Empirical Evidence For a Semantic Distance In a Patch: Investigating Symmetry and The Triangle Inequality Violations

In this article, we hypothesize that a metric underlies similarity within an active “patch” of a semantic space, meaning the subset of the semantic space to which attention is directed at a given moment and whose metric and content change constantly and continuously. We argue that violations of the symmetry and triangle inequality axioms, which serve as a central argument against the metric approach, result from the performance of similarity judgments in the context of different patches. To test our hypotheses, we constructed a weighted semantic network that enables us to identify in-context cases, as opposed to not-in-context cases. Our results and analysis support our claim that within a patch, the violations of the symmetry and triangle inequality axioms disappear.