Supplementary Material: Lifted Inference Rules with Constraints
نویسندگان
چکیده
Proof. To convert T into the canonical form with respect to variable x, we need to find an atomic constraint A which can equivalently represent all the subset constraints over x in T. Such an A can be obtained by enforcing that x belongs to the set difference of a) intersection of the subsets Ci’s such that there is a constraint of the form x ∈ Ci in T And b) union of the subsets Cj’s such that there is a constraint of the form x / ∈ Cj in T. In other words, A can be written as x ∈ (∩iCi) \ (∪jCj) where (x ∈ Ci) ∈ T ∀i and (x / ∈ Cj) ∈ T ∀j.
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