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Top1. Introduction
A very well-known knowledge representation is the rule structure of the form:
IF condition <antecedent> THEN action <consequence>
This structure is very simple to write, use and understand, but its drawbacks according to Michalski and Winston (1986) is that it can't capture the real-time systems and application or what so called variable precision logic. To overcome this drawback, Michalski and Winston (Michalski & Winton, 1986) proposed a rule structure called Censored Production Rule (CPR) that can deal with real time systems. Using CPR, the more time is available; the more conditions that might occur rarely can be checked. The CPR structure is as below:
IF condition THEN action UNLESS [c1,c2,c3,….cn]
where UNLESS slot contains the set of known censor conditions that might occur rarely and prevent the action to be concluded.
1.1. CPR
In this section, we explain the CPR in more details, the formal structure of CPR is:
IF condition THEN action UNLESS [c1,c2,c3,…cn]: Ɣ, δ
where Ɣ is the certainty value that the action will be taken given that the condition is true. δ is the maximum certainty value that can be achieved by checking censor conditions within the given time before the system response. The maximum value for δ is 1 and Ɣ <= δ. Ɣ = δ occurs when the time does not permit to check any of the censor conditions. To make the idea clear, let us have the following example:
IF X is bird Then X flies UNLESS [X is penguin:0.02, X has a broken wing:0.05, X is sick:0.01]: 0.8
The above rule says if we have a bird, then it flies with a certainty factor 0.8. This means 0.8 is the value for Ɣ. The 0.02 value for example scales how often this censor occurs and we shall call it Censor Importance (CI), and this value is added to Ɣ value whenever time permits. Now let us assume we have more time for the system response, we can check some censors until time does not permit. Let us assume that the time can allow us to check the first two censors, this will make the value of δ as:
δ = 0.8+0.02+0.05 = 0.87
This means after the above calculation, we can conclude X flies if it is a bird with certainty factor 0.87. For sure the writer of the rule can still write the censor conditions order based on their importance. The maximum value for δ is 1 and in this case, it means that all the censor conditions are listed in the slot and checked. In other cases, the value for δ is not 1 despite we have enough time to check all the listed censor conditions, but this means we are still have some unlisted unknown censor conditions. It is to be noted that if any of the censors is true, the action will not be taken. This means the relation between the censor conditions is OR relation.