If the swu-construction contains an eventive predicate in the embedded clause, its cooccurring past tense induces a past-TO interpretation, irrespective of its TP: (11a) has a present-TP (as indicated by the matrix clause present tense), and (11b) has a past-TP (as indicated by the matrix clause past tense). Examples in (11) both receive a past-TO interpretation, according to which the eventuality denoted by the embedded clause (called a described eventuality, hereafter) is temporally located in the past of the TP. This past-TO reading is available only with embedded past tense.10

In the presence of present tense in the embedded clause, TO is constrained to future time. Again, this is independent of whether TP is present or past. In (12a), the whole course of the described eventuality is construed as extending over the future time while its onset immediately follows the utterance time. This future-TO interpretation also arises from (12b): the described eventuality is not in progress at the contextually-supplied past TP, but it is located in the future of the TP. For instance, in Context 1 of (12b), the speaker is talking about her past epistemic state: at the utterance time she knows that Chelswu did not participate in the competition, but she considered it epistemically possible at the time when she bought the suit.

If an eventive predicate is inflected for progressive aspect as well as present tense, TO is located in the present or future time of TP. In each example of (13), the described eventuality is located at the same time as the TP (as shown in Context 1) or the time following it (as shown in Context 2). This TO-interpretation distinguishes them from their corresponding swu-sentences that do not contain the progressive: their TOs are restricted to future time, as we have seen in (12). In either of the present-TO or future-TO contexts, the swu-sentence with past tense is not felicitous.

If the progressive is realized with past tense, TO is in the past time of TP, as exemplified in (14). This past-TO interpretation also arises from the swu-sentence which is inflected only with past tense in its embedded clause. However, unlike such examples in (11), the described eventualities of (14) are construed as being in progress at the past time.

This section shows how TO is determined in a swu-construction that contains a stative predicate in its embedded clause. Since statives cannot occur with the progressive, TO is determined solely by tense marking: (i) past-TO with past tense, and (ii) nonpast-TO with present tense.

First, the swu-sentences in (15) illustrate that embedded past tense realized with a stative predicate induces a past-TO interpretation, just like the corresponding sentences with an eventive predicate in (11). In all of the swu-examples in (11) and (15), a described eventuality is temporally located prior to the TP.

In the presence of present tense, a stative predicate results in a nonpast-TO interpretation. This is parallel to the case where an eventive predicate is inflected for present tense and progressive aspect, as we have seen in (13).

The literature has assumed that lexical and grammatical aspect affects temporal interpretation by constraining the temporal location of ET with respect to the RT (Kamp & Rohrer 1983; Partee 1984; Dowty 1986; Hinrichs 1986; Klein 1994, inter alia). The following examples illustrate such meaning contributions of lexical and grammatical aspect in Korean. The eventive predicate ku thakca-lul olmki- ‘move the table’ and the stative predicate pappu- ‘busy’ occur in (17) and (18), respectively. As we have already seen in the preceding sections, the progressive -koiss- is compatible with eventives as in (17b), but not with statives as in (18b):

In (17) and (18), the RT is constrained by the time adverb ecey ‘yesterday’, but its exact temporal location is contextually determined (Partee 1984; Hinrichs 1986; Dowty 1986; Kamp & Reyle 1993, inter alia), e.g. in the above discourse context, the RT is the time at which the speaker met Chelswu in the library yesterday. Crucially, (17a) and (18a) have different temporal interpretations in terms of the ET-RT relationship. (17a) has a perfective interpretation, according to which the event of Chelswu’s moving the table has a culmination point within the RT. By contrast, (18a) receives an imperfective interpretation, i.e. the described state has no change within the RT, but it holds at the larger interval including the RT. This imperfective interpretation is available with eventive predicates as well, if they occur with the progressive -koiss-, as shown in (17b): the event of Chelswu’s moving the table holds at the larger interval including the RT.

This semantic function of the progressive has been observed in the literature (e.g. Vlach 1981; Moens & Steedman 1988; Parsons 1990; Kamp & Reyle 1993; De Swart 1998). Along the same lines, I analyze -koiss- as a kind of imperfective aspect, as given in (19a).12 The eventive untensed sentence radical in (19b) is unspecified in terms of the RT-ET relationship, but the ET of the described event is constrained to include the RT by -koiss-, as given in (19c):

Similarly, I assume that the perfective meaning (ET⊂RT) of examples like (17a) arises from a perfective aspect, which is phonologically null. It combines with an eventive untensed sentence radical, as follows:

Stative predicates have an imperfective meaning (RT⊆ET) by themselves, as we have seen in (18). I analyze it as being lexically encoded in the meaning of stative predicates, as follows:

While aspect relates ET and RT, tense is responsible for the temporal location of RT with respect to some evaluation time, such as the UT in a matrix clause. The examples in (22) illustrate that past tense locates RT prior to the UT, irrespective of the stativity of a predicate. In contrast, present tense constrains RT to be located in the nonpast time of the UT, as shown in (23).

These temporal meanings of Korean tenses are formalized in (24).13

In (24), I assume that RT is not existentially bound (cf. Prior 1967), but its exact temporal location is contextually determined, following dynamic semantic theories of temporal interpretation (e.g. Partee 1984; Hinrichs 1986; Dowty 1986; Kamp & Reyle 1993).

In Kratzer’s (1981; 1991) modal theory, a variety of modal flavors that arise from a single expression like must are not attributed to lexical ambiguity. Its core claim is that the modal flavor is contextually determined by two conversational backgrounds, i.e. Modal Base (MB) and Ordering Source (OS). The former first gives a set of accessible worlds to a modal sentence, and then the latter imposes a particular ordering among the accessible worlds. For instance, the epistemic modal reading of (25a) arises from the epistemic MB and the doxastic/stereotypical OS, and the deontic modal reading of (25b) arises from the circumstantial MB and the deontic OS:

(25a) asserts that in all worlds in which all of the facts given by the epistemic MB hold, and which are most highly ranked according to the OS, John has the flu. Similarly, (25b) says that among the worlds in which all of the facts in the circumstantial MB hold, the relevant rules rank most highly those worlds in which John goes to jail. The point here is that the modal expression must does not have two separate lexical entries for its availability of epistemic and deontic readings, but its modal readings are contextually determined by the two conversational backgrounds.

In this paper, I follow Kratzer’s assumption on a range of modal readings that arise from a single expression. I analyze the expression swu as encoding a modal meaning, but I do not postulate separate lexical entries for the range of modal readings available with the swu-construction (cf. (Mun 2016; Lee 2017). The translation of swu is given in (26), which incorporates Portner’s (1998) BEST-function:

According to (26), among the worlds in which all of the facts given by the MB hold, at least one of the worlds most highly ranked by the OS is one in which the prejacent proposition p of the swu-sentence is true.

I first provide the derivation of a swu-sentence that allows all three modal readings. The relevant example in (12) is reproduced below. I assume that examples like (27) contain a phonologically null perfective aspect, as discussed in the preceding section.

The compositional derivation of (27) is given in (28); the adnominal marker -(u)l and the matrix clause verb iss- ‘exist’ are assumed not to make any semantic contribution, and are thus analyzed as an identity function. The untensed sentence radical is first taken by perfective aspect, and then by present tense, as shown in (28a) and (28b), respectively. The adnominal marker -(u)l combines with the tensed embedded clause as in (28c), and the resulting phrase is taken by swu which encodes the modal meaning as in (28d). Next, the swu-phrase is taken by the matrix clause predicate iss- ‘exist’ as in (28e), and then present tense combines with the resulting untensed sentence radical as in (28f). Finally, the declarative mood in (28g) combines with the tensed sentence radical, which results in the final truth-conditional translation in (29).14

The two free variables t′ and t″ in (29) are existentially bound in discourse context.

According to the truth-conditional meaning in (29), the conversational backgrounds are evaluated in the nonpast time of the UT due to the matrix clause present tense. However, crucially, this compositionally calculated temporal interpretation is pragmatically restricted as well. Note that both epistemic and circumstantial modal bases cannot be interpreted with respect to the future time of the UT. This is because at the time of utterance, we cannot tell the future state of our knowledge or circumstances related to the described eventuality. This restricts the TP to the present time, yielding a present-TP interpretation. When it comes to the TO-interpretation, the ET of the described event is located within the future time of the UT. This is because the RT is in the nonpast time of the UT due to the embedded present tense, and the perfective aspect combining with the eventive predicate locates the ET within the RT. This correctly captures the future-TO interpretation of (27).

When past tense occurs in the embedded clause, a swu-sentence receives a past-TO interpretation, irrespective of the stativity of the embedded predicate. Among the relevant examples such as (11), (14), and (15), I repeat the swu-sentence below that contains an eventive predicate with past tense in the embedded clause. Assuming that sentences like (30) also contain a phonologically null perfective aspect, its semantic derivation is the same as the corresponding sentence with present tense in (27), except that the RT of the described eventuality is in the past of the UT due to the embedded past tense. Its final truth-conditional translation is provided in (31).

In (31), TP is in the nonpast time of the UT, but again, it is pragmatically adjusted to be cotemporal with the UT for the same reason as (29); that is, we cannot determine the truth value of the prejacent from the perspective of our future epistemic or circumstantial state. This yields a present-TP interpretation. The embedded past tense locates the RT prior to the TP, and the perfective aspect constrains the ET of the described event within the RT. This correctly results in the past-TO interpretation.

A swu-sentence with progressive aspect is also semantically derived in the same fashion as its corresponding sentence with perfective aspect. The only difference in the temporal interpretation is attributed to the progressive, by which the RT of the embedded clause is the same as or within the ET. The relevant example in (13a) and its final truth-conditional translation are given below:

The TP of (33) is also pragmatically constrained to the UT, i.e. the present-TP interpretation. The nonpast-TO is determined by interactions between the embedded present tense and the progressive aspect. The present tense restricts the RT of the described eventuality in the nonpast time of the UT, but its exact temporal location is determined by discourse context. The ET of the described eventuality extends over the RT due to the progressive. This correctly captures the nonpast-TO interpretation, where TO is located at or after the UT.

Exactly the same temporal interpretation arises from a swu-sentence with a stative predicate, but its imperfective interpretation is attributed to the lexically encoded meaning of the stative predicate. The relevant example in (16a) is repeated in (34), along with its final truth-conditional translation.

In (35), all the temporal reference intervals are located in the same way as in (33); TP is cotemporal to the UT, and the TO is located in the nonpast time of the TP.

This section has shown how the TP and TO interpretations of the swu-sentences are compositionally computed by interactions between tense and aspect. I provided a compositional derivation according to which swu-sentences with three modal readings receive a future-TO interpretation while their cooccurrence with stative predicates, progressive aspect, or past tense results in a past-TO or nonpast-TO interpretation. I propose that the availability of the modal readings in the swu-sentence is pragmatically determined by the temporal constraints on different kind of modal bases, as will be discussed in the next section.

Condoravdi (2002) introduces the diversity condition to account for what she calls a metaphysical interpretation in English modal sentences like She might have won the game. She argues that a metaphysical interpretation is available only with the description of a future eventuality since the truth value of its prejacent is not yet settled to be true or false. Conversely, with a past or present eventuality, its prejacent proposition is metaphysically settled at the time of TP, and thus the metaphysical interpretation is pragmatically ruled out. Condoravdi’s (2002) diversity condition is given below:

According to (36), there should be at least one world in which a prejacent proposition p is true, and another world in which it is false.

Condoravdi (2002) applies the diversity condition to the temporal restrictions on metaphysical modal bases to non-future TOs, drawing on English modal sentences with might. Rullmann & Matthewson (2018) show that the same TO-restrictions are extensively observed with circumstantial modals in other languages, and claim that the diversity condition suffices to account for their TO-restrictions.15 I argue that the non-epistemic readings with non-Future TOs are excluded in the Korean swu-construction for the same reason: when a modal utterance with swu is contextually construed as involving a circumstantial modal base, the dynamic (ability) and the priority (permission) interpretations can arise unless the TO is non-future, which would violate the Diversity Condition.

In the preceding section, we have seen how TOs are compositionally determined in the swu-sentences. The swu-sentence in (27) is available with the non-epistemic readings as well as the epistemic reading. I argue that this is because it receives a future-TO interpretation. In contrast, when TO is determined as past or present, the dynamic (ability) and the priority (permission) readings are pragmatically ruled out due to the diversity condition on the circumstantial modal base. More specifically, the occurrence of past tense in swu-examples like (30) constrains TO to be in the past time of the TP, which in turn violates the diversity condition. This eventually leads to the unavailability of the non-epistemic readings in (30).

The modal readings of the swu-sentence with progressive aspect or a stative predicate can be accounted for in terms of the diversity condition as well. The preceding section has shown that the TOs of such swu-sentences are correctly computed to be located in the nonpast time of the TP. In particular, due to the aspectual meaning of the progressive and a stative predicate, the ET of a described eventuality is construed as extending over its RT. This engenders an implicature that the described eventuality holds at the TP as well, unless discourse context specifies that the ET of the described eventuality is restricted only to the future time of the TP. This implicature causes the diversity condition to be violated, which in turn induces the infelicity of non-epistemic readings in swu-sentences occurring with the progressive or a stative predicate as in (32) and (34). Instead of such an imperfective swu-sentence, the corresponding perfective swu-sentence like (27), which does not pose any problem with the diversity condition, is preferred for non-epistemic readings.16

Unlike non-epistemic readings, there is no TO-restriction on epistemic readings. This is because the truth value of a prejacent proposition is not settled in epistemic modal bases, irrespective of whether the TO is future or non-future. In other words, when we utter an epistemically modalized sentence to describe a past or present eventuality, its prejacent proposition can still be true or false. Thus, the effect of the diversity condition is not observed in epistemic readings.

With regard to the TP of epistemic modals, a majority of previous studies have assumed that it is necessarily keyed to the utterance time, and thus a past perspective is not expressible with epistemic modals in natural language sentences (e.g. Groenendijk & Stokhof 1975; Picallo 1990; Iatridou 1990; Abusch 1997; Condoravdi 2002; Stowell 2004; Hacquard 2006; 2011). However, some authors like von Fintel & Gillies (2008) argue that a past-TP interpretation is actually available in natural language sentences, as illustrated with the following example:

von Fintel & Gillies (2008) argue that the modal utterance in (37) expresses the speaker’s past epistemic perspective on the truth value of the prejacent proposition.

In line with von Fintel & Gillies’s (2008) view, Rullmann & Matthewson (2018) develop a theory of modal-temporal interaction, according to which there is no grammatical TP-restriction on an epistemic modal base. They empirically support the theory by investigating the temporal interpretation of modal sentences in languages like Dutch, English, Gitksan (Tsimshianic), and St’át’imcets (Lillooet Salish). Specifically, they argue that their proposal is supported by Dutch, wherein TP is overtly expressed by tense marking on epistemic modals, as illustrated below:17

In (38a), the present tense realization with the necessity or the possibility modals results in a present-TP interpretation. In contrast, if the modals are marked with past tense, they give rise to a past-TP interpretation as in (38b).

It is noteworthy that the Korean swu-construction exhibits the same pattern as Dutch modal constructions. In the swu-construction, TP is determined by the matrix clause tense which scopes over the modal swu. Recall that the modal meaning is encoded only in the semantics of swu, and the semantic contribution of the matrix clause predicate iss- ‘exist’ is nothing but an identity function. In other words, the tense realization on the matrix clause predicate in the swu-construction is analogous to the overt tense markings on Dutch modals. Given the parallels in Dutch modal constructions and the Korean swu-construction, I argue that the empirical patterns observed with the latter provide further support for Rullmann & Matthewson’s (2018) claim that there should not be any grammatical restrictions on the past-TP epistemic readings.

Although expressing a past epistemic perspective is not grammatically constrained in the swu-sentence, it is often dispreferred over other types of Korean sentences that express a past epistemic perspective. For example, (39) contains the attitude verb sayngkakha- ‘think’ with past tense. It is preferred over the simple swu-sentence (39b) in the given context.

Rullmann & Matthewson (2018) account for why expressing a past epistemic perspective with English sentences containing modal auxiliary verbs are often dispreferred in some discourse context in light of various factors. Particularly, they attribute the empirical patterns to the fact that (i) English sentences with modal auxiliaries do not have overt markers for TP (unlike Dutch modal sentences), and (ii) the conversational backgrounds of the modal are not-at-issue. A swu-sentence is more like a Dutch sentence in terms of overt TP-marking, but the second point still holds for the Korean swu-construction. When we express the possibility or necessity of a proposition in view of our knowledge, we typically use the utterance time as our reference point for the time of our knowledge. While it is also possible for us to express a past epistemic perspective, this non-default past perspective cannot be easily established without any particular support of discourse context. In order to ensure that the perspective expressed is a non-default one, we tend to use other expressions or constructions that explicitly mark the non-default TP. This explains why using the attitude verb sayngkakha- ‘think’ with past tense in the matrix clause is preferred over its corresponding swu-sentence in (39).