[DL] incoherence in DL semantics?

[Rod Moten]

I am a new student to Description Logics. My background is in type theory.
In my endeavors to learn Description Logics, I came across an issue on which I
would like some clarification. Suppose someone defines a knowledge base with
Description Logic in which Meters and Centimeters are concepts. Whether 
Meters and
Centimeters are defined concepts are primitive concepts is immaterial. 
Naturally,
we expect Meters and Centimeters should be related, i.e. minimally Meters 
should
subsume Centimeters, which I write as Centimeters < Meters. If this is true 
then
for every interpretation I, I(Centimeters) is a subset of I(Meters), written
I(Centimeters) subseteq I(Meters), This is where I am having a problem.
  I(Centimeters) subseteq I(Meters) means that every element of
I(Centimeters) is an element of I(Meters).  However, each element in
I(Centimeters) has a different meaning in I(Meters). For example, 200 cm
  is not the same as 200 m, but 200 cm is 2 m. How do you reconcile this
problem of incoherence in Description Logics? Is there something about DL I 
missed?

Rod





Rod
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