A formal theory of qualitative size and distance relations between regions

We present a formal theory of qualitative distances between regions based on qualitative size relations. Using standard mereological relations, a sphere-predicate, and qualitative size relations such as roughly-the-samesize-as and negligible-in-size-with-respect-to, we define qualitative distance relations such as close-to, near-to, away-from, and far-away-from. Relations such as roughly-the-same-size-as and negligible-in-size-with-respect-to are contextdependent and vague. The primary focus in the formal theory presented in this paper is on the context-independent logical properties of these sorts of qualitative size and distance relations. We are especially interested in how these relations interact with familiar mereological relations. In developing our formal theory, we draw upon work on order of magnitude reasoning in Artificial Intelligence.

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