Constructing beliefs from products of quantities

 

Syntax

BD>product : A, B

where and B are the names of bases

The PRODUCT:  command is used for the construction of beliefs over products of uncertain quantities under certain conditions. These conditions are as follows. Suppose that the base A consists of the elements and that the base consists of the elements . Suppose also that we gather all the elements not in either or into the base C, and suppose that we label these elements .

1. The bases A and B must be disjoint. That is, the elements of the base A must not also appear in the collection B.
2. The collection A must be uncorrelated with the collection B for every unlocked belief store. That is, we must have for all . An error is reported otherwise.
3. For pairs of quantities , and for each we must have either

   

   or both, for every unlocked belief store. An error is reported otherwise.

The product formed by the pair will be constructed as the element named `Ai Bj', for all and all . Any preexisting elements with these names will be deleted, together with any data attached to them. This is unlike the BUILD:  command in that data attached to a pre-existing element is not here adopted by the replacing element.

The PRODUCT:  command is asymmetric to the extent that the command

BD>product : B, A

will construct different names (of the form `Bj Ai') for the same collection of products. Hence you should take care with the order given in the command.

Beliefs over the products are constructed only for unlocked belief stores, and the uncorrelatedness conditions relate only to these unlocked stores. Expectations over products are constructed only for unlocked expectation stores. The LOCK:  and ELOCK:  commands may be used to lock and unlock stores.

If the builddata  control is switched on, the PRODUCT:  command also constructs data from the product wherever possible. Similarly to the construction of data for the BUILD:  command, the maximum number of cases for which data is available for both and is used to construct the data for the new element

The following formulae are used to construct beliefs over the product, and between the product and other elements.