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The most common cause of one-to-many correspondences between a variable and a set of predications are labels shared with (non-scopal) modifiers, e.g. in a structure like she arrived very quickly. Here, the degree specifier is a non-scopla modifier on the adverb, which in turn is a non-scopal modifier on the arriving event; thus, all three share one label, and arrive is the ARG1 of quickly, which is the ARG1 of very. To pick out arrive in this scenario, we dis-prefer candidates that take any of the other candidates as their argument. This is a sound topological heuristic, essentially operationalizing a notion of semantic heads in groups of (logically) conjoined predications.
Far less frequent than the above are cases of two or more predications sharing their label but lacking argument relations among them. In the 1214 release of the ERG, the ‘existential be’ constructions can give rise to such configuration, e.g. in there were cats in the garden (mrs/991). Here, the preposition shares its label with the _be_v_there, but its external argument (ARG1) is the cats instance variable.
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