Subtraction in the Interactive Semioverse is a disciplined removal operation built from the Heyting implication. At the element level, a ⊖ b = a ∧ (b ⇒ ⊥) — the meet of a with the pseudo-complement of b. This is the largest element c such that c ≤ a and c ∧ b ≤ ⊥.
At the fragment level, fragment subtraction F ⊖ G is the least fragment containing {a ⊖ s(G) : a ∈ F}, where s(G) = ⋁_{x ∈ G} x is the fragment’s support (the join of all its elements). At the state level, subtracting a thing τ from state X removes the semantic support of τ’s thing fragment from every element of the carrier, then re-fragments.
Subtraction is distinct from forgetting. Forgetting (X \ τ) removes the handle’s semantic seed and all operators mentioning the handle — a syntactic deletion. Subtraction (X ⊖ τ) removes semantic support but preserves operator vocabulary. Subtraction is always at least as conservative as forgetting: S(X ⊖ τ) ≤ S(X \ τ). Both operations are compiled into interaction operators via the interface algebra.