  However, this functionalist solution to the problem of mixed compounds relies heavily on that theory’s monism—i.e., its insistence that the single role property \(F\) is a universal truth property. This might leave one wondering whether a solution is readily available to someone who rejects the existence of such a property. One strategy is simply to identify the truth of conjunctions, disjunctions, and conditionals with the kind of properties specified by (44), (45), and (46), respectively (as opposed to taking them to be realizers of a single truth property). Thus, e.g., the truth of any conjunction simply \(is\) to be an instance of the truth-function for conjunction with conjuncts that have the property that plays the \(F\)-role for them (Kim &amp; Pedersen 2018, Pedersen &amp; Lynch 2018 (Sect. 20.6.2.1). Another strategy is to try to use the resources of multi-valued logic. For example, one can posit an ordered set of designated values for each way of being true \(F_1 , \ldots ,F_n\) (perhaps according to their status as ‘heavyweight’ or ‘lightweight’), and then take conjunction to be a minimizing operation and disjunction a maximizing one, i.e., \(v(p \wedge q) = \min\{v(p), v(q)\}\) and \(v(p \vee q) = \max\{v(p), v(q)\}\). Resultingly, each conjunction and disjunction—whether pure or mixed—will be either true in some way or false in some way straightforwardly determined by the values of the constituents. For example, consider the sentences