,
Table 28: Minimum thresholds used in creating pairwise variables.
['MinCellCellAlignment MinTitleTitleAlignment', '0.6 0.0', 'MinCellQConsAlignment MinCellQChoiceAlignment', '0.1 0.2', 'MinTitleQConsAlignment MinTitleQChoiceAlignment', '0.1 0.2']
i, as defined in Section 3. We define variables over each element by overloading x(.) or y(.,.) notation which refer to a binary variable on elements or their pair, respectively. The pairwise variables are defined between pairs of elements; e.g., y(tijk,qℓ) takes value 1 if and only if the corresponding edge is present in the support graph. Similarly, if a node corresponding to an element of the problem is present in the support graph, we will refer to that element as being active. In practice we do not create pairwise variables for all possible pairs of elements; instead we create pairwise variables for edges that have an entailment score exceeding a threshold. For example we create the pairwise variables y(tijk,ti′j′k′) only if w(tijk, ti′j′k′)≥\textscMinCellCellAlignment.