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This post shows an example of General Class Axiom:

((walksLike some Duck) and (talksLike some Duck)) SubClassOf Duck

Isn't it the same as giving a necessary and sufficient condition on Duck? 

Duck EquivalentTo: ((walksLike some Duck) and (talksLike some Duck))

Aren't they logically equivalent? I've read this article as well, but I don't understand what General Class Axiom's real use for.

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MJ Park
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    Why do you think that equivalence is the same as subsumption? Equivalence is a subsumption in both directions, i.e. if you have `A EquivalentTo B` it holds that `A SubClassOf B` and `B SubClassOf A`. – UninformedUser May 12 '16 at 09:04
  • @AKSW Because I cannot find an example that differentiates inference results in these two cases. That is, the one should be subsumed to the Class Duck in the case of General Class Axiom and not in the case of EquivalentTo. – MJ Park May 12 '16 at 13:36

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The subsumption provides only one of necessary or sufficient, as AKWS remarked.

Example:

A1 instanceOf Duck

A2 instanceOf (walksLike some Duck) A2 instanceOf (talksLike some Duck)

With just the subsumption axiom, the queries:

Instances of Duck: A1, A2 Instances of walksLike some Duck: A2

With the equivalence axiom:

Instances of Duck: A1, A2 Instances of walksLike some Duck: A1, A2

Ignazio
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