Extraction of Belief Knowledge from a Relational Database for Quantitative Bayesian Network Inference

Algorithm 2

Input: FDs and probability distribution sets 𝑆₁,𝑆₂,…,𝑆_𝑛,

where 𝑆₁=𝑃𝐴₁, 𝑆₂=𝑃𝐴₂∣𝐴₁,…,𝑆_𝑛=𝑃𝐴_𝑛∣𝐴₁𝐴₂,⋯,𝐴_𝑛−1.

Output: A chain formula with independence conditions implied by FDs.

Begin

For every 𝑆_𝑘(𝑘>2) Do

 If FD = 𝑥_𝑘→𝑎_𝑘, substitute 𝑃𝑎_𝑘∣𝑎₁𝑎₂,…,𝑎_𝑘−1 with 𝑃𝑎_𝑘∣𝑥_𝑘,

 where 𝑥_𝑘 is a minimal set of 𝑎₁𝑎₂,…,𝑎_𝑘−1.

 End For

End.