Table 3.15 illustrates the influence of correlation between two basic context events on the probability Prob(e1 ∧ e2).

For conjunctions of literals with basic context events in the following inclusion-exclusion formula [50]:

$\begin{array}{l}Prob\left({E}_{1}\vee {E}_{2}\vee \cdot \cdot \cdot \vee {E}_{m}\right)\\ \text{\hspace{0.17em}}={\displaystyle \sum _{i=1}^{m}Prob\left({E}_{i}\right)}-{\displaystyle \sum _{i<j}Prob\left({E}_{i}\wedge {E}_{j}\wedge {E}_{k}\right)-}\\ {\displaystyle \sum _{i<j<r<s}Prob\left({E}_{i}\wedge {E}_{j}\wedge {E}_{r}\wedge {E}_{s}\right)+\cdot \cdot \cdot +{\left(-1\right)}^{\left(m+1\right)}Prob\left({E}_{1}\wedge {E}_{2}\wedge \cdot \cdot \cdot \wedge {E}_{m}\right)}\end{array}$

The above correlations can be taken into account by comparing each event with all other events in the same conjunction. Let e1 and e2 be two basic events, and let E be either a basic or complex event expression, the implications of correlation ...

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