Love as composition: a set-theoretic account of affective structure across relationship types

Ordinary language treats love as a polysemous term denoting distinct affective states for partners, children, friends, and parents. This paper formalizes an alternative view: love is a single atomic component, and apparent differences between types of close relationships arise from the additional components composed with it. Using a discrete set-theoretic framework, the paper introduces a signature of emotional atoms partitioned into love, overlays, and derivatives; axiomatizes their relations; and defines canonical relationship types as two-element sets. Five theorems establish (i) the invariance of love across canonical types, (ii) the non-triviality of their pairwise intersection, (iii) the localization of inter-type difference to overlays, (iv) the structural form of common identification errors, and (v) a criterion for pure love. The model extends Sternberg's (1986) triangular theory by introducing four relationship-specific overlays in place of three intra-romantic dimensions, and by explicitly distinguishing overlays from derivative components (jealousy, envy, possessiveness, fear of loss). The paper engages directly with anti-compositional philosophical accounts (Velleman, Kolodny, Jollimore), with the affective-neuroscience decomposition of love into separable systems (Fisher, Panksepp, Hazan-Shaver), and with the cross-cultural lexicography of love (Lomas), defending atomicity through a multiple-realizability argument that locates the model at the structural-phenomenological rather than neurobiological level.