When Knowledge size matter.

We are able to estimate the risk to receive the fruit on our head because our observations accumulated since our childhood. As young kid without any knowledge about the gravity we know that any object between our fingers will fall when we will release the object. Later, we will know that fruits in the tree fall when it is windy or when the fruits are ripe. If a program has this knowledge too, logically it will be able to estimate the risk to receive the fruit. The reasoning will be a succession of inferences. For example, the database contains these facts and rules (the probability that the fact is true is indicated in percent):

1 - 100% - A pear is a fruit.
2 - 100% - A pear grows in the top of a tree.
3 - 100% - The top of a tree is above the ground surface.
4 - 100% - A thing above the ground surface falls when released.
5 - 100% - A pear is a thing.
6 - 80% - A fruit is released when is ripe.
7 - 60% - A pear is ripe on October.
8 - 100% - We are on October.

The inferences are:

(1,6 => 9) A pear is a fruit + A fruit is released when is ripe = A pear is released when is ripe.

(9,7,8 => 10) A pear is released when is ripe + A pear is ripe on October + We are on October = A pear is released (0.8 x 0.6 x 1 = 0.48).

(4,5 => 11) Thing above the ground surface fall when released + A pear is a thing =A pear above the ground surface falls when released.

(11,10 => 12) A pear above the ground surface falls when released + A pear is released = A pear above the ground surface falls (1 x 0.48 = 0.48).

(2,3 => 13) A pear is in the top of a tree + The top of a tree is above the ground surface = A pear is above the ground surface.

(12,13 => 14) A pear is above the ground surface + A pear above the ground surface falls = A pear falls (1 x 0.48 = 0.48).

So the set of facts and rules above bring to the conclusion that a pear could fall with a probability of 48%.

This sort example shows that a software is able of reasoning but that requires an extensive and precise factual and procedural knowledge base.

But what happens when the knowledge base is incomplete, a fact is wrong or incertain , or different words are used for the same thing?

For example:

a) If the fact 6 is missing "A fruit is released when is ripe" ?

b) If the fact 7 is wrong "A pear is ripe on June" ?


c) If the fact 3 and 4 use two different terms soil and ground surface for the same thing: "The top of a tree is above the soil" and "A thing above the ground surface falls when released" ?

As for human, it will depend of the quantity of knowledge stored in the database.  

For the problem (a), the software can proceed by analogy, for instance the 2 facts below conduct to the hypothesis that a pear could fall like an apple :
- An apple falls from the tree when it is ripe.
- Apples and pears grow on tree.

For (b), the software can detect an error in the knowledge base. If for instance the knowledge base can contain these facts:
- Anjou, Bartlett, Bosc, Comice are pear varieties.
- Comice pears are harvested September through February.
- Bosc pears are harvested September through April.
- Barlett pears are harvested July through October.
So the fact (b) is illogical regarding the facts listed above and the program will warn there is an incoherence in its knowledge base and it will ask for checking of the fact (b).

For (c), the software can search a synonyms of soil and ground and then it will decide that both words design the same thing.

As a human, a program is able to support some incoherence in its knowledge base and ask to verify some weird facts.

But what kind of algorithms are required for this pseudo-human reasoning ?

To be continued...