both $\delta_1$ and $\delta_2$ are non-positive, and it is not necessary to evaluate the significance of speciousness at all. For example, if the measure is $MI_S$, then it is known that $MI_{S}\leq 0$. This case includes also a pathological special case which has to be checked separately. Namely, when $P(X)=P(C{=}c)=P(X,C{=}c)$, then all rules $Q\rightarrow C{=}c$ and $Q\rightarrow C{\neq}c$ have $\delta_1=\delta_2=0$ and would be considered specious. This could potentially lose interesting dependencies and therefore, it is required that there remains rule $X\rightarrow Q$ or $X\rightarrow \neg Q$ containing the same information as $Q\rightarrow C{=}c$.

The fourth case is the normal case where the significance measure is always evaluated.

for $i=K$ $2$\
take rule $r_i\in \mathcal{R}: Q \rightarrow C{=}c$\
for $j=1$ $i-1$\
take rule $r_j\in \mathcal{R}: X\rightarrow A=a$\
($Q=X$) ($Q=A$) ($C=X$) ($C=A$)\
reverse rules if needed\
resulting $Q'\rightarrow C'=c$ and $X'\rightarrow C'=a$\
($c\neq a$) ($\delta(X',Q')>0$)\
take next $r_j$\
$\delta_1=\delta_c(Q,C{=}c|X')$; $\delta_2=\delta_c(Q,C{=}c|\neg X')$\
\
(($Q'$ and $X'$) or ($Q'$ and $\neg X'$) equivalent)\
report equivalence and prune out $r_i$\
(($Q'\subset X'$) ($c=a$) ($M_c(r_i|r_j)\leq\theta)$)\
prune out $r_i$\
(($\delta_1\leq 0$) ($\delta_2\leq 0$))\
($n_x=n_{xc}=n_c$) check pathological case\
report Y-S paradox and prune our $r_i$\
($M_c(r_i|r_j)<\theta$)\
report and prune out $r_i$

Experiments
===========

Test setting
------------

The main 