Delta (Δ) is the comparison operation in the Interactive Semioverse, defined at three levels. At the interaction level, Δ_ix(A, B) = (A \ B) ∪ (B \ A) is the symmetric difference of two interaction surfaces. At the fragment level, Δ_frag(F, G) is the least fragment containing (F ∪ G) \ (F ∩ G). At the footprint level, Δ_foot(τ, τ’; X) = S_X(Δ_frag(F_{τ,X}, F_{τ’,X})) — the closure of the fragment delta.
Each level of delta captures a different kind of difference. The interaction delta is syntactic: which interaction terms does one thing have that the other does not? The fragment delta is semantic but local: what semantic values are in one thing fragment but not both? The footprint delta is semantic and closed: what difference remains after the full closure operator stabilizes the comparison?
The footprint delta can be quantified using the evaluation valuation: μ(Δ_foot(τ, τ’; X)) measures the magnitude of the difference between two things. This is compiled into an interaction operator by the Compare interface action: ⟦Compare(τ, τ’)⟧_iface computes and may materialize the footprint delta as comparison artifacts within the semioverse.