Lattice modeling is applied to investigate how the configurations of local chain juxtapositions may provide information about whether two ring polymers (loops) are topologically linked globally. Given a particular juxtaposition, the conditional probability that the loops are linked is determined by exact enumeration and extensive Monte Carlo sampling of conformations satisfying excluded volume constraints. A discrimination factor fL, defined as the ratio of linked to unlinked probabilities, varies widely depending on which juxtaposition is presumed. /log fL/s that are large for small loop size n tend to decrease, signaling diminishing topological information content of the juxtapositions, with increasing n. However, some juxtaposition geometries can impose sufficient overall conformational biases such that /log fL/ remains significant for large n. Notably, for two loops as large as n=200 in the model, the probability that passing the segments of a hooked juxtaposition would unlink an originally linked configuration is remarkably high, approximately 85%. In contrast, segment-passage of a free juxtaposition would link the loops from an originally unlinked configuration more than 90% of the time. The statistical mechanical principles emerging from these findings suggest that it is physically possible for DNA topoisomerases to decatenate effectively by acting selectively on juxtapositions with specific "hooked" geometries.