 There are various ways of defining the hybridization process depend on how much generality one wants, but the following minimally general definition is the easiest to work with. Start with two (generalized) consequence relations each on the same language, that language having a single primitive connective, #, say. The hybrid connective is then # as it behaves according to the intersection of the (generalized) consequence relations. This way of defining things requires us to re-notate the connectives to be hybridized. Thus sticking with the example just mentioned, we consider a copy of the pure ∧ fragment of ⊢CL, called ⊢∧ earlier in this section, but writing # for ∧—but let us still call this consequence relation ⊢∧—and similarly with the ∨ fragment. We are then interested in the behaviour of # according to ⊢∧ ∩ ⊢∨. (Where V∧ and V∨ are the classes of valuations on which # is associated respectively with the Boolean ∧ truth-function and with the Boolean ∨ truth-function, our intersective consequence relation is that determined by V∧ ∪ V∨.) This behaviour includes the semilattice properties of idempotence, commutativity and associativity, for example, since these are common to Boolean disjunction and conjunction. This particular hybrid connective is partially determined, since for example φ, ψ ≻ φ # ψ (a sequent formulation of the condition induced on consequence relations by ⟨T, T, T⟩) belongs to ⊢∧ ∩ ⊢∨. This by itself does not show that the hybrid is not fully determined, however, and to avoid entanglement with some issues about rules, this point is best illustrated in terms of the corresponding generalized consequence relations and their intersection, the latter satisfying neither of the conditions induced by the determinants beginning T, F: for ⟨T, F, T⟩, the condition that φ, φ # ψ ⊩ ψ (failing for # as ∨) or the determinant ⟨T, F, F⟩, for which the induced condition is φ ⊩ φ # ψ, ψ (failing for # as ∧). (Among issues about non-zero-premiss sequent-to-sequent rules that call for care is the fact that while for any such rule under which each of the intersected consequence relations is closed, their intersection is likewise closed, the converse is false: the hybrid consequence relation may be closed under rules under which the originals are not. In the present instance the rule: from φ ≻ ψ to ψ ≻ φ is an example. Similarly for generalized consequence relations the rule: from Γ ≻ Δ to Δ ≻ Γ makes the same point. This second version shows that the current example of hybridization, as conducted in Set-Set, yields a symmetric generalized consequence  relation.[11])