Unknown vs. false

[Strider]

I am trying to use Bayesian Networks (BN) in order model a chemical process. As input I receive rules on the form x1, x2, ..., xn -> y where the attributes are events (e.g. "high temperature at node n1"). The problem at hand is how to differentiate between the states "unknown" and "false". When setting up the BN I have support count for the events constituting the rules, so I am capable of filling in the conditional probability table for each node.

However, when running the system, should an event (as "high temperature at node n1") be stated as "false" as default, or "unknown"? It has for sure not occurred, but stating it as "false" would effectuate the (in)dependency assumptions made by the network structure, hence making it meaningless (in fact, all nodes would be stated either false og true...).

On the other hand, if "unknown" should be default, "false" would never be a valid state.

I hope this problem description was not too unclear, and I would be happy to receive hints/tips about articles or other sources of information dealing with this problem.

[Frank Jensen]

Your problem description is a bit unclear (to me at least...)

The rules you describe look deterministic to me, so I don't see how probabilities enter into the picture.

If you know that an event hasn't occurred, you should set the corresponding variable to "false".
If you don't know whether the event has occurred or not, leave the variable unspecified.

But I'm sure I have misunderstood your problem.

[Strider]

I will try to explain my problem in a better way.

The rules have probabilities attached to them, and this makes it possible to build a BN. In my BN I have a single target node. The purpose is to monitor this target node in order to raise an alarm if its probability exceeds a given level.

The process I am trying to monitor is of course time dependent. From the rules I have knowledge on the form "IF pressure on sensor 1 is above level x THEN high temperature on sensor 4 WITHIN 20 minutes". As mentioned I have probabilities attached to the rules as well.

If now, I set all nodes in my BN to "false", it will become useless since the target node will be "locked" to false until the event it models occurs. In other words, the notion of "false" is a bit difficult to handle since I for sure know that my target event has not occured, but it is the probability for it to occur that is interessting.

[Frank Jensen]

Usually, a time-dependent system is modeled using a time-sliced Bayesian network.  The nodes in a single slice would have states determined by the time instant represented by the slice.

The states of nodes in future time slices would be "unknown" (i.e., not set).  The states of the nodes in the time slice representing "now" would be set according to our observations: "true" or "false" for observed variables, not specified for the rest.