 In his syntactic accounts, Montague tended to treat ‘logical‘ words like determiners (the, a, every) and conjunctions (and, or, not) syncategorematically, i.e., not by means of lexical entries, but as the effect of specific syntactic rules; the reason for this decision is unknown, but it may be speculated that it was part of a characterization of grammatical meaning in terms of logicality, presumably along the lines of Tarski’s 1986 invariance criterion. As a consequence, a different rule is needed for John walks and sings than for John walks and Mary sings: syntactically the first one is a conjunction of verb phrases and the second one of sentences. However, the two meanings of and are closely related and a generalization is missed. As a general solution it was proposed to use rules (or alternatively general principles) that change the category of an expression – a change that corresponds with a semantic rule that ‘lifts’ the meaning. For instance, the meaning of and as a connective between verb phrases is obtained by lifting the meaning of the sentence connective \(\wedge\) to \(\lambda P\lambda Q\lambda x[P(x) \wedge Q(x)].\) The line of analysis has been extensively studied in Partee and Rooth 1983, Partee 1987, Hendriks 2001, and Winter 2001.