Formal Description Of The Solid Object And Hole In Spatial Reasoning

In this work, we introduce the formal system and it's model of the spatial reasoning, and how does the spatial semantics study evolves the Boolean connection algebra by the relation algebra.The solid region and the formal representation of the hole is one of the key technologies in spatial reasoning. We have introduce the formal definition of "hole", and discuss the property of internal connection and "hole". Also, we have given the formal definitions of connected solid,internal gap,absolutely dense solid domain in the region.Based on Diintsch's work, we have obtained the following new results:(1)We discuss the relation between the "hole" which has property of internal connection and the entity thoroughly, for example:in one-dimensional space,the entity doesn't have "hole", but in two-dimensional space,it is possible.(2)We prove the Bx, Bφ, Bωare loose, and they have connected domains in which nearly everywhere there are "holes', and the connected domains don't contain absolutely dense solid domain.(3)We structure a special RCC region model, which is completely different with Diintsch'smodel, it is by completely not intersect semi-open interval for starting point, and this region contains a absolutely dense solid domain (it is similar with the black hole In universe).