Given a database D with relations R and "foreign key" links F, the hypothesis language is the set of conjunctions of atoms

• A₁ = r₀(V₁₁, ..., V_1a) for r₀ of arity a
• A_i = r(V_i1, ..., V_ia) where r Î R with arity a
• A_i = V_j [<|=|>] v for a value v in the value hierarchy of A_i

• two literals share a variable only if there is corresponding link (cf. modes)
• no variable is more than i steps away from r₀.

e.g. D={r₀, r₁, r₂, r₃, ...}, F = {r₀[2]->r₁[1], r₀[3]->r₂[1], r₁[2]->r₃[1], r₂[2]->r₃[2], i=2.

H = r₀(X,Y,Z) & r₁(Y,U) & r₂(Z,R) & r₃(U,R) & X = x₀ & U=a.