The 0ze's in (1) are uniquely descriptive, while those in (2) are on one reading generic. What is simple about these examples is that their difference can be explained in terms of a single mode of modality, the temporal.
1.1. Semantic Framework
As a temporal model structure, take a quadruple <Y, %, 9, -C ), Y being a nonempty set (of moments), K an asymmetric and transitive relation on Y (previousness), and 9 a mapping of .Y-into subsets of a proper subset of a. Let S, t be any members of Y. .CSf is considered to be the (possibly empty) domain of individuals existing at the moment t. 'J? is to be thought of as the universe of all individuals existing at every, any, or no time. In terms of such model structures we may state truth and denotation conditions for various sorts of meaningful expressions of higher-order quantified tense logic without existence assumptions. Among these conditions will be the following. Let VJr) be the value (extension, denotation, referent) assigned to the expression r by the valuation V on (Y, '%, 58, C) at time t. More specifically, if x is any individual variable, VJx)=VJx)& for all S, t&-. (Variables do not change values from time to time.) If c is an individual name, V,(c)&, and may differ from VS(c). If P is an n-place predicate, Vt(P) is a mapping of 'JY" into {T, I, F} such that Vt(P) (Us, ,.., u,J=I only if at least one u@~, and Vt(P) (..., d ,... )=I iff V*(P) (..., e ,... )=I for d, ee.Qt. Then VJPaI . . . an)= =VtW W&A ..-, V$(a,J). Thus statements about nonexistents may but need not be truth-valueless (I). For statements exclusively about existents, on the other hand, bivalency is assumed.1
Truth-functional compounds may be characterized as in Fisk [MAF 1501; viz., as usual when no I is involved, but with I for the compound whenever any component takes I. Quantifiers are given the narrower 'ontic' interpretation of free logic and of Thomason's Q3 [MLM 140(6)]; i.e., quantzjied variables are restricted in range to SBt at a given time t. (Wider quantification over all of @ as in Montague [P 1091 presents no insuperable problems, but is not needed here.) Thus, where V' is just like V except for the possibility that VJX)#V'JX)&~,