Mereological inheritance

In recent investigations of Spatial Reasoning, Spatial Knowledge Representation, and Geographic Information Systems, a significant effort has been spent by many scholars of the area about the problem of representing properties of spatial objects by means of logical theories. An analogous effort has been the problem of analyzing the qualitative relations which can be established between two space regions. These investigations have led to a general framework of the field known by the term ``mereo-topology''. Though both the above mentioned approaches have proved to be successful in the investigation of formal and practically relevant aspects of spatial objects, no attempt has been carried out in the direction of integrating the approaches and looking at the relationship between a general logical theory of space and mereo-topology from an analytical point of view, in particular for exploiting the combinatorial behaviour of such an integrated model. This paper intends to fill the gap and analyze the behaviour of spatial formulae of a logical theory of space as objects which can be classified based on the behaviour they exhibit with respect to the parts and supertparts of the regions where they are true. We name these categories of behaviour inheritance modalities.