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$prop transforms a statement into a 'black box' proposition. This prevents Aito from analyzing the proposition and using its parts separately in the statistical reasoning.

In practice the difference between normal 'white box' expressions, and the $prop's black box expressions is: that the atomic expressions have a smaller bias, but a higher measurement error.

Consider the following example:

{ "tags" : "pen", "price" : { "$gte" : 200 } }

During the statistical reasoning: Aito may recognize that pens are often sold, and that over 200€ product purchases are somewhat common. As a result: Aito might assume the over 200€ pen to be a popular product.

Now, consider the expression:

{ "$prop" : { "tags" : "pen", "price" : { "$gte" : 200 } } }

The results of this expression will depend of the amount of data. If there are no over 200€ pens in the data: Aito will make no assumptions of the proposition's effect. On the other hand, if you have the data: Aito will recognize correctly, that the over 200€ pens are bought extremely rarely, and almost solely by corporations and wealthy individuals.


    { "$prop" : Proposition }

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