Binary tense theory claims that the mental representation of tense is based on the three binary distinctions in (114). Languages differ in the means used to express these oppositions: this can be done within the verbal system by inflection and/or auxiliaries, but it can also involve the use of adverbial phrases, aspectual markers, pragmatic information, and so on; cf. Verkuyl (2008).

Verkuyl (2008) claims that Dutch expresses all the oppositions in (114) in the verbal system: [+past] is expressed by inflection, [+posterior] by the verb zullenwill, and [+perfect] by the auxiliaries hebbento have and zijnto be. This leads to the eight-way distinction between tenses in Table 1, which is used in most Dutch grammars.

		present	past
synchronous	imperfect	present Ik wandel. I walk	simple past Ik wandelde. I walked
	perfect	present perfect Ik heb gewandeld. I have walked	past perfect Ik had gewandeld. I had walked
posterior	imperfect	future Ik zal wandelen. I will walk	future in the past Ik zou wandelen. I would walk
	perfect	future perfect Ik zal hebben gewandeld. I will have walked	future perfect in the past Ik zou hebben gewandeld. I would have walked

However, our discussion in Sections 1.5.2 and 1.5.4 departs from Verkuyl’s original claim that zullenwill can be used as a future auxiliary and argues that it is an epistemic modal verb in all its uses. We have further argued that it is only due to pragmatic considerations that utterances with zullen are sometimes interpreted with a future time reference; cf. also Broekhuis & Verkuyl (2014). If this is correct, the Dutch verbal system only expresses the binary features [±past] and [±perfect], and thus does not make an eightfold but only a fourfold tense distinction, as in Table 2. Since zullen is no longer used to define a separate set of future tenses, posteriority must be expressed by using e.g. adverbials such as morgentomorrow, as in Jan vertrekt morgenJan will leave tomorrow.

	present	past
imperfect	simple present Ik wandel/Ik zal wandelen. I walk/I will walk	simple past Ik wandelde/Ik zou wandelen. I walked/I would walk
perfect	present perfect Ik heb gewandeld/ Ik zal hebben gewandeld. I have walked/I will have walked	past perfect Ik had gewandeld/ Ik zou hebben gewandeld. I had walked/I would have walked

The revised view of the verbal tense system of Dutch implies that utterances in simple present/past should in principle be able to refer to any subinterval within present/past-tense interval i. This is illustrated in Figure 1, where the dotted line indicates the time line, for different possible worlds in which simple present/past sentences like Ik wandelI am walking and Ik wandeldeI walked are predicted to be true; note that the number of possible worlds is in principle infinite and that we have simply made a selection that suits our purpose. World 1 represents the situation in which eventuality k precedes speech time n or virtual speech-time-in-the-past n', i.e. the situation in which k is located in the actualized part ia of present/past-tense interval i. World 3 represents the situation in which k follows n/n', i.e. in which it is located in the non-actualized part i◊ of present/past-tense interval i. World 2, finally, represents the situation in which k occurs at n/n'. We have not yet mentioned time interval j, but its function will become clear shortly.

The representation of perfect-tense examples like Ik heb gewandeldI have walked and Ik had gewandeldI had walked in Figure 2 is virtually identical to that in Figure 1; the only difference is that eventuality k is presented as a completed autonomous unit within present/past-tense interval i, as indicated by the vertical line at the right edge of k.

The proposal outlined above overgenerates considerably. For example, it predicts that any simple-present sentence could be used to refer to the situation depicted in world 1 in Figure 1, whereas we would use a present perfect in most cases. However, Section 1.5.4.1 has shown that the prediction is actually correct in the more specific situation depicted in Figure 1, in which the speaker has a knowledge gap about the state of affairs in the actual world prior to speech time n (indicated by the fact that the split-off point of the possible worlds precedes n); example (115) can be used if the speaker does not know whether Els has already finished reading.

In the absence of such a knowledge gap, example (115) is infelicitous. The reason for this is pragmatic in nature. If the speaker knows that eventuality k precedes n, he can present k as a discrete, bounded unit that has been completed within the actualized part of time interval ia of present-tense interval i: since this can be described more precisely by the present perfect, Grice’s °maxim of quantity prohibits the use of the less informative simple present (cf. Sections 1.5.4.1, sub II, and 1.5.4.2, sub II, for further discussion). This reasoning rests crucially on the assumption that the tenses in Table 2 have a specific default interpretation: for example, simple present-tense clauses refer by default to the situation depicted in world 2 in Figure 1, while present perfect clauses refer by default to the situation depicted in world 1 in Figure 2; reference to the situations in the alternative worlds is possible, but only if the context provides special clues indicating that this is indeed what the speaker intends.

The following subsections will show that temporal and locational adverbials play an important role in providing such clues. The discussion will pay particular attention to how their status as clause adverbial or VP adverbial affects their meaning contribution. Subsection II begins with a discussion of temporal adverbials; it adopts the hypothesis put forward in Sections 1.5.4.1, sub III, and 1.5.4.2, sub III, that while temporal VP adverbials modify eventuality k directly, temporal clause adverbials do so indirectly by modifying the so-called present j of k, i.e. the subdomain of present/past-tense interval i within which k must be located and which is taken to be identical to i in the default case (as indicated in the two figures above). Subsection III will show that something similar holds for locational adverbials.

This subsection discusses the semantic contribution of the temporal adverbials to the meaning of the clause. We will adopt the standard assumption from Section 8.2.1 that VP adverbials are modifiers of the proposition expressed by the lexical projection of the verb. In terms of the tense representations in Figure 1 and Figure 2, this amounts to saying that VP adverbials are modifiers of an eventuality k. This is obviously true for durational adverbials such as drie uur (lang)for three hours in (116), which simply indicate the duration of k.

This is also true for punctual adverbials such as om 15.00 uurat 3 p.m. in (117), which locates the eventuality of Jan’s departure at 3 p.m. in the non-actualized part i◊ of present-tense interval i (where the choice of i◊ is due to the use of the simple present for the pragmatic reason discussed in Subsection I). The default interpretation of (117a) is that Jan will leave at 3 o’clock today, but this can easily be overridden by contextual factors; this is especially clear in example (117b), in which the clause adverbial morgentomorrow is used to indicate that Jan’s departure will take place at 3 o’clock on the first day following speech time n. Note that we have added the modal adverb waarschijnlijkprobably in order to distinguish between VP and clause adverbials; here we will ignore its semantic distribution (i.e. the introduction of possible worlds) in our discussion for the sake of simplicity.

The simplest way to account for the meaning contribution of the clause adverbial morgentomorrow in (117b) is to assume that it modifies the present j of k: representation (118) shows that j is taken to be identical to i by default, but that the use of the temporal clause adverbial restricts j to a subdomain of i; for ease of presentation we have marked the non-default interpretation of j (and k) with a prime.

If we assume that sentence (117a) is uttered at noon, as indicated in representation (118), its default interpretation would be derived as follows: the present j of k is taken by default to be identical to the present-tense interval i. Since the simple present is again restricted to the non-actualized part i◊ of present-tense interval i for pragmatic reasons, the sentence refers to eventuality k, since this is the first occasion after speech time n that fits the description om 15.00 uur (indicated by the number 3 in representation (118)). Note in passing that the sentence would refer to k' by default if it were uttered at 10 p.m., since this would then be the first occasion after speech time n that fits the description om 15.00 uur. Representation (118) also shows that the default interpretation of (117a) is overridden in (117b) by the clause adverbial morgentomorrow, which restricts the present of the eventuality to time interval j': as a result, sentence (117b) can only refer to k'.

Now consider the present prefect examples in (119). If we assume that sentence (119a) is uttered in the evening, its default interpretation would be that eventuality k occurred earlier in the day. The examples in (119b&c) show that this default reading can easily be overridden by adding a clause adverbial such as gisterenyesterday or morgentomorrow.

The simplest way to account for the meaning contribution of clause adverbials is again to assume that clause adverbials modify the present j of k; this is shown in representation (120), in which the various non-default interpretations of j and k are again indicated by primes.

The default interpretation would be derived as follows. First, the present j of the eventuality is taken to be identical to present-tense interval i. Since Subsection I has shown that the present perfect is restricted for pragmatic reasons to the actualized part ia of present-tense interval i, the sentence refers to eventuality k, since this is the first occasion preceding speech time n that fits the description om 15.00 uur; note in passing that the sentence would refer by default to k' if it were uttered at 8.00 a.m., since that would then be the first occasion prior to speech time n that fits the description om 15.00 uur. The default interpretation of (119a) is overridden in (119b) by the clause adverbial gisterenyesterday, which restricts the present j to the time interval j': as a result, sentence (119b) can only refer to k'. Similarly, the clause adverbial morgentomorrow in (119c) overrides the default interpretation of (119a) and restricts the present j to time interval j'': as a result, sentence (119c) can only refer to k''.

Representation (120) suggests that the VP adverbial om 15.00 uur locates the completion of the eventuality precisely at 3 p.m. However, this is not what this adverbial actually does: instead, it refers to a time at which the resulting state of eventuality k is true. This can be seen from examples such as (121), based on Janssen (1983), in which the adverbial al indicates that the completion of the eventuality of Jan’s departure took place before 3 p.m. This shows that the interpretations given in (120) are default readings of the modified structures in (119b&c), which can be overridden by adverbial modification (here: by al).

The examples discussed so far have all been in the present tense, but the account can also be applied to corresponding past tense cases (which will not be demonstrated here). We can conclude that the semantic interpretation of clauses with two temporal adverbials finds a natural accommodation and explanation in binary tense theory. This is a strong argument for binary tense theory, since Janssen (1983: fn.1) has shown that such cases are highly problematic for the Reichenbachian approach.

Binary tense theory also explains the strict word-order restriction that applies to the two adverbials. First, consider the examples in (122), which show that the adverbials morgentomorrow and om 15.00 uurat 3 p.m. can be used freely either as a VP adverbial or as a clause adverbial.

However, when the two adverbials co-occur in a single clause, there are severe restrictions on their distribution: the examples in (123) show that morgentomorrow must precede the modal adverbial waarschijnlijkprobably, while om 15.00 uur must follow it. Note in passing that we are not discussing cases such as Jan gaat morgen om 15.00 uur waarschijnlijk naar de bioscoop, in which the phrase morgen om 15.00 uur constitutes a single clause adverbial, as can be seen from the fact that it can occur in sentence-initial position as a whole: Morgen om 15.00 uur gaat Jan waarschijnlijk naar de bioscoop.

The use of the dollar sign in (123b) indicates that the reason for the unacceptability of this example is not syntactic but semantic in nature: it is simply incoherent. Since j contains eventuality k, the modifier of j must refer to a time interval which also contains the time (interval) indicated by the modifier of k. This is indeed the case in (123a), since morgen refers to a time interval which contains a point in time indicated by the adverbial om 15.00 uur, but this is not the case in (123b). For the same reason, an example such as (124) will only be felicitous if the addressee knows that there is a meeting the next day; if not, the addressee will correct the speaker or ask for more information about this meeting (Uh .. what meeting?).

It is often difficult to determine the exact semantic difference between using an adverbial as a VP adverbial or as a clause adverbial. Consider the simple present examples in (125):

Many speakers consider these examples to be near-synonyms, since they both refer to a dancing event on Saturday, but the semantic representations assigned to them under our current assumptions are quite different. In (125a) the present j of k is simply assigned the default reading, according to which it is identical to present-tense interval i; for pragmatic reasons, eventuality k is located in the non-actualized part i◊ of this interval and thus on the first Saturday after speech time n; cf. representation (126a). The interpretation in (126b) is more indirect: the present j of k is first restricted to the first Saturday in i◊, and then eventuality k is located in this restricted time interval; cf. representation (126b). Note that the continuous line below k refers to the time interval to which Saturday refers in (126a), but in (126b) it refers to the duration of k.

The difference in meaning can be highlighted by means of the scope paraphrases introduced for the detection of clause adverbials. While (125a) can be paraphrased as Het is waarschijnlijk zo dat Jan zaterdag gaat dansenIt is probably the case that Jan will go dancing on Saturday, example (125b) can be paraphrased as Het is zaterdag waarschijnlijk zo dat Jan gaat dansenOn Saturday it is probably the case that Jan will go dancing. The difference in meaning becomes even more obvious in examples such as (127) with the frequency adverb altijdalways.

Frequency adverbs such as altijdalways express that we are dealing with a recurring eventuality k in present/past-tense interval i. The VP adverbial op zaterdagon a Saturday in (127a) provides more precise information about the locations of k; it indicates that k occurs only (but not necessarily) on Saturdays, as in representation (128a), where s stands for Saturday. The clause adverbial op zaterdagon Saturdays in (127b), on the other hand, indicates that it is an inherent property of Saturdays that k occurs (although it may also occur elsewhere); cf. (128b).

Representation (128a) also shows that it is not necessary for k to occur on every Saturday for (127a) to be true, which is necessary for example (127b) to be true. Representation (128b) also shows that (127b) allows k to occur on other days, which would make (127a) false. This suggests that the examples actually express material implications: example (127a) can be paraphrased by (129a), while (127b) can be paraphrased by (129b).

This section has discussed a number of phenomena that find a natural account within the binary tense approach. Since temporal modification is still a relatively unexplored area in tense theory, we must leave it to future research to investigate the extent to which binary tense theory can be exploited in this area (although the reader may find some more information on this in Section 1.5.4). Subsection III now continues by showing that clauses with two locational adverbials can receive a similar account as clauses with two temporal adverbials.

This subsection discusses the semantic contribution of locational adverbials to the meaning of the clause. Again, we adopt the standard assumption from Section 8.2.1 that VP adverbials are modifiers of the proposition expressed by the lexical projection of the verb. In terms of tense representations like those given in Figure 1 and Figure 2, this amounts to saying that VP adverbials are modifiers of eventuality k. This claim is obviously true for example (130a), which simply locates the eventuality of Jan staying in a hotel in the present-tense interval i. However, it is less clear what the semantic contribution of the clause adverbial in Amsterdam in (130b) is.

Suppose that the sentences in (130) are used in a conversation about Jan, who is currently on vacation. The default reading of example (130a) would then be that the eventuality of Jan staying in a hotel occurs at speech time n, as depicted in (131): the present j of k is taken to be identical to the present-tense interval i, and k is taken to co-occur with speech time n.

Example (130b) would instead express that the eventuality of Jan staying in a hotel is restricted to the period in which he is visiting Amsterdam. This can be accounted for by assuming that the locational clause adverbial overrides the default interpretation in the same way as a temporal clause adverbial, namely by restricting the present j of the eventuality. This is shown in representation (132), where k is the eventuality of Jan being on vacation and k' is the eventuality of Jan staying in a hotel.

The discussion above has shown that locational and temporal adverbials are similar in that they modify the eventuality k when they are used as VP adverbials, but the present j of k when they are used as clause adverbials. As with temporal adverbials, the two uses of locational adverbials are not always easy to distinguish. Consider the examples in (133).

Many speakers consider these examples to be near-synonyms, since they both refer to a dancing event in Amsterdam, but the semantic representations assigned to them under our current assumptions are quite different. In (133a), the present j of k is simply assigned the default reading according to which it is identical to present-tense interval i. For pragmatic reasons, eventuality k is located in the non-actualized part i◊ of this interval; cf. representation (134a), which is essentially the same as (126a). The interpretation in (133b) is more indirect: the present j of k is first restricted to the first occasion in i◊ that Jan will be in Amsterdam, and then eventuality k is located in this restricted time interval; cf. representation (134b), which is essentially the same as (126b).

The difference in meaning can also be seen in the scope paraphrases. While (133a) can be paraphrased as Het is waarschijnlijk zo dat Jan in Amsterdam gaat dansenIt is probably the case that Jan will go dancing in Amsterdam, example (133b) can be paraphrased as Het is in Amsterdam waarschijnlijk zo dat Jan gaat dansenIn Amsterdam it is probably the case that Jan will go dancing. The difference in meaning again becomes more conspicuous in examples such as (135) with the frequency adverb altijdalways.

The frequency adverb altijd is used to express that we are dealing with a recurring eventuality k in the present/past-tense interval i. The VP adverbial in Amsterdam in (135a) provides more precise information about the location of k; it indicates that k only (but not necessarily) takes place in Amsterdam, as in representation (136a), where A stands for in Amsterdam. The clause adverbial in Amsterdam in (135b), on the other hand, indicates that it is an inherent (but not exclusive) property of Jan’s visits to Amsterdam that k occurs; cf. (136b).

Representation (136a) also shows that it is not necessary for k to occur on every occasion that Jan is in Amsterdam for (135a) to be true, while this is needed to make example (135b) true. Representation (136b) further shows that (135b) allows k to also occur in other places, while this would make (135a) false. This suggests that the examples actually express material implications: example (135a) can be paraphrased by (137a), while (135b) can be paraphrased by (137b).

The discussion above has shown that locational clause adverbials have more or less the same semantic impact as temporal clause adverbials. Locational and temporal clause adverbials can also co-occur. The examples in (138a&b) are simply repeated from above, showing that op zaterdag and in Amsterdam can both be used as clause adverbials; example (138c) shows that the two can also be combined. Examples such as (138c) can be seen as material implications with two conditions, (P & Q) → R: “if Jan is in Amsterdam and if it is Saturday, Jan goes dancing”.

The previous subsections have shown that clauses with multiple temporal/locational adverbial phrases find a natural accommodation and explanation in binary tense theory: used as VP adverbials, they modify the eventuality expressed by the lexical domain of the clause; used as clause adverbials, they modify the present of that eventuality. We have seen that the difference between the resulting interpretations can be made more prominent in the presence of the frequency adverb altijd; the interpretation can then be paraphrased by means of material implications, as illustrated by the example in (139), repeated from Subsection II.

We like to note that a similar semantic effect was found in Section A28.3, sub III, with respect to the distribution of supplementives. This would suggest that our proposal for temporal and locational adverbials could be extended to other adverbials and adjuncts in general. Since this proposal opens up a new research program, we leave this matter for future research.