Is it possible to implement mathematical deduce in semantic web?

Question

For example: we have premises a < b and b < c, can you deduce a < c in Semanric web?

Answer 1

With the help of a reasoner and by considering a, b and c as OWL classes (which are kind of equivalent to sets from set theory) you could do it.

For example the following ontology represent your premises:

Class: a
  SubClassOf: b

Class: b
  SubClassOf: c

Class: c

Now if you were to query for the subclasses (direct and indirect) of c you would retrieve a and b, showing that a is a subclass (⊂) of c without explicit assertion.

Note that you could also use the Semantic Web Rule Language if you want to infer information based on the values of a, b and c. You could look at swrlb:greaterThan or swrlb:smallerThan for that.