Yes, no, I don't know, and the significance of that.
If you adopt a closed world, and assume that all queries which fail to be answered represent a negated answer, then you have a system that cannot reason in the face of incomplete knowledge. If, on the other hand, you have a system which can answer yes, no, or I don't know, you DO have a system that can reason with incomplete knowledge. Now, consider that it is unlikely that anything could know everything, and what a miserable failure it would be if it assumed it did.
Follow this example closely by looking at the following axioms and facts:
MutuallyDisjoint(Male, Female)
MutuallyDisjoint(LivingThing, NonLivingThing)
MutallyDisjoint(Reptile, Mammal)
MutuallyDisjoint(Lion, Zebra)
SubsetOf(Male, Animal)
SubsetOf(Female, Animal)
SubsetOf(Animal, LivingThing)
SubsetOf(Mammal, Animal)
SubsetOf(Zebra, Mammal)
SubsetOf(Bottle, NonLivingThing)
SubsetOf(CokeBottle, Bottle)
InstanceOf(Zelda, Zebra)
InstanceOf(SomeParticularCokeBottle, CokeBottle)
the next rule says that if something is a subset of a set or a superset of a set, we can assume that the set can be considered a subset of itself.
Subset(x, y) -> Subset(y, y) & Subset(x, x)
the next rule establishes that anything that is an instance of a set is also an instance of a set which contains that set.
InstanceOf(x, y) & SubsetOf(y, z) -> InstanceOf(x, z)
the next rule establishes that if anything is an instance of some set, and their is another set that is mutually disjoint with that set, then that thing cannot be an instance of the other set or any subset of that set.
InstanceOf(x, y) & MutuallyDisjoint(y, z) & SubsetOf(w, z) -> ~InstanceOf(x, w)
Now here is the important point I wish to make. There could be thousands of things in the knowledge base. We wish to encode what that thing is explicitly at the most specific level. We have said Zelda is a zebra. By the above rules, we also know that Zelda is a mammal, an animal, and a living thing. But, we also know that Zelda is NOT a non living thing, NOT a bottle, and NOT a coke bottle without having to explicitly say so. There could be thousands, even a million things that Zelda is NOT, and we know that.
But if we queried if Zelda is a male, the answer is: "I don't know." And, that is the CORRECT answer. An incorrect answer would be "YES" or "NO".
Note: We have not made explicit statements that Zelda is NOT a bottle, but the system knows Zelda is NOT a bottle. But we also have not made explicit statements that Zelda is NOT a male, but the system is able to give a different answer, that being: "I don't know."
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Edited by - bishop_pass on June 8, 2001 9:54:47 PM