Question

In a database, a rule is defined as (P1 and P2) or P3? R1 (0.8) and R2 (0.3), where P1, P2, P3 are premises and R1. R2 are conclusions of rules with certainty factors (CF) 0.8 and 0.3 respectively. if any running program has produced P1, P2, P3 with cf as 0.5, 0.8. 0.2 respectively, find the cf of results on the basis of premises.

A. CF(R1=0.8), CF(R2=0.3)
B. CF(R1=0.40), CF(R2=0.15)
C. CF(R1=0.15), CF(R2=0.35)
D. CF(R1=0.8), CF(R2=0.35)

Answer 1

The correct cf of the results based on the premises for the database rule defined with conditions P1, P2, and P3, and conclusions R1 and R2 is CF(R1=0.40) and CF(R2=0.15), which corresponds to option B.

Step-by-step explanation:

We are given a database rule with conditions (P1 and P2) or P3, leading to conclusions R1 with certainty factor (CF) 0.8 and R2 with CF 0.3 respectively. The conditions P1, P2, and P3 are provided with CFs 0.5, 0.8, and 0.2.

Firstly, let's calculate the combined CF for P1 and P2 using the multiplication rule of probability: P(P1 AND P2) = P(P1) × P(P2) = 0.5 × 0.8 = 0.4.

Now, using the addition rule of probability for P(P1 AND P2) OR P3, we have P(A OR B) = P(A) + P(B) − P(A AND B), which in this scenario translates to CF = 0.4 + 0.2 − (0.4 × 0.2) = 0.6 − 0.08 = 0.52.

Following the database rule, we combine this result with the CF of the conclusions R1 and R2. This involves multiplying the CFs: CF(R1) = 0.8 × 0.52 = 0.416 and CF(R2) = 0.3 × 0.52 = 0.156. These values can be rounded to 0.4 and 0.15 respectively.

Based on the calculations, the cf of the results based on the premises is CF(R1=0.40), CF(R2=0.15), therefore the correct answer is B.