Mereogeometries : A Semantic Comparison

We compare several geometrical theories based on mereology () in a unified framework. Most theories in this area lack in formalization and this prevents any systematic logical analysis. We overcome this problem by isolating a common domain in R and, selecting natural interpretations, we use this framework to show several interdependencies among primitive relations of these theories. We conclude that, for dimension n ≤ 3 and with some additional assumptions, most of the theories considered are equivalent in the provided interpretation