Toward spatial reasoning in the framework of rough mereology

Rough mereology is a paradigm allowing to blend main ideas of two potent paradigms for approximate reasoning : fuzzy set theory and rough set theory. Essential ideas of rough mereology and schemes for approximate reasoning in distributed systems based on rough mereological logic were presented in [13], [14], [17]. Spatial reasoning is an extensively studied paradigm stretching from theoretical investigations of proper languages and models for this reasoning to applicational studies concerned with e.g. geographic data bases, satellite image analyses, geodesy applications etc. We propose a rough mereological environment for spatial reasoning under uncertainty. We confront our context with an alternatively studied mereological context defined within Calculus of Individuals [10] by Clarke [5] and developed into schemes for spatial reasoning in [2], [3] where the reader will find examples of linguistic interpretation. We outline how to define in the rough mereological domain the topological and geometrical structures which are fundamental for spatial reasoning; we show that rough mereology allows for introducing notions studied earlier in other mereological theories [2], [3], [5]. This note sums up a first step toward our synthesis of intelligent control algorithms useful in mobile robotics [1], [7], [8].