Sequence-of-Tense Phenomena
Hornstein (1990) argues that sequence-of-tense phenomena, which are illustrated in (1), can also be accommodated under the neo-Reichenbachian approach.
(1)

is ambiguous. On one reading, (1) is true if at some past time John heard that Mary was pregnant at a prior time. On the other reading, the time of being pregnant is the same as the time of hearing. The latter reading, where the temporal interpretation of the embedded Event time is dependent on the matrix Event time, is taken as an instance of the sequence-of-tense phenomenon. Hornstein claims that when a finite clause is embedded under a past time clause as in (1), the temporal dependency on the matrix Event time is signaled by a change in the surface form of the embedded verb. In (1) with the sequence-of-tense interpretation, the underlying tense of the embedded verb is actually the simple present, and the surface past tense form is just the morphological manifestation of the temporal dependency on the matrix Event time. Under Hornstein’s analysis, the temporal structure of (1) with the sequence-of-tense interpretation is represented by (2), where the sequence-of-tense (SOT) rule applies to the basic tense structure, yielding the derived tense structure.
(2)

In (2), the matrix S point (S1) is interpreted as denoting the utterance time. The sequence-of-tense rule links the embedded S point (S2) with the matrix E point (E1); S2 is interpreted as contemporaneous with E1. Since the embedded E point (E2) is associated with S2,E2 is also interpreted as contemporaneous with E1. This yields the correct interpretation; the time of being pregnant is the same as the time of hearing. Hornstein argues that the sequence-of-tense rule is optional with finite clauses. The non-sequence-of-tense analogue of (1) is given in (3).
(3) John heard that Mary is pregnant
Here, the surface present tense form is signals that the sequence-of-tense rule is not applied. Its tense structure is represented by the left side of the arrow in (2). Since the embedded S point (S2) is not associated with the matrix E point (E1) or anything else, the default rule requires S2 to be interpreted as denoting the utterance time. This yields the correct interpretation for (3), namely, Mary’s pregnancy is contemporaneous with the moment of utterance.
Hornstein (1990) argues that while the sequence-of-tense rule is optional with finite clauses, it is obligatory with infinitive clauses. This captures the fact that the temporal interpretation of an embedded infinitive clause always depends on that of the embedding clause. Let us first consider (4a–c) (cf. Baker 1989, 442).
(4)

Under Hornstein’s analysis, the temporal structure of (4a–c) is represented by (5).
(5)

In (16), the sequence-of-tense rule applies to the basic tense structure, yielding the derived tense structure. Note that in (5), the S point is lacking in the temporal structure of the embedded infinitive clause. Hornstein assumes that the S point is tied to a tense morpheme. In an infinitive clause, where the tense morpheme is lacking, the S point is absent as well. When the S point is absent in the embedded clause, the sequence of-tense rule associates the embedded R point (R2) with the matrix E point (E1). This is the case in (5), and R2 is interpreted as contemporaneous with E1. Since the embedded E point (E2) is associated with R2,E2 is also interpreted as contemporaneous with E1. In (4a), for example, this yields the correct interpretation that the time of being in the correct room is contemporaneous with the matrix Event time.
As pointed out by Baker (1989) and Enc¸ (1996), among others, there are cases where a different temporal interpretation is assigned to an infinitive complement.
(6)

I argue that the temporal structure of (6) is represented by (7).
(7)

In (7), the sequence-of-tense rule applies to the basic tense structure, yielding the derived tense structure, where the matrix E point (E1) is associated with the embedded R point (R2). Adverbial modification alters the basic tense structure in accordance with the meaning of an adverb. I argue that in the same way, the lexical meanings of verbs like hope, promise, want, and expect may alter the basic tense structure of their infinitive complement. These verbs assign a later time to their infinitive complement. They dissociate the embedded E point (E2) from the embedded R point (R2), shifting the former to the right of the latter. In (6a), for example, this yields the correct interpretation that the time of being in the correct room is in the future relative to the matrix Event time, that is, the time of hoping. Note that this dissociation of the embedded E and R points in the derived tense structure does not violate the CDTS. Baker (1989) also observes that adjectives like certain assign either the same or a later time to their infinitive complement.
(8)

The temporal structure of (8) is either (5) or (7). This analysis correctly captures the fact that the tense interpretation of an infinitive complement is determined by the lexical meaning of the matrix predicate.
I also argue that exactly like infinitive complements, subjunctive complements also obligatorily undergo the sequence-of-tense rule. As examples, consider (9a–b).
(9)

I argue that exactly like the matrix verbs in (6), verbs selecting subjunctive complements like demand, request, and insist assign a later time to their complement, dissociating the embedded E point (E2) from the embedded R point (R2) and shifting the former to the right of the latter. The temporal structure of (9a–b) is also represented by (7). In (9a), for example, this correctly yields the interpretation that the time of going there is in the future relative to the matrix Event time, that is, the time of demanding.