property rights apply. The simple plans of subdivision that are used in defining property rights on the surface of the earth are being replaced by far more complex 3D spatial definitions. An important issue in the framing of these definitions is that they must be correct and unambiguous, because an error or ambiguity in the definition of the extent of a property can lead to expensive legal disputes. This paper explores an axiomatic approach to the problem of defining what is a valid definition of a 3D Cadastral objects (parcels). This paper addresses: 1. Modelling and validation of a single cadastral parcel; and 2. Modelling and validation of a complete spatial partition.