Past time reference in a language with optional tense

In this paper, I analyze the verbal suffix -uŋil in Washo as an optional past tense. It is optional in the sense that it is not part of a paradigm of tenses, and morphologically tenseless clauses are also compatible with past time reference. Specifically, I claim that -uŋil is the morphological exponent of a tense feature [past], which presupposes that the reference time of the clause, denoted by a temporal pronoun, precedes the evaluation time. Meanwhile, morphologically tenseless clauses lack a semantic tense restricting the value of the reference time pronoun. In comparing this analysis with one containing a covert non-future tense in morphologically tenseless clauses, I show that the range of empirical contexts that distinguish these analyses is quite narrow. However, I offer a novel argument against a covert tense analysis based on the lack of Maximize Presupposition effects. Crucially, the fact that -uŋil does not form a paradigm of tenses results in a failure for Maximize Presupposition to apply. The proposed analysis places cross-linguistic variation at the level of the paradigm of tense features, namely whether they are present or absent, and if present, whether obligatorily so. This case study from Washo thus reveals what a language where tense features are optional can look like, and more generally contributes to the growing body of literature on cross-linguistic semantics devoted to uncovering the ways in which temporal interpretation can be achieved in natural language.


Optional tense?
Much work on cross-linguistic variation in tense systems has been devoted to the analysis of morphologically tenseless languages, i.e., languages that lack grammatical markers restricting the location of the reference time of a clause. 1 Meanwhile, other cross-linguistic work has focused on variation between languages that have morphological tense systems. 2 The picture that emerges from this work, at least implicitly, is one where there is a dichotomy between tensed and tenseless languages. On the one hand there are languages with tense paradigms where tenses are obligatory in finite clauses. On the other hand, there are languages that lack such morphemes altogether. In other words, tense appears to be an all-or-nothing category.
Such a state of affairs does not follow from a purely semantic perspective. Indeed, as work on temporal reference in both tensed and tenseless languages has shown, there is a variety of means by which the temporal reference of a clause may be identified, including tenses, but also temporal adverbs and contextual factors (see Tonhauser 2015 for a recent overview). Consider (1). The adverb yesterday locates the reference time on the day prior to speech time. The past tense on the verb dance is required by the morpho-syntax of English in this environment, even though in the presence of the adverb its semantic contribution is seemingly superfluous.
That is, from a semantic point of view, the past tense in (1) is not required to determine the reference time of the clause. Thus, in principle, we might expect to find languages that have morphological tenses that are not obligatory in cases where the reference time can be identified through other means, linguistic or contextual.
Such a possibility has recently been discussed in the typological work of Plungian and van der Auwera (2006). These authors identify several of the world's languages where the morphological marking of past temporal reference is optional. The optional tense markers in such languages tend to appear sporadically in discourses with past temporal reference, and morphologically tenseless clauses can also have a past interpretation. Not belonging to a full-fledged paradigm of tenses, these optional tense markers have a distribution quite different from tenses in languages like English. Plungian and van der Auwera nevertheless argue that such morphemes should be considered true tenses. This finding raises several interesting questions for the formal analysis of tenses, including the following: Do optional tenses have the same inter-pretation as tenses in languages with full, obligatory paradigms?; What does it mean for a tense to be optional?
In this paper, I aim to address these questions by investigating past temporal reference in Washo (Hokan/isolate; California and Nevada). In Washo, the verbal suffix -uNil is compatible only with past temporal reference, but morphologically tenseless clauses are also compatible with past temporal reference (Jacobsen 1964(Jacobsen , 1996. For instance, the morphologically tenseless clause in (2) can have either a past or present temporal interpretation, 3 whereas (3) can only have a past interpretation. 4,5 (2) háPaši ∅-haPaš-i 3-rain-ind 'It is raining.' / 'It rained.' / 'It was raining.' (3) háPašuNili ∅-haPaš-uNil-i 3-rain-past-ind 'It rained.' / 'It was raining.' I argue for an analysis of -uNil as a past tense, with a semantics parallel to that of past tense in languages like English. 6 That is, the first question posed above receives a positive answer: past tense in Washo and English have the same interpretation, despite the past tense in Washo being optional. 7 I furthermore argue that morphologically tenseless clauses such as (2) lack a tense feature that semantically restricts the location of the reference time. Thus, in response to the second question posed above, optional tense marking in Washo corresponds to optionality in whether a tense feature is present. In clauses with -uNil, there is a semantic tense feature [past]; in tenseless clauses, there is no tense feature.
In arguing that morphologically tenseless clauses contain no tense feature, I explicitly compare my analysis with one where a phonologically covert non-future tense feature is posited in morphologically tenseless clauses, following Matthewson (2006) for St'át'imcets. Such an analysis has initial plausibility because, as previewed in (2), 3 Morphologically tenseless clauses may also receive future interpretations in certain contexts; see Sect. 2.2. 4 Examples (2) and (3) are presented 'out of context' for the purposes of exposition; further data used in this paper to substantiate the claims made are forthcoming in later sections. 5 A finite clause in Washo consists minimally of a verb stem inflected for person (prefixes) and a category that I refer to in this paper as mood (suffixes). Verb stems themselves may be morphologically complex, and may also be marked with negation, causative, or aspectual morphology (Jacobsen 1964(Jacobsen , 1996. For the purposes of this paper, I will only use verb forms in the independent mood (-i), except where the dependent mood (-aP) is syntactically required, such as in the complement of propositional attitude verbs, and in temporal when-clauses; -aP is also the default mood marker in narrative contexts (Jacobsen 1964). I will also generally avoid using examples including aspectual morphology to control for the temporal effects of aspect. As indicated in the translations of (2) and (3), aspectually unmarked verb forms can receive perfective or imperfective interpretations. Orthographic and glossing conventions are listed in the appendix. 6 A formal framework for making this claim precise will be made explicit in Sect. 1.3. 7 In this respect, I concur with Cable (2016) in his recent analysis of a similar phenomenon in Tlingit; more on this in Sect. 6. morphologically tenseless clauses are restricted to past or present interpretations in most contexts. In fact, I will also show that even where morphologically tenseless clauses can receive a future interpretation, an analysis invoking a non-future tense makes the same predictions as my analysis in a number of cases. I then offer a novel argument against a non-future tense analysis based on the pragmatic blocking principle Maximize Presupposition (Heim 1991;Percus 2006;Schlenker 2012, among others). This principle implores a speaker to use a sentence with the strongest presupposition compatible with her knowledge. Since the presupposition of a past tense is stronger than the presupposition of a non-future tense, Maximize Presupposition predicts the past tense to be used whenever its presupposition is satisfied, contrary to fact. I propose that tenseless and -uNil-marked clauses are not the right sort of competitors to enter into a Maximize Presupposition competition. Under my analysis, the fact that -uNil is not a member of a paradigm of tenses is crucial, and effectively prevents the pragmatic competition between tensed and tenseless clauses. This study thus indirectly sheds light on the nature of presuppositional alternatives, which, to my knowledge, has only been explored in well-studied Indo-European languages such as English, German, and French.
This paper proceeds as follows. In Sect. 2, I describe the interpretation of morphologically tenseless clauses, and in Sect. 3 the interpretation of clauses containing -uNil. In Sect. 4, I present my analysis of both morphologically tenseless clauses, and clauses containing -uNil. Then in Sect. 5, I present my novel argument for a tenseless analysis of morphologically tenseless clauses based on Maximize Presupposition. In Sect. 6, I discuss an apparent counter-argument to my claim that -uNil is simply a past tense, namely the observation that it often gives rise to a cessation inference in addition to its vanilla past tense meaning. I argue that such inferences are conversational implicatures, which may be cancelled, and thus not part of the conventional meaning of -uNil. Section 7 outlines further issues in past temporal reference in Washo to be explored in future research, while Sect. 8 concludes. In the remainder of this section, I outline the methodology used in this paper, and lay out the details of the formal framework within which I couch my analysis.

Methodology
Unless otherwise indicated, the data for this paper come from my own primary fieldwork with two Washo elders, Steven James and the late Ramona Dick. Both learned Washo natively growing up, although English is today the main language of communication within the Washo community. The working language for conducting interviews with speakers was English. Unless otherwise stated, a sentence presented without a diacritic signals that both speakers have judged the sentence as acceptable in the context provided. In an acceptability judgment task, the researcher presents a context (usually orally in this case) to a speaker, and then presents a Washo sentence to the speaker, and asks if the sentence sounds ok in that context. I use # to indicate that a sentence was not accepted by speakers in the context provided, and ? to indicate variation between speakers. Sentences taken from the Washo reference grammar (Jacobsen 1964) are adapted to the glossing conventions and slightly modified orthography used in this paper. Examples taken from texts are presented with contextual information about the plot at the time when the example appears. The texts were collected, transcribed, and translated by Dr. William Jacobsen Jr. in the 1950s with Washo speakers Bertha Holbrook, Hank Pete, and John Wiger. The texts (recordings and transcriptions) are available from the California Language Archive (http://cla.berkeley.edu). I assume that attestation in a text is tantamount to a positive acceptability judgment of a native speaker.

Formal background on tense
Before continuing, I outline my assumptions about the formal framework I will be using to make my claims and analysis precise. As is standard, I take tenses to constrain the relation between utterance time (UT) and reference time (RT), while aspects constrain the relation between eventuality time (ET) and reference time (Klein 1994;Reichenbach 1947). The need for three distinct times can be illustrated with the English past perfect as in (4): (4) When we arrived at Steven's house, he had already left.
Here, UT is the speech time, while ET of the main clause is the time of Steven's leaving, and RT is the time named by the when-clause, i.e., the time of our arrival at Steven's house. Thus, the past tense in the main clause locates RT in the past of UT, while the perfect aspect locates ET in the past of RT.
Furthermore, I assume a pronominal/referential theory of tense, whereby the RT of a clause is represented as a temporal pronoun (Abusch 1997;Heim 1994;Kratzer 1998;Partee 1973). Being a pronoun, it bears an index i, and receives its value from an assignment g. A tense feature, then, is interpreted as a partial identity function, which places a presupposition on the possible values of the temporal pronoun to which it is adjoined. I illustrate with the English example in (5). The T head in (5a) bears the index 1, and receives its value from the assignment g as in (5b-i). The feature [past] is a partial identity function that introduces the presupposition that the reference time denoted by T 1 is located before the utterance time t c , shown in (5b-ii). I assume that the sister to T denotes a predicate of times, as in (5b-iii). 8 The temporal pronoun then saturates the temporal argument, returning the proposition in (5b-iv). 9 (5) Ramona arrived.
a. Syntax: TP T [past] T 1 AspP Ramona arrive 8 I refer to this node as AspP, as is standard, although I will mostly abstract away from the contribution of aspect in this paper. 9 I assume an LF-based framework in the style of Heim and Kratzer (1998). Temporal precedence is abbreviated with the symbol <.
b. Semantics: Thus, under this view there are two pieces that correspond to what we know as tense in a language like English: a temporal pronoun denoting the reference time, and a feature that restricts the value of that pronoun.
With this background in place, I will re-state my proposal about optional tense in Washo and foreshadow my analysis within this framework. First, -uNil in Washo is the morphological exponent of the feature [past], and receives the same interpretation as the English past tense in (5). Second, in morphologically tenseless clauses, tense features are absent. Although I still posit a temporal pronoun denoting the reference time in such cases, its value is not semantically restricted by a tense feature. 10 The bipartite nature of tense in this framework thus allows us to tease apart the reference time of a clause from the features that constrain its value, and make a more nuanced claim about what exactly is optional in an 'optional tense' language.

Past and present interpretations of unmarked matrix clauses
In this section, I outline the interpretation of morphologically tenseless clauses in Washo, starting with matrix clauses. As I have already indicated, such clauses are readily compatible with either present or past interpretations. In particular, they are compatible with both present-and past-oriented adverbials, as shown in (6) Importantly, lexical aspect (Aktionsart) does not entail a particular temporal reference. For instance, whereas (6) contains a state with present temporal reference, (8) and (9) contain states (bišapuP 'hungry', iPi 'exist', and beleweP 'be lying around') with past temporal reference. Meanwhile, (10) and (11) both contain the same verb stem gamaP 'eat up', an accomplishment, although the temporal reference is present in (10) and past in (11). 11 (8) a. Context: What did you eat for dinner last night?
daNal-a house-loc PiPiyé:si P-iPi-e:s-i 3-existneg-ind 'We were hungry, but there was no food in the house.' (9) a. Context: In the Spring, some Washos arrived at where the Donner Party had set up camp the previous Autumn. The reference time of a morphologically unmarked clause can be anaphoric to a time previously mentioned in the discourse, for example to a time named by a whenclause. In (12)-(13), the RT-setting clause is also morphologically tenseless, while in (14), a time introduced in a clause containing -uNil 'past' serves to set the RT of the tenseless clause.
(12) a. Context: A mother bear was about to go out to gather food, leaving her children behind. PePé:siš P-eP-e:s-i-š 3-cop-neg-ind-sr 'They looked for them, but no one was there.' (Donner Expedition story) The first clause of (12) furthermore shows that we are dealing with reference times rather than eventuality times. Here, the prospective aspect -ašaP places the event of the bear going to gather food after the reference time. In this case, RT and ET do not overlap. A bit later in the story, we find out that the bear goes to gather food, indicating that -ašaP is not a future tense, i.e., -ašaP does not place RT in the absolute future of UT.
For completeness, and for the sake of cross-linguistic comparison, I also show here that morphologically tenseless clauses can refer to a reference time interval that spans both the past and present. 12 In both (15) and (16), a plurality of events whose time trace spans both the past and present are described using a single morphologically tenseless verb form. 13 (15) a. Context: Your son is in the next room reading, so you're watching his kids in the living room. First, Ramona starts jumping around, so you tell her to stop, and she does. Then, Jonathan starts jumping around, and your son comes in to ask what all the noise is about. You tell him ... 12 Matthewson (2006) first showed that such examples were possible for morphologically tenseless clauses in St'át'imcets, and subsequent research has shown that these are also possible in Hausa (Mucha 2013) and Tlingit (Cable 2016). The context for (15) is adapted from Cable (2016), and the context for (16) is adapted from Mucha (2013). 13 Parallel sentences where a morphologically tenseless clause can have a reference time that overlaps the past, present and future seem to not be possible. This doesn't seem too surprising, however, since future interpretations typically require an overt future or modal, or a very specialized context, as will be shown in the following subsection. In sum, morphologically tenseless matrix clauses are compatible with both past and present reference times. Those reference times may be named by a temporal adverbial, or they may be anaphoric to a time made available from the context, e.g., a time introduced in a previous clause. This state of affairs is compatible with my claim that such clauses do not contain a tense feature that semantically restricts the value of RT.
Let us now turn to future interpretations of tenseless matrix clauses. As we will see, although future temporal reference is often dispreferred for unmarked clauses, future interpretations are licensed in certain environments.

Future interpretations of morphologically tenseless clauses
Morphologically tenseless clauses often resist a future interpretation. For instance, speakers judge co-occurrence with the future-oriented adverb wádiN dewp'áw1t 'tonight' in (17) as unacceptable. Instead, speakers prefer to have an overt future marker, such as the prospective aspect -ašaP in (18) However, future interpretations of morphologically tenseless clauses are not systematically absent. For instance, (19) shows a question-answer pair regarding dinner plans in the future of the utterance time, but without any future marking. (20) is a similar example, and shows that the future interpretation is not derived from the lexical meaning of the verb do:da 'make', and that these types of sentences can be used to talk about a third person's plans. Such examples are admittedly quite rare, and while both speakers accepted dialogues of this sort, there is definitely a preference to mark future-oriented matrix clauses with some sort of future morphology. The fact that a plan is at issue in (19) and (20) seems crucial for licensing the future reading here, and I will make use of this fact when analyzing these clauses in Sect. 4.2.1.
Another case where we find morphologically tenseless clauses with future temporal reference is shown in (21)-(22), where a series of conjoined clauses receive future interpretations without any future morphology. Notably, the first two clauses contain the sequential morpheme -ud, which serves to indicate forward progression in a narrative, similar to English 'then'. In (21), the event of sleeping in the first clause is in the future of the utterance time. Only the final clause is marked with the intermediate future -tiP, while the first clause contains sequential -ud. In (22), Mother Bear is giving instructions to her children about what they are supposed to do when she leaves to gather food. No overt future markers are present in any of the clauses, even though the events described are to occur in the future of the utterance time. 15,16 (21) a. Context: The baby has been feeling sick, and is very cranky. You think that if she has a nap she will feel better.
(23) a. Context: You're telling me about yesterday's weather. b. háPašudi ∅-haPaš-ud-i 3-rain-seq-ind déPešgáNaPi ∅-dePeš-gaNaP-i 3-snow-begin-ind 'It was raining, and then it began to snow.' Another case where future interpretations of morphologically tenseless clauses are licensed is in conditional antecedents, as will be shown in the next subsection.
In sum, morphologically tenseless clauses can receive past, present, and in limited cases future temporal reference.

The interpretation of embedded tenseless clauses
Here I briefly describe the interpretation of morphologically tenseless clauses in embedded environments. A more general discussion of the temporal interpretation of embedded clauses is postponed until Sect. 3.2, after I have introduced the interpretation of clauses marked with -uNil.

Relative clauses
Morphologically tenseless relative clauses can receive either a "back-shifted" or "simultaneous" interpretation relative to the matrix eventuality time. In (24), the context provides a past RT situated some time in the week prior to speech time. The event of people coming to the party is therefore located in the past of speech time in this morphologically tenseless clause. The embedded clause is likewise morphologically tenseless, but is interpreted temporally prior to the eventuality time of the matrix clause; the inviting to the party occurs prior to the arriving at the party.
(24) a. Context: You are telling me about a party you hosted last week.
b. míPlew miPleP-w every-hum.pl dibóNiyišgi di-boNi-i-š-gi 1-invite-ind-sr-subj.rel Pí:biPi P-i:biP-i 3-come-ind 'Everyone who I invited came.' (embedded RT < matrix ET) In (25), the reference time of the main clause, which is morphologically tenseless, is the time of Mother Bear searching for her children, in the past of speech time. The RT of the embedded clause, also morphologically tenseless, is simultaneous with that time.
(25) a. Context: Mother Bear is searching for the deer who killed her children.
She comes across a heron sitting by the river. Thus, morphologically tenseless relative clauses can receive an interpretation which is either back-shifted or simultaneous relative to a morphologically tenseless main clause with past temporal reference.

Complement clauses
A morphologically tenseless complement clause can receive a temporal interpretation simultaneous to the eventuality time of a morphologically tenseless matrix clause. In (26), the time of being named Tim is simultaneous with the time of thinking, which is in the past of speech time, given the context. In (27), the time of being sick is simultaneous with the time of thinking, also in the past of speech time, given the context.
Pum-hamu-i-Na 2-think-ind-but 'This morning you came to see me, but you thought I was sick.' (embedded RT = matrix ET → simultaneous reading) Meanwhile in (28), the matrix RT and overlapping ET are located in the present, while the embedded RT is in the past of the matrix ET. In (29), the past time of playing cards in the embedded clause precedes Steven's thinking time.
(28) a. Context: You arrive home from shopping, and find that the chicken you had cooked before you left is gone. As far as you know, only your son has been at home.

Antecedent of conditionals
The antecedent of a conditional is an embedded environment where a morphologically tenseless clause can receive a temporal interpretation in the absolute future of the utterance time. For instance, the context of (30) sets up a future reference time of the day following utterance time. In (31), the future-oriented adverb wát 'tomorrow' co-occurs with a morphologically tenseless clause in the antecedent. 17 (30) a. Context: We are discussing our plans for tomorrow, which are dependent on the weather.
Furthermore, the reference time of the antecedent clause may be in the future of the reference time of the consequent. This is shown in (32).
(32) a. Context: Herman is expecting his cousin to come some time this week, but you don't know exactly when. But if his cousin is going to arrive tomorrow, then Herman must be happy now. b. wát wat tomorrow

Herman Herman
Pí:yeluP P-i:yeluP 3-cousin In sum, the data from embedded contexts is consistent with the hypothesis that morphologically tenseless clauses in Washo contain no semantic tense restricting temporal reference.

The interpretation of -uNil in matrix contexts
Clauses containing -uNil are only compatible with past time reference. In (33), a verb marked with -uNil co-occurs with the past-oriented adverb watlí: 'this morning', which speakers judge acceptable. By contrast, speakers judge (34) and (35) unacceptable, where a verb marked with -uNil co-occurs with the adverbs wá:diN 'now' and wát 'tomorrow', respectively.
(33) watlí: watli: morning wáNawuNili w-aNaw-uNil-i static-good-past-ind 'It (the weather) was nice this morning.' In the absence of temporal adverbs, -uNil is also only compatible with past reference times. For instance in (36), repeated from above, the context makes salient the past time when the Washos arrived at the Donner Party camp, and -uNil is used. Meanwhile, in (37), the context makes the speech time salient, and speakers find the sentence unacceptable in the context.
(36) a. Context: In the Spring, some Washos arrived at where the Donner Party had set up camp. b. gesú:dumuNiludi ge-su:dum-uNil-ud-i 3.obj-look.for-past-seq-ind t'ánuNa t'anu-Na person-nc PePé:siš P-eP-e:s-i-š 3-beneg-ind-sr 'They looked for them, but no one was there.' (Donner Expedition story) (37) a. Context: It's noon, and I ask you what your son is up to now. It turns out that he has been sleeping all day, and in fact he is still asleep! b. # diNá:m di-Na:m 1.poss-son These data are compatible with the hypothesis that -uNil is a past tense, restricting the reference time to the past of the evaluation time (i.e., speech time in matrix clauses).
Verbs marked with -uNil can anaphorically refer to a past reference time. In (38), the reference time of the clause léyowePé:suNili 'I didn't go' is anaphoric to the past time of playing cards made salient by the context and the previous clause. In the dialogue in (39), the reference time of speaker B's response is anaphoric to the time asked about by speaker A, i.e., the time immediately before speaker A called.
(38) a. Context: I know you usually go to the Seniors' Center to play cards on Friday, and I ask if you went last week.
Evidence that -uNil locates reference time as opposed to eventuality time comes from the interaction with prospective aspect. For instance in (40), the reference time is set up in the context as the past time that Steven was looking for his lottery ticket, whereas the eventuality time of winning money is in the future of that time, which is marked with the prospective aspect marker -ašaP.
(40) a. Context: Steven had the winning numbers in the lottery, but when he went to look for his ticket, he couldn't find it anywhere. b. t'é:k'eP t'e:k'eP much heyéPemašaPuNilaš ∅-heyePem-ašaP-uNil-aP-š 3-win-prosp-past-dep-sr gitbehúweP git-behuweP refl-ticket páyhayi ∅-payP-ha-i 3-lose-caus-ind 'He was going to win a lot of money, but he lost his lottery ticket.' There is also evidence that -uNil is not a terminative aspect, based on the diagnostics of Bohnemeyer (2002). First, according to Bohnemeyer terminative aspects should allow past perfect readings with reference-time-setting adverbs or past-oriented whenclauses, which is not the case for -uNil. For instance, a past perfect interpretation for -uNil in (38) is not possible, even though the context sets up that the speaker had gone to the Seniors' Center before last Friday. Second, the interruption of the post-state of an event is fine for -uNil, as in (41) He was sleeping, then he woke up, and then he went to sleep again.' Since -uNil behaves like a tense in the relevant respects, including having anaphoric uses, and relating reference time to utterance time, I conclude that it should be analyzed as a past tense.

The interpretation of -uNil in attitude complements
Before going on to my analysis, let us first consider the interpretation of -uNil in attitude complements. What we find is that -uNil embedded under propositional attitude verbs gives rise to the same types of readings as the English past tense, specifically so-called Sequence of Tense (SOT) effects (Ogihara 1989).
The observation for English is that a past tense stative embedded under a past tense attitude verb can receive two readings, as in (42): a "simultaneous" reading, where the state of being sick holds at the time of saying, and a "back-shifted" reading, where the state of being sick is in the past of the time of saying.
(42) Katie said that Nico was sick.
a. Katie said: "Nico is sick." "simultaneous" reading b. Katie said: "Nico was sick." "back-shifted" reading Under Ogihara's influential analysis, an embedded tense is optionally deleted under identity with a c-commanding matrix tense. Cross-linguistic research has shown that there is variation in whether languages make use of such a SOT rule, and also in which embedded environments such a rule applies (e.g., Arregui and Kusumoto 1998;Grønn and von Stechow 2010;Kubota et al. 2009Kubota et al. , 2012Ogihara 1989;Sharvit 2014). Furthermore, there is somewhat of a debate as to whether a SOT rule, which is syntactic in nature, should be used or is necessary to account for a seemingly semantic phenomenon (Altshuler and Schwarzschild 2012;Gennari 2003;Kubota et al. 2009Kubota et al. , 2012Sharvit 2014). An analysis of the temporal interpretation of attitude complements in Washo is forthcoming in Sect. 4. For now we observe that the data for Washo -uNil pattern remarkably similar to the facts for the English past tense. Note that throughout this subsection, I exclusively focus on past interpretations of -uNil-marked and morphologically tenseless clauses.
A simultaneous reading is available for a stative predicate marked with -uNil embedded under an attitude verb also marked with -uNil, as shown in (43). When presented with the context in (43a), a speaker volunteered the form in (43b). This shows that the simultaneous reading is available, since the context provides that the time of being named Tim is simultaneous with the time of thinking the addressee's name is Tim (since, presumably, the speaker would only say "Hi Tim!" if she thought the addressee's name was Tim at that time). 19 (43) a. Context: You see a man in the street and say 'Hi Tim!' He tells you his name isn't Tim. You apologize, and say: b. Tim Tim Tim However, when I first tried to replicate this pattern with another speaker, his reaction indicated that the back-shifted reading for embedded -uNil was not only possible, but more salient, as shown in (44c) Speaker: (laughing) "Sounds like Tim used to be your name." MRB: "Like he changed his name?" Speaker: "Yeah." Upon discussing this example further with this speaker, he did later accept the same judgment that (43) could also be used in this context that favors the simultaneous reading. So while the the back-shifted reading is possible for -uNil embedded under -uNil, the simultaneous reading is also available. Another example showing that the simultaneous reading is available for an embedded stative predicate marked with -uNil is in (45), which was accepted by both speakers (modulo gender differences; the example here is shown for the male speaker). In the context provided, the backshifted reading is in fact quite implausible. 21 Footnote 19 continued straightforwardly by relying on the lexical inferences associated with individual-level predicates. This point is also important for cross-linguistic comparison, since Tonhauser (2011) shows that only a simultaneous reading is possible for embedded clauses in the tenseless language Paraguayan Guaraní. Note, however, that the same patten holds for stage-level states as well, such as (1).

Ryan Ryan
Pí:duNili P-i:d-uNil-i 3-say-past-ind 'Ryan said Steven was sick.' 20 A reviewer remarks that using think in the past tense with a first person subject is often used to convey a meaning that can be paraphrased as "I now know that ... not ...." The examples provided in (1) in footnote (19) and in (45) di-hamu-uNil-i 1-think-past-ind 'When I was a boy, I thought Reno was big.' #'When I was a boy, I thought Reno used to be big.' Thus, -uNil behaves like the English past tense in both matrix and embedded environments. These facts would be surprising if -uNil was not a tense, but rather a temporal adverb, since temporal adverbs normally don't display these sorts of effects.
For completeness, I briefly describe the readings available for a morphologically tenseless clause embedded under a propositional attitude marked with -uNil, and for a clause marked with -uNil embedded under a morphologically tenseless attitude verb. In the first case, both a simultaneous reading and a back-shifted reading are available.
In (46), two contexts are provided, one which favors the simultaneous reading, and one which favors the back-shifted reading. Speakers find the Washo form in (46b) acceptable in both contexts.
(46) a. Context A: You see a man in the street and say 'Hi Tim!' He tells you his name isn't Tim. You apologize, and say . . . Context B: You run into your old friend. His name used to be Tim, but you heard that he changed his name since you last saw him. b. Tim Tim Tim di-hamu-uNil-i 1-think-past-ind Context A: 'I thought your name was Tim.' (simultaneous reading) Context B: 'I thought your name used to be Tim.' (back-shifted reading) By contrast, a verb marked with -uNil embedded under a morphologically tenseless attitude verb only has a back-shifted reading. Using our now familiar mistaken identity context, speakers find the form in (47) unacceptable in the target context for the simultaneous reading.
(47) a. Context: You see a man in the street and say 'Hi Tim!' He tells you his name isn't Tim. You apologize, and say: di-hamu-i 1-think-ind Intended: 'I thought your name was Tim.' Speaker comment: 'I thought your name used to be Tim.' The fact that the simultaneous reading is unavailable can be exploited by speakers, who may choose this form to unambiguously signal that the back-shifted reading is the one intended. For instance, after presenting a speaker with the context in (48a), she volunteered the form in (48b).
(48) a. Context: You were planning a trip, and your friends came over to say goodbye, but when they arrived, you had already left on the trip. When you get back . . . b. lé: le: poss-house-loc lí: li: prt léyowePudiš le-iyeP-uweP-ud-i-š 1-go-hence-seq-ind-sr 'They said they came to look for me, but I had already left.' (time of looking-for < time of saying) In sum, the readings available for the different combinations of morphologically tenseless and tensed clauses under attitude verbs is summarized in (49). This summary is only for past interpretations of combinations of -uNil-marked and morphologically tenseless clauses. A more detailed investigation of matrix and embedded clauses with other temporal reference combinations must await another occasion.

Analysis
In this section, I formulate my analysis of -uNil as a past tense, and of morphologically tenseless clauses, couched within the pronominal/referential theory of tense (Abusch 1997;Heim 1994;Kratzer 1998;Partee 1973) as outlined in Sect. 1.3. While I focus mostly on past interpretations, I also provide an analysis for the cases where morphologically tenseless clauses can receive a future interpretation. I also compare my analysis with two alternatives, which I both reject. We begin with the simplest case, the analysis of -uNil.

Analysis of -uNil
I propose that -uNil receives the same interpretation as English past tense. It places a presupposition that the identity of the temporal pronoun (given by the assignment function g) is before the utterance time t c . We will begin with matrix clauses. The syntactic structure I assume for (3) is given in (50).
The sister to T , labeled here as AspP, denotes a predicate of times. 22 The temporal pronoun generated as the head of T saturates the time argument, deriving a proposition that is true if it rains in w at time g (1), with the added presupposition that g(1) is located prior to utterance time. This semantic derivation is provided in (51), ignoring the contribution of mood morphology.
This analysis captures the co-occurrence patterns with temporal frame adverbials in (33)-(35). Assuming that temporal adverbials also place constraints on the identity of the reference time, as in (52), it is clear why a verb marked with -uNil is only compatible with past-oriented adverbs.
(52) a. watlí: w,g,c = λt.t ⊆ this.morning b. wá:diN w,g,c = λt.t ⊆ now c. wát w,g,c = λt.t ⊆ tomorrow In the case of watlí: 'this morning', the constraint placed of the reference time does not conflict with the presupposition of -uNil, and so is acceptable. However, the constraints placed by wá:diN 'now' and wát 'tomorrow' conflict with the presupposition of -uNil, resulting in a contradiction. This is made explicit in (53)-(55), where (53) with no contradiction is acceptable, while (54) and (55) Recall from Sect. 3 that under attitude verbs, the embedded clause can receive either a "back-shifted" or "simultaneous" reading relative to the matrix clause. Since this observation is also found for the past tense in English under attitude verbs, I will simply borrow aspects of various analyses developed for English. In doing so, I do not wish to take a stand here on the correct way to derive these effects for English; rather, my goal is to present an analysis that is able to handle the data while being consistent with the main claims of this paper.
Let us begin with the "simultaneous" reading, as in (43) and (45). In this case, the emprical effect to be accounted for is that the embedded -uNil seems to have no contribution, in the sense that it does not induce a further backward shift in time. Rather, the time of the embedded clause is bound to that of the matrix clause.
I follow the general idea widespread in the literature that in these cases, there is simply no semantic tense in the embedded clause, despite the presence of the past tense morphologically. There are various technical means for implementing this idea, including tense deletion under identity with a c-commanding tense (e.g., Ogihara 1989), positing a "zero" past tense in the embedded clause (e.g., Heim 1994), or non-local licensing of past tense morphology (e.g., Kusumoto 2005;Stowell 2007).
Whatever the right way of doing this is, the structure and semantics for the simultaneous reading in (43) should look something like (56), again ignoring mood. There is only one past feature in the structure, namely the one in the matrix clause. There is no semantic past tense in the embedded clause, and the temporal variable is abstracted over to deliver a predicate of times as the complement of the attitude verb, and the time of the embedded clause is bound to the attitude time (the attitude-holder's now, t ). 23 (56) a. TP AspP CP TP

AspP
Tim degumdíPyeP M-eP '2-be named Tim' To obtain the "back-shifted" reading, as in (44), I follow Abusch (1997) and Heim (1994) in positing res-movement of the temporal pronoun and its tense feature. The key ingredients of the analysis are as follows. First, there is movement of the past tense of the embedded clause to the matrix clause, so that it is not interpreted under the scope of the attitude verb. Second, the context must provide a temporal acquaintance relation, R, such that the attitude holder bears R to the lower past time in w at t. The content of R is essentially a description by which the attitude holder represents a time to herself. This is necessary for the temporal de re interpretation of the back-shifted reading. Third, we posit the Upper Limit Constraint, which prevents the lower tense from denoting a time after the eventuality time of the higher clause. 24 For reasons of space, I won't go through a compositional analysis here. A sample LF for the back-shifted reading in (44) is given in (57a), where the res-moved tense and its trace are underlined. The truth conditions are given in (57b).
i. g(1) < t c and g(2) < t c (past tense presupposition) ii. g(1) ≤ g(2) (Upper Limit Constraint) 25 iii. c provides R such that R(g(1))(sp)(t )(w ) = 1 (acquaintance relation) In sum, borrowing fairly standard assumptions about the semantics of the past tense in English allows us to give a satisfactory analysis of matrix and propositional attitude complements containing -uNil. 26 The remarkable similarities between -uNil in Washo and the past tense in English can thus be captured by giving them the same analysis. I now turn to the analysis of morphologically tenseless clauses.

Analysis of morphologically tenseless clauses
For morphologically tenseless clauses, I propose the same structure and semantics as clauses with -uNil for all the relevant pieces, except that there is no tense feature restricting the reference of the temporal pronoun. The syntax and semantics of (2) is thus given in (58)-(59).
Since there is no presupposition placed on the value of the temporal pronoun, the analysis predicts that morphologically tenseless clauses are in principle compatible with past, present, or future time reference. We have seen that this is indeed the case, with several examples of each in Sect. 2. For concreteness, the analysis for (6) and (7) is given in (60)-(61), where the temporal adverbs wá:diN 'now' and watlí: 'this morning' are compatible with morphologically tenseless clauses. Thus, in these cases, the identity of the reference time is only restricted semantically by the temporal adverbs themselves, and not a semantic tense. 25 This is not quite the correct presupposition that the Upper Limit Constraint imposes. Technically, the Upper Limit Constraint imposes a constraint on time concept functions f , whose output must be a time that is not later than the attitude holder's 'now'. See Heim (1994)

cook(ch)(sp)(g(3))(w) ∧ g(3) ⊆ this.morning
However, the analysis also predicts that future-oriented adverbs should also be possible with morphologically tenseless clauses, contrary to fact. Under my analysis, the semantics of (17) comes out as in (62), assuming an analysis of wá:diN dewp'áw1t 'tonight' parallel to (52), which does not explain why the sentence is judged as unacceptable.
Following Tonhauser (2011) for Paraguayan Guaraní, I propose that future reference times in Washo are in general not available. That is, in a case like (62), there is no suitable referent available for g(4), since it is in the future of the utterance time. My idea is roughly the following: in a branching times model of temporal and modal reference (Thomason 1970(Thomason , 1984, the past and future are asymmetrical, in the sense that the past is settled, while the future is not. I contend that this asymmetry is significant for the availability of reference times for morphologically tenseless clauses in Washo. Specifically, only reference times on the subsets of histories that are already settled can be referred to in morphologically tenseless clauses. Nevertheless, we do find that morphologically tenseless clauses can sometimes receive absolute future reference. Such cases include examples like (19) where a plan for the future is at issue, cases like (22) where a clausal conjunction with the sequential morpheme -ud licenses a future interpretation, and in conditional antecedents as in (30)-(32). My proposal is that future interpretations are available in planning contexts and conditionals due to the presence of a silent modal operator, and in conjunctions with -ud because a reference time is asserted to exist, rather than being referred to. In the remainder of this sub-section, I discuss each of these cases in turn, and then I discuss the interpretation of relative clauses and complement clauses.

Unembedded future interpretations and plans
In certain cases like (19) and (20), the latter repeated in (63) below, we find that future time reference of a morphologically tenseless clause is possible. In this context, there is a plan for what Mona will cook later on after the utterance time. I argue that this is crucial for the licensing of the future reading of the morphologically unmarked future interpretation of such sentences.
To implement this idea, I borrow the metaphysical modal operator plan of Copley (2002Copley ( , 2008 and Thomas (2015), which is designed to account for futurate readings of present tense sentences in English, such as (64). (64) The Red Sox play the Yankees tomorrow.
Copley argues that such futurate readings involve both a presupposition and an assertion regarding a director d towards a proposition p. The presupposition is that d directs p in a world w at time t, while the assertion is that d is committed to p in w at t. Informally, what it means for d to direct p is that d has the ability to bring about that p, and that d is committed to bring about that p. The director d is committed to p in w at t if in all the best worlds metaphysically accessible from w according to d's desires in w, there is a time t in the future of t where p is true. So for (64), we can take Major League Baseball (or its executives) to be the entity directing the proposition that the Red Sox play the Yankees tomorrow, and committed to bring about that the Red Sox play the Yankees tomorrow.
The meaning contributions of plan can then be modeled as a modifier of a predicate of times P in (65), where BEST (Portner 1998) picks out the best worlds of the modal base MB according to the bouletic ordering source OS d , here relativized to the director d's desires in w at t.
For the analysis of (19) and (63), I propose that plan applies to the embedded AspP, returning a predicate of times, where the time argument is then saturated by a temporal pronoun denoting the utterance time. That is, (19) has present temporal reference, but is future-oriented because plan introduces a time t in the future of g(1). The final semantics for B's response in (19) is then given in (66).

make(soup)(sp)(t )(w )] defined only if d directs λt λw .make(soup)(sp)(t )(w ) in w at g(1)
The analysis correctly predicts that cases like (62a) should be unacceptable due to presupposition failure. Specifically, the presupposition that there is a director d that has the ability to bring it about that it rains in the future is not satisfied.

Conditional antecedents
Recall that not only can morphologically tenseless clauses in conditional antecedents have absolute future time reference, as in (30)-(31), but their reference time can also be in the future of the consequent time, as in (32), repeated here as (67). (67) a. Context: Herman is expecting his cousin to come some time this week, but you don't know exactly when. But if his cousin is going to arrive tomorrow, then Herman must be happy now.

Herman Herman
Pí:yeluP P-i:yeluP 3-cousin Herman's cousin comes tomorrow, he is happy now.' Since this observation is similar to the one described by Tonhauser (2011) for Paraguayan Guaraní, I adopt her analysis of conditionals, whereby they explicitly assert the existence of times, which can be either in the past, present, or future of the utterance time. 27 I assume a conditional operator cond with the semantics in (68). It ensures that the antecedent P is interpreted at worlds w that are best according to an epistemic modal base MB and a stereotypical ordering source OS at a world w and time t, which I take to be standard assumptions for conditionals (Kratzer 1986(Kratzer , 2012. cond furthermore asserts the existence of a time t at which P is interpreted, which can be a past, present, or future time. The truth conditions for (67) are then given in (69).
Nothing in the semantics of cond restricts the relation between t and t . In the case of (67), the temporal adverbs impose constraints on the values of t and t , and so here the antecedent time is in the future of the consequent time. The modal aspects of the conditional are sufficient to license a future interpretation of a morphologically tenseless clause.

Sequential -ud
Morphologically tenseless clauses can also receive a future interpretation in conjoined structures, such as (22) Recall that in such constructions, the sequential morpheme -ud occurs in all nonfinal conjuncts to indicate forward narrative progression, similar to English '(and) then'. However, -ud also occurs with the same forward progression meaning in conjoined clauses with past temporal reference, as in (23). Furthermore, as shown in (36) and (41), -ud can co-occur with the past tense -uNil. Therefore, -ud must not contribute future time reference.
I propose a semantics for -ud given in (71), whereby it asserts the existence of a time t where P is true, and introduces a temporal relation of precedence between t and another time t, which is identified with the reference time of the following clause. The time t can be a past or future time. 28 To keep things simple, I will exemplify how the analysis works with just two conjoined clauses, namely the last two clauses in (70). I assume the structure of a biclausal conjunction as in (72). Given that -ud can co-occur with -uNil, I assume that -ud adjoins above TP, where the temporal variable in the clause is abstracted over to deliver a predicate of times as the first argument of -ud, as required by (71). The temporal variable in the second clause (the clause not marked with -ud) is also abstracted over, so that it can be identified with the open temporal variable of the -ud-marked clause by the conjunction operator conj in (73).
(72) TP AspP λtλw.P(t)(w) The meaning of -ud applied to the predicate of times it embeds is given in (74). It returns a predicate of times t, which is true at w if there exists a time t such that the addressee burning the deer children to death is at t , and t is before t. The truth conditions of the whole conjunction (i.e., the last two clauses in (70), and ignoring the causative 'for me' part of the second clause), are given in (75).
I assume that the final translation of the whole conjunction involves existential closure over an open temporal variable, as in (76). The idea is that the assertion of the existence of a time, together with the temporal precedence relation t < t, is enough to license an absolute future interpretation for a morphologically tenseless clause. This means that the morphologically tenseless clauses in (70) are predicted to be compatible with future temporal reference, and this prediction is upheld.
(76) (72) g,c = λw.∃t∃t [burn.to.death(deer) The truth conditions provided here for conjunctions with -ud also predict that the conjoined clauses can have past temporal reference, and in particular are compatible with -uNil. This prediction is also upheld. For morphologically tenseless clauses, this is shown in the analysis of (77) given in (78). Meanwhile, the truth conditions for (79), which contains -uNil, are given in (80). The contribution of -uNil is the presupposition that t , the reference time of the clause containing -uNil, be prior to the utterance time t c , which is compatible with the proposed truth conditions for the conjunction containing -ud. 29 (77) a. Context: You're telling me about yesterday's weather. 29 I use x and y to represent the third person pronominal arguments in (80).

b. háPašudi
∅-haPaš-ud-i 3-rain-seq-ind déPešgáNaPi ∅-dePeš-gaNaP-i 3-snow-begin-ind 'It was raining, and then it began to snow.' (79) a. Context: In the Spring, some Washos arrived at where the Donner Party had set up camp. b. gesú:dumuNiludi ge-su:dum-uNil-ud-i 3.obj-look.for-past-seq-ind t'ánuNa t'anu-Na person-nc PePé:siš P-eP-e:s-i-š 3-cop-neg-ind-sr 'They looked for them, but no one was there.' (Donner Expedition story) In sum, the constructions where future interpretations of morphologically tenseless clauses are available in Washo can be accounted for under my analysis. In all these cases, a modal operator and/or temporal precedence relation licenses future interpretations.

Relative clauses and complement clauses
Finally, I briefly discuss morphologically tenseless relative and complement clauses, and sketch their analysis. As observed in Sect. 2.3, morphologically tenseless relative clauses can receive either a back-shifted or simultaneous interpretation relative to the matrix eventuality time; see (24)-(25). I provide the proposed truth conditions for (25), repeated here as (81), in (82), setting aside a compositional analysis for reasons of space.
(81) a. Context: Mother Bear is searching for the deer who killed her children.

to(x)(y)(g(1))(w)∧ sit(x)(g(2))(w)]
Since (81b) is biclausal, there are two temporal pronouns in the structure. However, there are no tenses constraining the identities of g(1) and g(2) in (82), and nothing constraining the temporal relation between them. This analysis thus correctly predicts that relative clauses can in principle have a temporal interpretation that is either simultaneous or back-shifted relative to the matrix time.
Recall also from Sect. 2.3 that morphologically tenseless clauses embedded under a morphologically tenseless attitude predicate can receive both "simultaneous" and "back-shifted" readings, just like tensed clauses. The analysis developed for -uNilmarked clauses can thus be extended to these cases as well, minus the presuppositions of the past tense. For the simultaneous reading, as in (26)-(27), the temporal variable in the embedded clause is abstracted over and identified with the attitude holder's 'now' in the matrix clause, just like in (56). The only difference between cases like (26) and (56) is the additional presupposition in (56) that the time denoted by the temporal pronoun in the matrix clause be located before utterance time. Similarly, the analysis for the back-shifted interpretation of (28) parallels that for tensed clauses given in (57). Just like in (57), the embedded temporal pronoun undergoes res-movement so that it is not interpreted under the scope of the attitude verb. We must likewise assume the Upper Limit Constraint and a temporal acquaintance relation for these cases as well; only the additional past tense presupposition is absent in (28).
This analysis can also handle the 'mix-and-match' cases, where a tenseless clause is embedded under a tensed clause, and a tensed clause is embedded under a tenseless clause; see (49) for a summary of the possibilities. In the former case, both simultaneous and back-shifted readings are possible. As before, the embedded temporal pronoun can either be abstracted over, or undergo res-movement to obtain the desired readings. The latter case is interesting, since here the simultaneous interpretation is unavailable. For the back-shifted reading, we need res-movement, as before. However, to obtain the simultaneous reading for tensed embedded clauses, we needed to say that semantically there is no tense in the embedded clause. But this does not seem possible when a morphologically tensed clause is embedded under a morphologically tenseless attitude predicate-the downstairs tense must be interpreted. This appears to be evidence in favor of a deletion-based account of embedded tense (e.g., Ogihara 1989), whereby an embedded tense may be optionally deleted under identity with a matrix tense to obtain the simultaneous reading. That is, in a case like (56), the deletion of the embedded past tense is licensed by the presence of the upstairs past tense. In cases like (47), however, there is no upstairs tense to license such a deletion, and so the downstairs tense must be interpreted, and no simultaneous reading is available.

Null non-future tense
In this subsection, I explore and reject two alternative analyses for morphologically tenseless clauses that appear to have some initial plausibility. The first would be to say that morphologically tenseless clauses do contain a tense after all, just a phonologically silent one, following Matthewson (2006) for St'át'imcets. Under Matthewson's analysis, a covert tense morpheme restricts the value of a temporal pronoun in morphologically tenseless clauses (or what she calls "superficially" tenseless clauses). This morpheme, defined in (83), appears in all finite clauses, and restricts the value of the temporal pronoun to non-future intervals. The syntax and semantics of (2) would then be as in (84) (85) TP g,c = λw.rain(g(1))(w) defined only if no part of g (1) is after t c A major empirical advantage of this analysis is that it predicts the co-occurrence restrictions with temporal adverbs that were problematic above, without the additional assumption that future reference times are unavailable. Specifically, (17) would be analyzed as in (86), where the contradiction between the presupposition of nonfut and the semantics of the future-oriented adverb explains why the sentence is judged unacceptable.
(86) a. # wá:diN wa:diN today dewp'áw1t dewp'aw1d evening háPaši ∅-haPaš-i 3-rain-ind Intended: 'It will rain tonight.' b. (86a) g,c = λw.rain(g(2))(w) ∧ g(2) ⊆ tonight defined only if no part of g (2) is after t c This analysis can also handle cases of absolute future time reference in planning contexts such as (19) and (63), also by appealing to the plan operator as before. I argued that such cases in fact involve present temporal reference with a future time introduced by plan. Thus, adding the presupposition that no part of g(1) be located after t c as in (87) still predicts futurate readings to be possible in planning contexts such as (19B).
(87) a. [ [ [ šú:pk'eN lí: di-do: (1), and no part of g(1) is after t c On the face of it, this analysis appears to have difficulty in other cases where future temporal reference is possible in morphologically tenseless clauses, such as in conditional antecedents, and conjunctions with -ud. First, it was observed that conditional antecedents not only can receive absolute future reference, but also that the time of the antecedent can be in the future of the time of the consequent. The analysis with nonfut tense seems to make the wrong prediction in this case. Even if we assume that nonfut is a relative tense where the evaluation time can be shifted to the consequent time, the analysis in (88) for (67) would still predict that the antecedent time must be in the non-future of the consequent time. Moreover, in the case of (67) where the consequent time overlaps with utterance time, the presupposition of nonfut in the antecedent clause contradicts the contribution of the temporal adverb, and so (67) is predicted to be unacceptable, contrary to fact.
defined only if no part of t and no part of t is after t c However, caution is warranted in interpreting the results here. While it is indeed the case that the tensed analysis considered here cannot straightforwardly deal with the facts, there remain difficult issues regarding tense in conditionals, even for well-studied languages like English. Consider (89), from Kaufmann (2005, p. 268).
(89) If I come out smiling, the interview went well.
In (89), the consequent clause contains a past tense, but is interpreted in the future of the utterance time. The antecedent clause contains a present tense, but is interpreted in the future of consequent time. Note that this example cannot be saved by positing a plan operator in the antecedent clause. The conditional does not have the reading 'If it is planned that I come out smiling. . . '. The point of bringing up this example is to highlight that the modality of conditionals can influence the interpretation of tenses in sometimes unexpected ways. Therefore, it is far from clear that temporal interpretation in conditionals should serve as a litmus test for deciding between the tensed and tenseless analysis for morphologically tenseless clauses, in Washo and across languages.
Second, we observed that conjunctions with -ud allow absolute future time reference. If we carry over the analysis of -ud from Sect. 4.2.3, together with the assumption that nonfut appears in every finite morphologically tenseless clause, the analysis of (22)/(70) is the same as before, but with the additional presuppositions that no part of the temporal variables in either clause can be located after t c , as shown in (90). 31 31 Again, we restrict ourselves to the final two clauses for simplicity. Thus, it is predicted that such clauses can only have non-future temporal reference, contrary to fact.

(add)(t )(w) ∧ pound(deer)(add)(t)(w) ∧ t < t]
defined only if no part of t and no part of t is after t c Let us now take stock. An analysis involving a null nonfut tense in morphologically tenseless clauses can account for future planning contexts just as well as the tenseless analysis, and can provide an explanation for the temporal adverb co-occurrence facts.
The nonfut analysis appears to fail for conditionals, but I argued that conditionals are not the best place to look to distinguish the two theories. This leaves future interpretations with -ud, where the nonfut analysis does in fact stumble. The restriction to non-future times is simply too strong in this case, and makes the wrong predictions. Thus, the range of extant data that empirically distinguish my analysis from the nonfut analysis is in fact quite narrow. In Sect. 5, I will offer a new argument against the nonfut analysis based on (the lack of) Maximize Presupposition effects. First though, I will compare my analysis with the truly tenseless analysis of Tonhauser (2011).

No T head in morphologically tenseless clauses
Another possible analysis would be to claim that morphologically tenseless clauses completely lack a T node or temporal pronoun at all, following the analysis of Tonhauser (2011) for Paraguayan Guaraní. The syntax and semantics of (2) would then be as in (91)-(92). However, since (92) denotes a predicate of time, the additional Matrix Clause Rule in (93) needs to be invoked in order to deliver a proposition, where t rt is the reference time of the clause. The final translation of (2) is then given in (94). Under this analysis, there is no need to posit a temporal pronoun or T projection in morphologically tenseless clauses, which may be desirable given that there are no morphological reflexes of T, and the value of the reference time is left unconstrained.
Since the identity of the reference time under this account would still be identified through regular pragmatic/anaphoric principles (e.g., Bittner 2014), the predictions made by my analysis and Tonhauser's would be identical, at least for matrix clauses.
However, there are two reasons why my analysis is better suited to the Washo data. First, unlike Paraguayan Guaraní, Washo is not a tenseless language. That is, there is at least one morpheme in Washo that can be analyzed as a tense, namely -uNil, so we need to appeal to tense at least in some cases. It then becomes a question of whether a completely tenseless analysis (i.e., one lacking T at all) for morphologically tenseless clauses in Washo is overall more parsimonious than the one I am pursuing. I suggest that my analysis is actually more parsimonious overall than one that treats morphologically tensed and tenseless clauses as involving fundamentally different structures (i.e., structures with or without T and its projections). Second, the data from embedded contexts is different for Washo and Paraguayan Guaraní. Tonhauser shows that a back-shifted interpretation for tenseless clauses embedded under attitude predicates is not attested, and uses this fact as an argument against representing tense in embedded clauses, and for her analysis more generally. However, as we have already seen, this is not the case for Washo, since tenseless clauses embedded under attitude predicates can receive a back-shifted interpretation. This observation provides support for the idea that a temporal pronoun is represented syntactically in Washo. 32 In the analysis sketched above in Sect. 4.2.4, the embedded temporal pronoun undergoes res-movement in order to derive the back-shifted reading. Although morphologically tenseless clauses in Washo and Paraguayan Guaraní pattern similarly in many key respects, the (un-)availability of back-shifted readings in embedded contexts constitutes an interesting point of variation between the two languages, which ultimately require different analyses.

Presuppositional alternatives
Recent work on presuppositions and blocking has seen increasing use of Maximize Presupposition (MP), a principle that requires that a sentence with the strongest presupposition be chosen amongst its alternatives (Heim 1991;Percus 2006;Schlenker 2012). A somewhat simplified version of MP is given in (95), adapted from Schlenker (2012).

(95) Maximize Presupposition:
If a sentence S is a presuppositional alternative of a sentence S , and the context C is such that a. the presuppositions of S and S are satisfied within C b. S and S have the same assertive component relative to C c. S carries a stronger presupposition than S then S should be preferred to S Tensed and tenseless clauses in Washo fall under the criteria in (95), and so should be subject to MP. Let's illustrate with (3) as S and (2) as S . Their semantic analyses are repeated below in (96) and (97), respectively.
First, for a C where g(1) < t c , the presuppositions of both S and S are satisfied (vacuously for S ). Second, both have the same asserted component: relative to a C where g(1) < t c , the asserted component for both S and S is that it rains in a world w at time g(1). Finally, the presupposition of S is stronger than that of S , since S does not carry any temporal presupposition. Thus, based on (95), S and S are the right sort of candidates to compete as alternatives, and so a clause containing -uNil should be preferred over a tenseless clause in any context where the presuppositions are met, i.e., whenever there is a topical past reference time in the context. Tenseless clauses, having a weaker presupposition, should then only be used when the presuppositions of -uNil are not satisfied, i.e., when the reference time includes a non-past time. Sauerland (2002) in fact capitalizes on exactly this prediction for his argument that the present tense in English is vacuous (i.e., carries no temporal presupposition), and only receives its non-past interpretation as an 'anti-presupposition' that it only be used when the presuppositions of the past tense are not satisfied.
However, the predictions are plainly wrong for the Washo facts, since tenseless clauses readily appear in contexts where the presuppositions of -uNil are satisfied. This poses a problem for MP as stated in (95), since it seems to not apply. This is quite problematic, since, as argued by Schlenker (2012), MP can be derived from more general Gricean pragmatic principles, which are presumably universal, or at least should not be systematically absent in any given language.
The culprit, I suggest, is located in the if-clause of the statement of MP in (95). Since the application of MP is conditionalized on whether S and S are presuppositional alternatives, it must be the case that tensed and tenseless clauses in Washo are not the right kind of presuppositional alternatives that MP can apply to.
Typically, the presuppositions that are compared by MP are carried by lexical items that form a scale of strength. Some widely-discussed examples in the literature include {a, the}, {all, both}, and {think, know}, whereby the elements on the right of each pair carry stronger presuppositions than those on the left. In principle, one could propose a scale of {∅, past}, where ∅ represents the absence of a lexical element rather than a null member of a paradigm. Since past carries a stronger presupposition, MP should apply, but this is exactly the prediction we wish to avoid to account for the Washo data. It seems then that a scale of the sort {∅, past} should be ruled out. I suggest that the reason this is so is because the resulting sentences to be compared by MP do not have an identical syntactic structure. In particular, the presence or absence of a tense feature is enough of a structural difference that the resulting sentences cannot be compared by MP, and do not trigger its application. In other words, the existence of a paradigm is crucial to generate the alternatives that enter into a MP competition.
In support of this view, note that whereas English {all, both} form an appropriate scale for MP, {∅, both} do not. Note the contrasts in (98)-(100), given that the current US President (Barack Obama at the time of writing) has exactly two children. The MP-based analysis for the contrast between (98)-(99) holds that both must be used, since its presuppositions, which are stronger than those for all, are satisfied in the context. But a similar explanation cannot explain why both (99) and (100) are acceptable in the same context. The presuppositions of both sentences are satisfied in the context, and the presuppositions in (99) are stronger, yet (100) is not blocked. We seem to be in a situation just like the one for Washo tensed versus tenseless clauses. I suggest we can make sense of the data in a parallel way: (99) and (100) are simply not comparable, since (99) has extra structure that (100) lacks, even though their presuppositional asymmetry in principle would otherwise trigger MP. 33 The relevant paradigm for the MP competition is {all, both}, and sentences with the same asserted content but not containing a member of the paradigm do not form part of the alternative set.
The apparent puzzle regarding the non-application of MP can thus be understood when we narrow down the sorts of sentences that count as presuppositional alternatives in the first place. Crucially, the MP alternatives must be generated from a set of lexical items that form a paradigm, and in the case of the optional past tense in Washo, we have only a single-membered paradigm. Following Percus (2006), Singh (2011), and others, we must therefore add extra conditions to define the morphological items that generate the MP alternatives, to supplement the definition in (95). Crucially, as the optional tense data show, there must be a constraint that neither member of the scale be ∅, i.e., the absence of a morpheme. I formulate this idea in (101).

(101) Paradigmatic Presuppositional Alternatives:
If α, β is a scale, where α, β = ∅, and S is a sentence containing α, and S is a sentence containing β in the same terminal node where S contains α, then S is a presuppositional alternative to S.
If this line of reasoning is correct, then the lack of MP effects serve as another argument against an analysis of morphologically tenseless clauses as containing a null nonfut tense. Under such a scenario, the elements {nonfut, past} would form a paradigm of tenses. Alternatives generated by the paradigm would enter into an MP competition, since the presuppositions of past are a subset of the presuppositions of nonfut. Then, by MP, sentences containing nonfut should in most contexts carry the anti-presupposition that the past presupposition is not satisfied, i.e., it should effectively function as a present tense, which is the undesired prediction. Thus, the lack of MP effects serves as a novel argument against a null nonfut in morphologically tenseless clauses in Washo, and potentially other languages as well. 34 The idea that Maximize Presupposition should be relativized to morphological paradigms can help us understand the relation between morphological and semantic markedness. In the case of {∅, -uNil}, as well as {∅, both}, we observe a symmetry between semantic markedness and morphological markedness. That is, the ∅ member of each pair represents both semantic vacuity and morphological vacuity, while the morphologically marked member is also the semantically marked member, i.e., has semantic import. This situation contrasts with the typical cases where MP is invoked. For instance, in the case of {a, the}, both members of the paradigm are equally morphologically marked, and each are semantically marked (Heim 1991). However, the carries a stronger presupposition, and wins out in an MP-based competition when its presuppositions are met. In the case of English present versus past tense, both members of the paradigm are morphologically marked. However, in Sauerland's (2002) analysis, only the past tense is semantically marked, while the present tense is semantically vacuous. 35 In this case, MP applies, and the present tense only receives its apparent meaning as an anti-presupposition when the presupposition of the past tense is not satisfied. Meanwhile, in their analysis of the singular/plural contrast (in English), Sauerland et al. (2005) argue that the morphologically unmarked singular form is actually the semantically marked one, while the morphologically marked plural form is semantically unmarked. Once again, MP is invoked to explain the distribution of these forms. The singular is used whenever its presuppositions are met, while the plural is used in the elsewhere case, and acquires its apparent meaning as an antipresupposition. 36 By contrast, in the case of {∅, -uNil}, morphological and semantic markedness align, and we find that MP does not apply. This is precisely the type of scale that (101) rules out.
These observations are summarized in (102). What we can glean from this is that an MP competition does not apply when only one and the same member of the pair is both semantically and morphologically marked. In this case, then, there is a sense in which there is actually no pair to begin with, the 34 Note that Cable's (2016) analysis for Tlingit predicts that MP should require that past marking is used whenever its presuppositions are satisfied, since he posits a null nonfut tense whenever the optional past tense is not used. Cable also posits a constraint on including as many topic times as possible within the denotation of the reference time pronoun, which may obviate the MP competition in certain contexts. 35 See Thomas (2015) for arguments against this view. 36 See Farkas and de Swart (2010) for arguments against this view, and an alternative analysis. members of which can be compared by MP. 37 Perhaps it is not so surprising, then, that a constraint like MP does not apply in cases exactly like the optional past tense in Washo, or in cases with both the versus plain the in English. This case study thus reveals something about the nature of presuppositional alternatives and MP, specifically the range of its application in natural language.

Cessation implicatures
There are certain pieces of data that potentially cast doubt on my analysis of -uNil as simply a past tense, parallel to the past tense in English. As observed by Jacobsen (1964), -uNil seems to contribute more than just a past temporal reference, it also "indicates an interruption or cessation of the action or condition expressed by the theme to which it is affixed" (Jacobsen 1964, p. 607). He goes on to say that -uNil "also commonly expresses a semantic linkage with the following verb, in cases where the action or condition expressed by the latter is not the normally expected sequel of the one expressed by the verb to which -uNil is affixed -cases where the first action is interrupted, thwarted, nullified, rejected, or counteracted by the second action" (Jacobsen 1964, p. 607).
In support of these claims, Jacobsen provides several examples where cessation readings seem to occur. For instance, (103) gives rise to a cessation of state reading according to Jacobsen. Namely, the state of being on the ground, marked with -uNil, comes to an end when the subject comes to his senses.
(103) k'uléwePuNiludi ∅-k'ule-iweP-uNil-ud-i 3-be.lying.down-direction-past-seq-ind hámuguyú:getiPaP ∅-hamuguyu:g-etiP-aP 3-think.straight-inch-dep 'He lay on the ground, and then he came to his senses.' (Jacobsen 1964, p. 608) For eventive predicates marked with -uNil, it is the result state of the event that ceases to hold. For instance in (104), the predicate táw1niPgišuweP 'go to town' is marked with -uNil, and as the following clauses indicate, the result state of being in town no longer holds. Meanwhile in (105), the result state of an eating event, i.e., that food has been ingested, no longer holds, given the following clause.
(105) PémluyuNilige P-emlu-uNil-i-ge 3-eat-past-indobj.rel sesmáPyi ∅-sesm-aPy-i 3-vomit-away-ind 'He ate it and then he vomited it up.' (Jacobsen 1964, p. 608) Finally, (106)-(107) seem to give rise to what Jacobsen describes as an unexpected result reading. In (106), the expected result of jumping on someone who is asleep would be that they wake up, while in (107), one might reasonably expect someone to enjoy food that has been fed to them, though this characterization of (107) might be a bit tenuous here.
(106) míwiP mi-wiP 2-3 malá:NaPéPešgayapgap'1luNilišgiNa ∅-mele-aNaPe-iPiš-gayab-gap'1l-uNil-i-š-gi-Na 3-jump-on-motion-over-aroundpast-ind-sr-subj.rel-but méPidaNa m-eP-i-da-Na 2-cop-ind-there-nc mémc'iyé:saš m-emc'i-e:s-aP-š 2-wake.up-neg-dep-sr 'He kept jumping on you while going by, but where you were, you didn't wake up.' (Jacobsen 1964, p. 609) (107) gebúPuyuNilišgiNa ge-buPu-uNil-i-š-gi-Na 3.obj-feed-past-ind-sr-subj.rel-but gala:mé:saP ∅-gala:m-e:s-aP 3-like-neg-dep 'They fed it to him, but he didn't like it.' (Jacobsen 1964, p. 608) Interestingly, such inferences associated with optional past morphology are not unique to Washo. Cable (2016) notes that the Tlingit decessive (optional past tense) is described by Leer (1991) as having similar cessation and unexpected result implications. Moreover, Plungian and van der Auwera (2006) characterize languages with optional past tenses as giving rise to these implications when the past tense morpheme is present. For this reason, Plungian and van der Auwera claim that optional past tenses in these languages in fact conventionalize more than simply a meaning of past temporal reference. Rather, these languages have what they call 'discontinuous' pasts, which conventionalize a meaning of "past and not present", unlike languages like English, where past tense does not conventionalize anything specific about the present. Cable (2016) shows that in Tlingit, the cessation inference is merely an implicature, and not part of the conventional content of the decessive. Evidence from Washo also suggests that the cessation interpretation of -uNil is an implicature. In contexts where cessation of a state is asserted, -uNil is not required, as shown in (108)-(109). In fact, in (109), one speaker actually showed a dispreference for marking the verb whose post-state no longer holds (marked here by ? The fact that the cessation inference is an implicature indicates that it is not part of the conventional content of -uNil. Thus, we can maintain an analysis where -uNil simply encodes past time reference, and any extra information that is apparently conveyed by -uNil can be treated as an implicature. I leave the exact characterization and analysis of the implicature for future research, though see Cable (2016) on deriving the cessation and unexpected result implicatures for the decessive in Tlingit. Of particular interest would be to test embedded uses of -uNil and what types of inferences are available (or not) in embedded contexts.

Further issues in past temporal reference in Washo
There remain several open issues related to past temporal reference in Washo that are still in need of further research. One major issue that I have abstracted away from in this paper is that in addition to -uNil, Washo additionally possesses a series of "graded tenses", also known as temporal remoteness morphemes following Cable (2013). These morphemes are also verbal suffixes, and indicate the degree of remoteness between the speech time and the event named by the verb phrase. There are three past temporal remoteness morphemes described by Jacobsen (1964), shown in (112)-(114): -leg 'recent past', -ayP 'intermediate past ', and -lul 'distant past'. with multiple tenses, when we view tenses as features placing presuppositions on the value of a temporal pronoun. So long as the presuppositions of individual tenses do not conflict, or they place restrictions on distinct variables, there is in principle no reason why multiple tense features in a clause could not co-occur. But much more work needs to be done to investigate this matter in Washo.
Another question for further research is the status of the suffix -uNil on nouns in Washo. Jacobsen (1964) describes this use of -uNil as describing a deceased individual. When attaching to a noun whose referent in the context is known to be alive, it has the force of profanity. Examples of each of these uses are given in (116)-(117).
(116) diyéyaluPuNil di-yeyaluP-uNil 1.poss-relative-past 'my dead relatives' (Jacobsen 1964, p. 482) (117) sukúkuPuNil suku∼red-uNil dog∼plpast MéPigi M-eP-i-gi 2-beind-subj.rel 'You damn dogs!' (Jacobsen 1964, p. 482) This fairly narrow range of interpretations of -uNil on nouns potentially points to an analysis where -uNil in these cases is not an instance of nominal tense. However, all the nouns given by Jacobsen are those that denote permanent properties with respect to the lifetime of the individual, which may be the source of the implication that the referent of the noun is deceased when combined with -uNil. A much more systematic investigation of -uNil with a wider variety of nouns is in order before drawing any conclusions about this use of the suffix. In any case, there is somewhat of a debate in the literature over whether grammatical temporal modifiers of nouns should be analyzed as true tenses (Nordlinger and Sadler 2004;Thomas 2014;Tonhauser 2007), so I will not even speculate at this point whether we want to extend the current analysis of -uNil as a past tense to these nominal cases, though it remains an interesting question for future research.

Conclusion
I have argued that the verbal suffix -uNil in Washo should be analyzed as a past tense, parallel with past tense in English. Strikingly, the interpretation of -uNil is highly similar to that of English past tense, as both give rise to simultaneous and backshifted readings in propositional attitude complements, for instance. Meanwhile, I argued that morphologically tenseless clauses are also semantically tenseless. Within the formal framework adopted, this means that there is no tense feature restricting the value of a temporal pronoun. However, I argued on the basis of back-shifted readings in embedded clauses that a temporal pronoun is still represented in morphologically tenseless clauses. That is, morphologically tenseless clauses lack tense features, but still contain a temporal pronoun. My analysis thus makes precise what it means for a language to have optional tenses, and provides a window into the nature of crosslinguistic variation in the domain of tenses and temporal reference. Specifically, we observe that tense need not be an all-or-nothing category, in the sense that tense features may not form complete paradigms in all languages that have tenses. 39 The results of this paper raise important issues in the analysis of tense and temporal interpretation cross-linguistically. First, instead of the rigid two-way split between tensed versus tenseless languages that we began with at the beginning of the paper, a three-way typology of tense systems emerges. Languages can be morphologically tensed or tenseless, and within the tensed languages, tenses may be obligatory or optional. On the morphological side, this view has already been advanced by Plungian and van der Auwera (2006). A novel contribution of this paper has been to extend this hypothesis to the semantics, where I argued that there is at least one language where semantic tenses are present in some, though not all, finite clauses. Thus, what 'optional tense' means from a semantic point of view is that sometimes a reference time variable is semantically restricted, and sometimes not. In other words, we have found another case of variation in tense systems of the sort that we already knew existed from cross-linguistic research, namely in the means through which a language places restrictions on temporal variables.
Second, the cessation inference associated with -uNil (Jacobsen 1964) was shown not to be part of the conventional meaning, but rather a cancellable implicature. Cable (2016) also makes this observation for the optional past in Tlingit. This cross-linguistic finding calls into question Plungian's contention that optional pasts have a semantics distinct from an ordinary past tense in English-like languages, and whether 'discontinuous past' is in fact a linguistic category at all. At the heart of this issue is the lack of paradigmatic opposition between tensed and tenseless forms, and how the shape of tense paradigms affects the interpretation of morphologically tensed and tenseless clauses, both within and across languages. On the one hand, the absence of a full paradigm of tenses gives rise to a cessation inference for sentences containing an overt past tense. On the other hand, morphologically tensed and tenseless clauses do not compete in a Maximize Presupposition-based competition. This latter fact motivated a modification to the traditional definition of MP, where the set of alternatives is crucially relativized to full morphological paradigms. This study in optional tense thus provides a window into the broader issues of presuppositional alternatives, and how the shape of morphological paradigms contributes to semantic interpretation.
Third, this paper offered a novel argument against a phonologically null non-future tense analysis of morphologically tenseless clauses based on the lack of Maximize Presupposition effects. Based on the empirical data alone, I showed that both my analysis and a non-future tense analysis of such clauses in Washo are almost indistinguishable, except for future interpretations of clausal conjunctions with sequential -ud, where my analysis fares better. Given the narrow range of data that distinguish the analyses empirically, the new theoretical argument from Maximize Presupposition is welcome, particularly since the analysis of morphologically tenseless clauses cross-linguistically has been the subject of much recent debate. Crucially, this argument is afforded to us by the fact that Washo is an optional tense language. While I believe this argument can in principle be extended to the analysis of other languages with optional tense, 39 An interesting avenue for further research would be to examine other optional syntactic operations, e.g., optional wh-movement, as suggested by a reviewer. and also to languages with exclusively morphologically tenseless finite clauses, it is an empirical matter what kind of analysis is appropriate for an individual language.
Finally, the Washo data in this paper contribute to a growing body of work on temporal reference cross-linguistically. While the focus was on past interpretation, this study also raised the issue of future interpretation, particularly for morphologically tenseless clauses. There is much more to be said here, both for Washo and other languages, and there seems to be much important cross-linguistic variation here. First, whereas Washo allows future interpretations of morphologically tenseless clauses in planning contexts, this is not possible in St'át'imcets, where an overt future marker must be used (Lisa Matthewson, p.c.). Under the analysis I presented, this would amount to variation in the availability of a covert plan operator. Second, a reviewer notes that future interpretations of morphologically tenseless matrix clauses in Mandarin Chinese can also be licensed by a plan context or a conditional, but non-plan futures require a modal, just like in Washo. However, a future interpretation is also licensed in complement clauses in Mandarin Chinese. This does not seem to be the case for Washo, where a future marker is required for future interpretations of complement clauses, but more work needs to be done here. The nature of future interpretation, and how it differs from past and present interpretation, remains a critical and open issue ripe for further research. q = question; rec.past = recent past; refl = reflexive; restr = restrictive; sbj = subjunctive; seq = sequential; sr = switch reference; static = prefix on weather verbs; subj = subject; subj.rel = subject relative; theme = anaphoric sentence connective theme; vis = visual evidential.