I read “Qualitative Spatial Representation and Reasoning”, should you?

Are you considering using QSR to solve your research problem? Looking at “Qualitative Spatial Representation and Reasoning” (A. G. Cohn and J. Renz) and need help deciding if you want to spend the time reading the paper?

Deciding whether or not to use QSR to solve a particular problem is an important first step. Do you need to do spatio-temporal reasoning about objects in space? Are you looking for qualitative information, such as “Object A is close to Object B and partially covers Object C” or are you looking for detailed quantitative information, such as “Object A is 5 mm from Object B”? QSR deals with qualitative information.

Let’s assume that qualitative spatial reasoning will suffice for your research problem, how do you decide what theory to use.  This paper gives you an overview of the current (2007) state of affairs in QSR and will help you figure out where to start your reading.

Here are some questions you will need to answer:

1. What kind of spatial entities will exist in your representation?
   1. points?
   2. Lines?
   3. Regions?
   4. Physical Objects?
   5. Geographic Regions?
      
2. How will you describe the relationships between these entities?
   1. Topology?
   2. Sizes?
   3. Distances?
   4. Relative Orientation?
   5. Shape?

Most of the QSR community takes regions as the primitive spatial entity, if your problem requires dealing with lines and points, keep reading to see if you can find a theory that fits your requirements.

Read this paper to find a few more questions that you should answer, which will lead you toward one or another theory.

Consider this: what primitive non logical symbols should be allowed/be in your theory without needing definition? Can you constrain them in terms of a set of axioms? To make it mathematically elegant and to have a system with a simply set of symbolic inferences, it is necessary to make the set of primitive non logical systems small. Unless you agree with Hayes and want a more complicated, but larger, richer and more natural set of symbolic inferences and thus set of primitives. An example class of primitives are relations between entities.

Reasoning over a chosen spatial entity, is the equivalent of finding the particular set of relations among all possible sets. There are an infinite number of set of relations unless we restrict ourselves to JEPD (Jointly exhaustive and pairwise disjoint). That is, each pair of entities can belong to exactly one of the JEPD relations (assuming binary relations). EC(a,b) means, that Externally Connect is a to b. A relation contains a number of tuples, one for each pair of entities that belong to it. An infinite number of squares lined up side by side would be EC{(a,b),(b,c),(c,d),….} and EQ{(a,a),(b,b),(c,c),(d,d),… } (eq = equal).

How will you represent and describe these relations among entities, what will you use? Come back tomorrow for those answers and more.

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