Complex-Valued Representation of Relevance and Semantic Relations for Claim-Evidence Pairs with PSO Boundary Calibration

Abstract

This study constructs f(c,e), a complex-valued function in a polar form as a measure of relevance and semantic orientation between claims and evidence, where the modulus component represents semantic relevance and the angle component represents semantic orientation, which reflects the direction of the relationship between claims and evidence. The function is proven to have four mathematical properties: well-definedness, boundedness, continuity, and symmetry. Particle Swarm Optimization (PSO) is used to determine the angular boundaries that partition the semantic orientation space into support, not enough information, and refute relation zones. This approach ensures that the resulting zone boundaries reflect the characteristics of the empirical data distribution. The angular boundary calibration experiment was conducted using two datasets, namely SNLI and FEVER, and with two embedding models, namely all-MiniLM-L6-v2 and mxbai-embed-large-v1. The PSO results were evaluated using the F1-macro objective function. The obtained F1-macro ranged from 0.4105 to 0.59888, with the combination of SNLI and mxbai-embed-large-v1 producing the highest value. In this experiment, zone separation was descriptively clearer for SNLI than for FEVER, with SNLI exhibiting wider NEI zones and less overlap among relation distributions.