 Thus the local range is not very informative as to the precise significance of such a rule as (∨E) and it is natural if one thinks of the rules as giving the meanings of the connectives they govern (a perspective mentioned in Section  1)  and wants to distill this information into a semantics in terms of valuations, to consider the global range. To do so we make use of the partial order ≤ on the underlying set U of valuations (for the language under consideration) defined by: u ≤ v if and only for all formulas φ, if u(φ) = T then v(φ) =  T.[15]  As Garson (2001) observes, the global range of the introduction and elimination rules for ∨ (and again we could equally well cite the sequent calculus rules in this connection) is the set of all V ⊆ U such that for all u ∈ V and all formulas φ and ψ, the following condition is  satisfied:[16]