Hamida Demirdache & Myriam Uribe-EtxebarriaUniversity of Nantes/LLING (EA 3827)

& University of the Basque Country/Basque Center for Language Research (LEHIA)

The Syntax of Time Arguments*

Abstract. This paper develops the model of temporal interpretation presented in Demirdache & Uribe-Etxebarria(1997, 2000, 2002, 2004, 2005; henceforth D&U-E). The following three proposals are defended. (i) Tenses, aspectsand time adverbs (uniformly analyzed as covert/overt PPs) are spatiotemporal predicates projecting their time-denoting arguments into the syntax as Zeit-phrases (sections 1-2). (ii) The time intervals projected into the syntax aseither covert arguments of tenses and aspects, or as overt arguments of temporal prepositions can, just as any DP, berestrictively modified and enter into anaphoric dependencies –where anaphora is construed as either covaluation or(semantic) binding. In simple tenses, covaluation between the external and internal arguments of Aspect yieldsperfective aspect, whereas semantic binding yields neutral aspect (sections 3-4). (iii) Temporal interpretationinvolves computing ordering relations and anaphoric dependencies between time intervals. Temporal computation issubject to economy conditions governing (the representations generated at) each step of a given temporal derivation(section 5).

1. Tenses, Aspects and Time Adverbs as Spatiotemporal Predicates

The model of temporal interpretation developed in D&U-E aims at uniformly defining temporalrelations in terms of elementary and isomorphic semantic and structural primitives. The thesisunderlying our model is that tenses, aspects and time adverbs express spatiotemporal relations–precedence, subsequence or inclusion – between time intervals. To illustrate, consider thefollowing paradigm.

1a. Kim was working this morning. She finished at noon.b. Kim was working this morning. She still hasn't finished.2. Kim is working.3. Kim was working in 2001.

The progressive in (1) presents the described situation as having no temporal bounds, neither aninitial, nor a final end-point. In particular, although the sentence is in the past, no assertion ismade regarding the culmination of the working event: Kim might (1a) or might not (1b) havefinished working at utterance-time (UT-T). We can thus analyze the progressive as ordering twotimes intervals: the time for which an assertion is made (the AST-T, in the sense of Klein 1995)and the time at which the event or state denoted by the VP occurs or holds (EV-T). As noassertion is made about whether the event of working culminated, the time for which the speakermakes an assertion must be a subinterval of the event-time. The ordering relation established byprogressive aspect is thus the topological relation of inclusion: the AST-T is ordered within the EV-T, as illustrated by the temporal schema in (4a).

*We thank Brenda Laca, Patricia Cabredo, Javi Ormazabal, Arnim von Stechow, Tim Stowell, Karen Zagona, andtwo anonymous reviewers for insightful comments and questions. This research was partially funded by theLaboratoire de Linguistique de Nantes/EA 3827, the University of the Basque Country (9/UPV 00033-13888-2001;9/UPV 00114.130-16009/2004), and the Spanish Ministry of Science and Technology (MICYT)/FEDER (BFF2002-04238-C02-01). The work reported here is part of Program #4 (“Clausal Architecture”) of the CNRS FédérationTypologie et Universaux Linguistiques.

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4a. Progressive b. Present c. Time adverb AST-T UT-T AST-T

—[——[———]——]——> —[——[———]——]——> —[——[———]——]——>EV-T AST-T 2001

The present in (2) tells us that the subinterval of the time of the event for which the speakermakes an assertion (that is, the AST-T) overlaps with speech-time. We can thus analyze thepresent as ordering two time intervals: the UT-T and the AST-T. The ordering relation is once againthe topological relation of inclusion: UT-T is ordered within the AST-T, as illustrated in (4b).

Finally, the adverb in (3) serves to locate the past subinterval of the time of the event forwhich the speaker maker an assertion (that is, the AST-T) within the time designated by 2001. Wecan thus analyze the time adverb as ordering two time intervals: the AST-T and the time denotedby 2001. This relation is once again one of inclusion: a past subinterval of the time of working(namely, the time for which an assertion is made) is ordered within the time designated by 2001,as illustrated in (4c).

We conclude that the semantic contribution of tenses, aspects and time adverbs to thetemporal interpretation of a sentence can be uniformly described in terms of elementarytheoretical primitives: topological relations established between time intervals. To formallycapture this generalization, D&U-E propose that tenses, aspects and time adverbs are predicatesof spatiotemporal ordering with the three corollary assumptions given below.

5a. Spatiotemporal predicates take time-denoting argumentsb. Spatiotemporal predicates project their (temporal) argument structure in the syntaxc. Spatiotemporal relations are uniformly defined in terms of an abstract basic semantic

opposition: +/-central coincidence in the location of an entity, the Figure, with respect tothe Ground, following Hale (1984).

By assuming that tenses, aspects and time adverbs introduce time-denoting arguments, we adopta referential approach to the semantics of Tense. This approach, directly inspired by Reichenbach(1947) and spelled out in a wide variety of ways (Enç 1987, Kamp & Reyle 1993, or Partee 1984,among many others), establishes a parallel between the semantics of tense and that of pronouns.Time spans (introduced by tenses, adverbs or temporal connectives) are referential expressionsand as such enter into anaphoric dependencies. By further assuming that the time spansintroduced by tenses are discourse referents projected into the syntax as temporal DPs —or Zeit-phrases in Stowell's (1993) terminology— we adopt a tradition of analysis initially explored inthe work of Stowell (1993, 1995a, 1995b) and Zagona (1990, 1993, 2003).

We have argued for a strict parallel between the semantics of tenses, aspects and timeadverbs: they are uniformly analyzed as predicates establishing topological relations betweentime-denoting arguments. We now establish a strict parallel between the syntax of tenses, aspectsand time adverbs by developing isomorphic structural representations for these categories thatcapture the semantic parallel established. In so doing, we extend proposals initially put forth inZagona (1990) and Stowell (1993) for the syntax of Tense, first to the syntax of Aspect and thento the syntax of time adverbs.

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1.1. The Syntax of Tense: Zagona (1990) and Stowell (1993)

Zagona (1990) and Stowell (1993) develop structural representations for temporal interpretationwhere Tense is decomposed syntactically into its semantic components.

The phrase structure for Tense proposed by Stowell (simplified for expository reasons) ispresented below. Tense is a two place predicate establishing a relation of temporal orderingbetween two time-denoting arguments projected in the syntax in specifier positions. The externalargument of T° is a reference-time (REF-T; typically, UT-T in a matrix clause) and its internalargument, the time of the event (EV-T).

6. The Phrase-Structure of TenseTP2

REF-T T’2T° VP2

EV-T VP

1.2. The Syntax of Aspect: D&U-E (1997, 2000, 2002)

We have argued that Aspect, just like Tense, is a spatiotemporal predicate establishing anordering relation between two time-denoting arguments and projecting its temporal argumentstructure into the syntax. The null hypothesis is that Tense and Aspect are assigned isomorphicstructural representations. This proposal is illustrated in (7).

7. The Isomorphic Syntax of Tense and AspectTP2

REF-T T’UT-T 2

T° ASP-P2 REF-T ASP’AST-T 2

ASP° VP2EV-T VP

(7) breaks down both Tense and Aspect syntactically into their respective semantic components.The functional heads ASP° and T° each relate two temporal arguments. The external argument ofT° is a reference-time (UT-T in an independent or matrix clause). T° orders this reference-timewith respect to its internal argument, the time of the assertion. The external argument of ASP° isitself also a reference-time (the AST-T). ASP° orders this time interval with respect to its internaltemporal argument, the time of the event denoted by the VP.

Tenses and aspects are further defined in terms of identical semantic primitives. Thespatiotemporal predicate AFTER, which establishes a relation of temporal subsequence betweentwo time spans, can have either a temporal value (past tense) or an aspectual value(retrospective/perfect aspect). The spatiotemporal predicate WITHIN, which establishes a relationof temporal coincidence between two time spans, can have either a temporal value (present tense)or an aspectual value (progressive aspect). The spatiotemporal predicate BEFORE, which expresses

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temporal precedence between two time spans, can have either a temporal value (future tense) oran aspectual value (prospective aspect).

We have defined the external argument of Aspect as the assertion-time following Klein(1995: 687):

«The Assertion-time [AST-T] is the time for which an assertion is made or to whichthe assertion is confined; for which the speaker makes a statement.»

Klein's proposal allows us to formally capture the traditional idea that the role of grammaticalaspect is to focus a time interval in the temporal contour of the event described by a sentence.Smith (1991: 91) gives the following definition of grammatical, viewpoint, aspect:

«Aspectual viewpoints function like the lens of a camera, making objects visible tothe receiver [...] And just as the camera lens is necessary to make the object availablefor a picture, so viewpoints are necessary to make visible the situation talked about ina sentence. [...] We shall say that the part focused by a viewpoint is visible tosemantic interpretation [...] What is focused has a special status, which I will callvisibility. Only what is visible is asserted [...].»

The time span focused by Aspect is the time of the assertion. The question remains, however, asto why viewpoint aspect serves precisely to focus, pick up, a time interval within the internaltemporal structure of the described event. The proposal that aspects are spatiotemporal predicatesoffers a straightforward answer to this question.

Aspects are dyadic predicates with inherent lexical meanings (WITHIN, BEFORE, AFTER),establishing ordering relations between two time spans. The relation established between the timespan focused by Aspect (the AST-T) and the interval which defines the time of the described eventcan be one of inclusion, precedence or subsequence. When this ordering relation is one ofinclusion, as in (8a), the aspectual viewpoint is said to be progressive or durative. When thisordering relation is one of precedence, as in (8b), the viewpoint is said to be prospective. Finally,when this relation is one of subsequence, as in (8c), the viewpoint is said to be retrospective(perfect aspect).

8a. Progressive b. Prospective c. Retrospective/ Perfect AST-T AST-T EV-T EV-T AST-T

—[——[———]——]—> —[———][———]—> —[———][———]—>

EV-T

1.3. The Syntax of Time Adverbs

Once we assume that time-denoting arguments are represented syntactically as temporal DPs orZeit-phrases, then the null hypothesis is that these arguments can be modified, just as any DPcan. This is precisely the thesis defended by D&U-E (2002, 2004): time adverbs are semanticallyand syntactically restrictive modifiers of temporal DPs, Zeit-Ps, projected in the syntax, asarguments of the functional categories T° and ASP°.

We establish a semantic and a syntactic parallel between nominal and temporal restrictivemodification. (9a) illustrates the syntax of nominal modification: the modifier restricts the

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reference of its sister NP. Temporal modification has the same syntax. Time adverbs are base-generated adjoined to the temporal argument that they modify —that is, to the Zeit-P whosetemporal reference they restrict. Restrictive modification is established via predication: themodifier is predicated of a nominal/DP argument in (9a), a temporal/Zeit-P argument in (9b).

9a. Syntax of Nominal Modification b. Syntax of Temporal ModificationNP AST-T/EV-T2 2

NP MODIFIER AST-T/EV-T MODIFIER

(PP / CP...) (PP)‘in the house’/‘that is in the house’ ‘in 2000’/‘after Kim left’

D&UE argue that all time adverbs, whether they have the syntax of PPs (takingnominal/sentential complements —e.g. after Christmas/Kim left) or bare DPs (e.g. Sunday), areanalyzed as temporal PPs relating two arguments. The external argument of a temporal PP/adverbis the covert time span whose reference it restricts: either the assertion-time or the event-time ofthe clause in which it occurs, as shown in (9b). Its internal argument can be an overt timeargument (e.g. 2000/Christmas/meeting). We spell out here more precisely the internal syntax ofovert Zeit-Ps, adapting recent proposals by Pratt & Francez (2001; henceforth P&F) for thesemantics of temporal nouns.

P&F argue that temporal nouns –namely, those nouns that can serve (in)directly to pick outa time interval– are interpreted as predicates of times. A calendar noun like Sunday will beinterpreted directly over time-intervals –that is, as a property of time intervals as in (10a) where irepresents the type of time intervals. Sunday thus denotes the set of intervals which are Sundays.1

10a. Sunday: λi.SUNDAY(i) b. each Sunday: λJ.∀i[SUNDAY(i)→ J(i)]

Determiners/quantifiers in temporal NPs are similar to the familiar nominal determiners exceptthat they denote relations between predicates of times rather than predicates of individuals, as in(10b) where J stands for a temporal property variable. Each in (10b) thus has the standardmeaning of a universal generalized quantifier, except that it relates sets of intervals: the set ofintervals which are Sundays is required to be a subset of the set of intervals having the temporalproperty J. The universal quantifier thus maps any temporal predicate J to the statement that Jholds of each interval which is a Sunday. Within a framework where time intervals are argumentsof spatiotemporal predicates projected in the syntax as temporal DPs/Zeit-phrases, the proposalthat generalized temporal quantifiers can serve as meanings for these DPs is very appealing as ittakes the parallel between nominal and temporal reference/quantification a step further. Wetherefore propose the syntax in (11) for temporal and non-temporal nouns in temporal contexts(e.g. meeting)2, which transparently reflects the semantics given in (10).

1P&F's further assume an operation of contextualisation applying to (10a) and introducing a context variable. Sundaywould thus denote the property of being a set of intervals which are Sundays within a given temporal context.

See D&U-E (in progress) for extensive discussion of scope interactions between overt quantified Zeit-Ps (e.g.each sunday) and the covert Zeit-Ps (AST-T/EV-T) projected as arguments of Tense and Aspect.2For P&F, a temporal preposition which takes meeting as its complement coerces the meaning of the event noun intoa predicate of times (from type e to i) —during the meeting means during the running time of the meeting.

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11a. ZEIT-P b. ZEIT-P2 2Z° NP Z° NP

each/two/the/a 2 (THE) 2SIT-T NP SIT-T NP

Sunday/meeting Sunday

The temporal interval argument of the noun (represented as SIT-T) is projected onto its externalspecifier position. Z° can either be an overt quantifier (e.g. each, two or most), an (in)definitedeterminer (11a), or an implicit determiner as (11b). We take this silent determiner to be thedefinite determiner since bare (singular) calendar nouns allow either a deictic definiteinterpretation (the unique Sunday which precedes or follows speech-time) or an anaphoricdefinite interpretation.

The syntax of restrictive temporal modification is given below. Modification isestablished via predication: the PP modifier is predicated of (takes as external argument) the AST-T. As we shall see in section 3.1, in a simple past tense sentence such as (12), the AST-T and theEV-T are cotemporal. This is why the described event is viewed as including both its initial andfinal bounds (perfective aspect): the time of the assertion is the time of Kim's leaving. Note thatsince these two intervals coincide (see (12d-e)), modifying the AST-T is temporally equivalent tomodifying the EV-T.

12 Kim left before/after Christmas, in December.

a. 3 b. 3 c. 5AST-T PP AST-T PP 3 PP

2 2 AST-T PP 3P° ZEIT-P P° ZEIT-P 2 P° ZEIT-P

BEFORE/AFTER 2 IN 2 P° ZEIT-P IN 2Z° NP Z° NP BEFORE/AFTER 2 Z° NP

(THE) 2 (THE) 2 Z° NP (THE) 2 SIT-T NP SIT-T NP (THE) 2 SIT-T NP

Christmas December SIT-T NP DecemberChristmas

d. before Christmas in December e. after Christmas in DecemberAST-T=EV-T CHRISTMAS UT-T CHRISTMAS AST-T=EV-T UT-T

——[—[—————]—[————]—]—[——]—> ——[—[————]——[————]—]—[——]—> DECEMBER DECEMBER

The internal argument of the spatiotemporal predicate BEFORE/AFTER/IN is an overt Zeit-P. Itsexternal argument is a silent/covert Zeit-P. In (12a), the predicate BEFORE/AFTER restricts thereference of its external argument (the AST-T ) by establishing a relation ofprecedence/subsequence between this interval and the SIT-T of its internal argument Christmas.Likewise, in (12b), the predicate IN restricts the reference of the AST-T by establishing a relationof inclusion between the AST-T and the SIT-T of Christmas. (12c) illustrates the syntax ofrecursive modification: two PPs are adjoined to —and thus predicated of— the AST-T (itselfcotemporal with the EV-T). The time of Kim's leaving thus falls before/after Christmas and withinDecember, as illustrated in (12d/e).

This proposal extends to temporal adverbial clauses which by hypothesis are temporal PPsrelating two time-denoting arguments. In particular, D&U-E analyze the adjunct clause in (13a)as a PP modifier of the AST-T of the main clause in which it occurs (AST-T1). The prepositionAFTER/BEFORE establishes an ordering relation between AST-T1 and the AST-T of the adjunct

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clause (AST-T2). The clause selected by P° is itself analyzed as a covert temporal relativepredicated of AST-T2, as sketched in (13b). Predication is established via null operatormovement3. The temporal connective AFTER thus orders AST-T1 after the time interval (AST-T2)which has the property of being a past time interval at which Kim's arrival occurs.

13a. Terri left after Christmas/after Kim arrived.

b. PP

3AST-T1 PP2

P° [ZEIT-P (THE) CHRISTMAS]AFTER [ZEIT-P (THE) AST-T2 [CP λi[TP UT-T AFTER i & i = i’ & ARRIVE (KIM)(i’)]]]

Crucially, under this analysis, the internal argument of the preposition (which on the surface hasthe syntax of a clause) is in fact a Zeit-P, a temporal DP, ultimately denoting the past timeinterval at which Kim arrived. This analysis fits nicely with P&F's proposal for the semantics oftemporal adverbial clauses: an implicit quantifier applies to the sentential complement clause(Kim arrived) which itself denotes a property of times (those times at which Kim arrived), andturns it into a generalized temporal quantifier. The complement clause thus ends up denoting thetime interval at which Kim arrived.

1.4. Towards an Isomorphic Syntax for Tenses, Aspects and Time Adverbs

The hypothesis that time adverbs are PPs predicated of temporal arguments allows us to representtenses, aspects and time adverbs in terms of identical semantic and structural primitives: (i)spatiotemporal predicates projecting a maximal projection in the syntax, and (ii) time-denotingarguments projected in the external/internal specifier positions of these predicates. The semanticand syntactic parallel thus established is illustrated in (14).4

3See D&UE (2002, 2004b) for empirical arguments that relativization involves movement of a temporal operator,and a detailed analysis of temporal adverbial clauses.4In Stowell (1993), the structure for the Zeit-P denoting the EV-T is as given in (i). T° selects a Zeit-P argument (Z° isan existential quantifier binding the temporal variable inside the VP). Generalizing his proposal for the syntax of theEV-T to the syntax of the AST-T, would yield (ii) where T°, ASP° and P° all select a Zeit-P as internal argument.i. ZEIT-P2

Z° VP2EV-T VP

ii. Syntax of Tense Syntax of Aspect Syntax of Time adverbs TP ASP-P PP2 2 2

UT-T T’ AST-T ASP’ AST-T/EV-T P’ 2 2 2

T° ZEIT-P ASP° ZEIT-P P° ZEIT-PWITHIN 2 WITHIN 2 WITHIN 2

AFTER/BEFORE Z° ASP-P AFTER/BEFORE Z° VP AFTER/BEFORE Z° NP2 2 2AST-T ASP-P EV-T VP SIT-T NP

This proposal yields an even stricter parallel between the syntax of tense, aspect and time adverbs than that in (14).See D&UE (in progress) for discussion.

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14. Syntax of Tense Syntax of Aspect Syntax of Time AdverbsTP ASP-P PP2 2 2

ZEIT-P T’ ZEIT-P ASP’ ZEIT-P P’ (REF-T) 2 (AST-T) 2 (AST-T/EV-T) 2

T° ASP-P ASP° VP P° ZEIT-P

WITHIN 2 WITHIN 2 WITHIN 2AFTER/BEFORE ZEIT-P ASP-P AFTER/BEFORE ZEIT-P VP AFTER/BEFORE Z° NP

(AST-T) (EV-T) 2SIT-T NP

Our proposal yields the typology of spatiotemporal predicates illustrated in (15-16). Notice thatthe syntax of time adverbs in (15), be it locating or durative time adverbials, transparently reflectsour proposal: these adverbs are indeed PPs, headed by spatiotemporal preposition expressingsubsequence (‘after’, ‘since’), coincidence (‘in’, at, ‘during’), or precedence (‘before’, ‘until’).

15. Typology of Spatiotemporal PredicatesSubsequence

AFTER

CoincidenceWIHIN

PrecedenceBEFORE

Tense Past‘Passé composé’5 Present Future

Aspect Retrospective (perfect, ‘passé composé’)

Progressive Prospective

Locatingadverbs

after DP / CPat, in, during DP; when CP

before DP / CP

Durationaladverbs

from DP; since, DP / CP for DP; while CP until DP / CP

16a. TensePast Present Future

AST-T UT-T UT-T UT-T AST-T

—[———]—[———]—> —[———[———]——]—> —[———]—[———]—> AST-T

b. AspectRetrospective Progressive Prospective

EV-T AST-T AST-T AST-T EV-T

—[———]—[———]—> —[———[———]——]—> —[———]—[———]—> EV-T

c. Time adverbsafter 1924 in 1924 before 1924

1924 AST-T/EV-T AST-T/EV-T AST-T/EV-T 1924—[———]—[—————]—> —[——[—————]——]—> —[—————]—[———]—>

1924

2. Progressive and Retrospective Viewpoints

We now illustrate this model with an analysis of two aspectual viewpoints: progressive viewpointand retrospective or perfect viewpoint. 5D&U-E (2002) analyze the French ‘passé composé’ as the spatiotemporal predicate AFTER. It can have either atemporal value (simple past) or an aspectual value (present perfect). This is why it has a double classification in (15).

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2.1. Progressive Viewpoint

Progressive viewpoint was defined as the spatiotemporal predicate WITHIN. The temporal phrasestructure of a progressive sentence is illustrated in (17).

17. Present Progressive Past Progressivea. Kim is eating lunch. b. Kim was eating luncha’. TP b’. TP

2 2UT-T T’ UT-T T’2 2

T° ASP-P T° ASP-P

WITHIN 2 AFTER 2 AST-T ASP’ AST-T ASP’2 2

ASP° VP ASP° VP

WITHIN 2 WITHIN 2EV-T VP EV-T VP

In (17a/a’), the progressive establishes a topological relation of inclusion between its external andinternal arguments: it orders the AST-T within the EV-T. It thus focuses/picks up a subinterval ofthe EV-T that includes neither its initial nor its final bounds, as in (18a). The present is likewisedefined as the spatiotemporal WITHIN, ordering the UT-T within the AST-T, as in (18b).

AST-T UT-T

18a. —[——[————]——]—> b. —[——[————]——]—>

EV-T AST-T

The event described by (17a) is presented as unbounded, ongoing because the progressivefocuses/picks up an interval in the internal temporal contour of the event that includes neither itsinitial, nor its final bounds.

The past progressive sentence in (17b) has the same phrase structure except that this timeT° is the spatiotemporal AFTER. The progressive orders the AST-T within the EV-T, yielding (19a).The past in turn orders the UT-T after the AST-T, yielding (19b).

EV-T AST-T UT-T

19a. —[——[————]——]—> b. —[———]—[———]—>AST-T

Note that the UT-T is never ordered with respect to the final bound of the event: T° onlyestablishes a subsequence relation between UT-T and a subinterval of the event-time —namely,the AST-T. Since the AST-T does not include the endpoints of the event, no assertion is made aboutwhether the event of eating culminated before speech-time —although the sentence is in the past.Kim thus might or might not have finished lunch at speech-time.6

6D&U-E (2002) adopt a recursive VP shell structure allowing for a more fine-grained representation of event-structure. The VP is assigned the complex event-structure in (i) where each subevent projects a temporal argumentdefining its running time. Event decomposition in (i) entails that the progressive orders AST-T within EV-T1. Thisanalysis correctly predicts that in, say, Kim was/is opening the door, progressive viewpoint focuses a subinterval of

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2.2. Retrospective or Perfect Viewpoint

The temporal syntax of a perfect sentence is illustrated below. The perfect in (20a) is thespatiotemporal AFTER, ordering the AST-T after the EV-T. It thus picks up a time interval after thetime that defines the EV-T, yielding (21a). The past is also the spatiotemporal predicate AFTER. Itorders the UT-T after the AST-T, yielding (21b).

20. Past Perfect Present Perfecta. Terri had eaten lunch. b. Terri has eaten lunch.a’. TP b’. TP2 2

UT-T T’ UT-T T’2 2T° ASP-P T° ASP-P

AFTER 2 WITHIN 2 AST-T ASP’ AST-T ASP’2 2

ASP° VP ASP° VPAFTER 2 AFTER 2

EV-T VP EV-T VP

EV-T AST-T EV-T AST-T UT-T

21a. —[———]—[———]—> b. —[———]—[———]——[———]—>

The time of the described event (TERRI EAT LUNCH) in (21b) is thus presented as completed priorto a past reference-time —namely, our AST-T. This aspectual viewpoint has been termedretrospective in the literature: the described eventuality is viewed (as completed) from theperspective of a reference-time, itself in the past.

The present perfect in (20b) has the same phrase structure except that this time T° is thespatiotemporal WITHIN. The perfect orders the AST-T after the EV-T, yielding (22a). The present inturn orders the UT-T within the AST-T, as in (22b).

EV-T AST-T EV-T AST-T

22a. —[———]—[———]—> b. —[———]—[——[——]——]———> UT-T

The described event is thus viewed, retrospectively, as completed, as having culminated prior to areference-time (our AST-T), itself overlapping with UT-T in (22b). 7

the time defining the activity of opening the door (the speaker asserts that Kim is/was in the process of opening thedoor), and not a subinterval of the time defining its resulting state.i. VP12

EV-T1 VP1 Process/Activity2V° VP2 Result State2

EV-T2 VP27The complex event-structure given in (i) footnote (6) allows D&U-E to uniformly derive the three readings of thepresent perfect from the proposal that the perfect is the spatiotemporal predicate AFTER. The perfects focuses a(ny)time after EV-T1 in (i) above. If this time happens to fall after the final bound of EV-T2 —that is, if the perfect focuses atime after the interval defining the result state of the described event— an existential present perfect is generated (theperfect indicates the existence of some past event located prior to UT-T). In contrast, if the perfect focuses the interval

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3. The Viewpoint of Simple Tenses: Perfective or Neutral Viewpoint

We have argued that the covert temporal DPs, projected in the syntax as arguments of either T°or ASP°, can be restrictively modified by overt temporal DPs (time adverbs). We now show thatthese covert arguments can enter into anaphoric relations. This hypothesis will allow us to derivethe aspectual viewpoint of simple tenses, which we contend is either perfective or neutral.

3.1. Perfective Viewpoint

The role of ASP° is to overtly specify the relation holding between the event-time and the time forwhich an assertion is made. When ASPº is not morphologically overt, D&U-E assume that therelation between the AST-T and the EV-T is established via anaphora.

For reasons that will become clear in section 3.2 below, we do not follow D&U-E here inassuming that anaphora involves binding. Rather, we assume that anaphora is achieved via eitherbinding or covaluation (coreference).

The distinction between binding and covaluation (Reinhart 1997) is illustrated with the twoanaphoric construals of (23) —truth-conditionally not equivalent. In (23a), his and Kim arecovalued. Covaluation is the assignment of identical semantic values (referents) to two DPs. Thisreading entails that we, for instance, do not love Kim's father. In contrast, in (23b), his istranslated as bound variable. This reading entails that we do not love our respective fathers.

23. Only Kim loves his father.a. Covaluation: Only Kim λx[x loves his father] & his = Kimb. Binding: Only Kim λx[x loves x's father]

Within a model where time spans are discourse referents projected in the syntax as time-denotingDPs, we expect them to enter into relations of anaphora —just as individual-denoting DPs do.Anaphora can be established via covaluation. Covaluation between the AST-T and the EV-T willensure that these time intervals end up ultimately ordered relative to each other —when there isno morphological aspect to overtly specify the relation holding between these two intervals.

To illustrate this proposal, we run through the derivation of a simple past tense sentence. In(24b), Tº orders the UT-T after the AST-T, yielding (24c). ASPº having no morphological content,the ordering relation between the AST-T and the EV-T is established via anaphora. Anaphora in(24b) is covaluation/coreference. Coreference yields an ordering of exhaustive coincidence: theAST-T and the EV-T are cotemporal (24d). They denote the same time interval: the time for whichan assertion is made is the time of Terri's crying. The EV-T has thus been indirectly ordered (viacovaluation) in the past relative to UT-T.

immediately after the final bound of EV-T1 —that is, EV-T2— a resultative/continuative present perfect is generated(the perfect presents a state associated with the occurrence of some past event or state as continuing until UT-T). SeeD&UE (1997b, 2002) for extensive discussion.

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24. Past Tense without Morphological Aspecta. Terri criedb. TP2 c. UT-T AFTER AST-T

UT-T T’ 2 ——[—————]———|——>

T° ASP-P AST-T UT-T

AFTER 2AST-Ti ASP’ d. Covaluation2

ASP° VP ——[—————]———|——>2 AST-T=EV-T UT-T

EV-Ti VP

TERRY'S CRYING

Covaluation explains why the event described by a simple past tense is portrayed in its entirety—so-called Perfective or Aoristic Aspect. The event is viewed as including both its initial andfinal bounds because the AST-T is cotemporal with the EV-T.

3.2. Neutral Viewpoint

Laca (to appear) points out that D&U-E's analysis of simple tenses incorrectly predicts all simpletenses to be perfective. Laca shows that, although the simple past in French is indeed perfective,the simple present and future are compatible with either perfective or imperfective viewpoint, asthe paradigms of adverbial modification in (25-27) show. With perfective aspect, modification ofan activity verb by a punctual locating adverb yields an inceptive or sequential construal (theinterval denoted by the punctual adverb centrally coincides with the initial bound of the EV-T). Incontrast, with imperfective aspect, modification of an activity verb by a punctual adverb, yields aconstrual where the described event is understood as ongoing at the REF-T provided by the adverb(the interval denoted by the punctual adverb centrally coincides with a subinterval of the EV-T).

25. Simple Pasta. À 1h30, Cécile déjeuna.

‘At 1h30, Cécile ate.’b. Quand nous arrivâmes à la maison, Maryvonne pleura.

‘When we arrived home, Maryvonne cried.’

The simple past behaves as expected: (25a) only allows an inceptive construal and (25b), asequential construal. In contrast, the simple future and present are ambiguous, allowing either, (i)an inceptive/sequential, or (ii) an ongoing construal of the described event.

26. Simple Futurea. À 1h30, Cécile déjeunera.

‘At 1h30, Cécile will eat.’ i. At 1h30, Cécile will start eating.ii. At 1h30, Cécile will be eating.

b. Quand nous arriverons à la maison, Maryvonne pleurera. ‘When we will arrive home, Maryvonne will cry.’

When we get home i. Maryvonne will cry.

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ii. Maryvonne will be crying.

27. Simple Presenta. À 1h30, Cécile déjeune.

‘At 1h30, Cécile eats.’ i. At 1h30, Cécile starts eating.ii. At 1h30, Cécile is eating.

b. Quand nous arrivons à la maison, Maryvonne pleure. ‘When we arrive home, Maryvonne cries.’

When we get home i. Maryvonne starts crying.ii. Maryvonne is crying.

The example below from Demirdache (2003) nicely confirms the generalization that the simplefuture in French allows imperfective readings.

28. À midi, Zoé marchera depuis vingt minutes.*‘At noon, Zoé will walk since twenty minutes.’

(At noon, Zoé will have been walking for twenty minutes.)

Laca concludes that the simple present and future in French have neutral viewpoint aspect (in thesense of Smith 1991): they are compatible with either perfective or imperfective viewpoint. Incontrast, the simple past is perfective. The challenge is then to incorporate formally neutralviewpoint aspect within our model.

We maintain the two generalizations underlying D&U-E's analysis of simple tenses.Namely, (i) Aspect serves to overtly/morphologically specify the ordering relation between theAST-T and the EV-T; (ii) when this relation is not overtly specified, it is established via anaphora.To incorporate neutral viewpoint, we merely carry this reasoning one step further. Anaphorabetween individual-denoting noun phrases is established via either covaluation or (semantic)binding. As was shown in (23), the readings that obtain can be distinguished in the appropriatecontext. The default hypothesis is then that anaphora between time-denoting DPs can likewise beestablished via either covaluation or binding and, further, that the resulting temporal construalscan be distinguished. Recall that covaluation yields an ordering of exhaustive coincidence: theAST-T is cotemporal with the EV-T. The resulting viewpoint is perfective: the event is viewed asincluding both its initial and final bounds. Now, if anaphora were to be established via binding,then the resulting viewpoint would in fact be neutral:

29. Terri crieda. ASP-P b. AST-T λi[CRY (TERRI) (i)] 2

AST-T ASP’ c. AST-T ⊆ EV-T d. AST-T ⊇ EV-T2 AST-T AST-T

λev-t VP —[—[———]—]——> —[—[———]—]——>2 CRYING CRYING

EV-T VP

CRY (TERRI)

The event/assertion-times are merely temporal variable arguments, which for convenience wehave chosen to label EV-T/AST-T (but we might just as well have chosen i to stand for these

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variables over intervals). λ-abstraction over the temporal variable of the verb, in (29a), creates apredicate which takes the AST-T as external argument. (29b) states that the AST-T has the propertyof being an interval at which TERRI CRY is true. Now (29b) will hold if either the AST-T isincluded within an interval at which Terri cries (imperfective viewpoint (29c)), or if the AST-T

includes/is cotemporal with an interval at which Terri cries (perfective viewpoint (29d)). In sum,when ASP° is empty, semantic binding of the EV-T by the AST-T yields neutral viewpoint.

We have argued that when there is no morphological aspect overtly specifying the orderingrelation between the AST-T and EV-T, this relation is established via anaphora. The defaultassumption is that anaphora can be interpreted as either covaluation or binding. Covaluationyields perfect viewpoint aspect, binding yields neutral viewpoint aspect.8

4. The Interaction of Time Adverbs with Tense and Aspect

We now illustrate how our model handles the interaction of temporal modifiers with tense andaspect. We argue that Tense never directly determines the time reference of a temporal modifier.

4.1. Time Adverbs and the Simple Past Tense

The temporal derivation in (30) illustrates the interaction of time adverbs with the simple past.Note that the modifier yesterday does not have the overt syntax of a PP, but rather of a bare NP.Bare time adverbs are analyzed as concealed PPs (D&U-E 2004b, 2005, Jespersen 1931 or Kamp& Reyle 1993 among others). Under this proposal, temporal adverbs are uniformly analyzed asPPs headed by a spatiotemporal predicate relating two times. P° can be overt (on Sunday, inJune) or silent (yesterday, Sunday) —in which case it expresses central coincidence (WITHIN).

30. Terri cried yesterday/on Sunday.a. TP3 b. AST-T UT-T

UT-T T’ ——[—————]———|——> 3T° ASP-P c. Covaluation

AFTER 4 AST-T=EV-T UT-T

AST-T ASP’ ——[—————]———|——>3 3AST-Ti PP ASP° VP d. Modification

2 2 AST-T=EV-T UT-T

P° ZEIT-P EV-T VP —[—[—————]—]——|—>∅/ON 2 TERRI CRY YESTERDAY/SUNDAY

Z° NP(THE) 2

SIT-Ti NPyesterday/Sunday

A temporal PP is predicated of the AST-T in (30). The head of this PP (∅/ON) restricts thereference of its external argument (the AST-T) by ordering this interval within the SIT-T of its

8We leave open at this stage the question of (cross-linguistic) variation in the construal of simple tenses. Why is thesimple past perfective in say French or Spanish, but not in Dutch where it is aspectually neutral? Why do the simplepresent and future tenses in French, but not in Spanish, have neutral viewpoint aspect? See Laca (to appear) forinteresting proposals.

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internal argument. Since there is no morphological aspect in (30), the AST-T and the EV-T arecovalued (30c). The EV-T is thus indirectly located (via covaluation) within the interval denotedby the Zeit-P [(THE) yesterday/Sunday], as shown in (30d). (Note that covaluation andmodification are not ordered relative to each other in (30)).

We now turn to the trickier well-known example given below where a present time adverbmodifies a past tense sentence. We run through the temporal derivation of (31) in (31a-d).

31. Terri cried today.a. TP3 b. AST-T UT-T

UT-T T’ ——[————]—|———> 3T° ASP-P c. Covaluation

AFTER 4 AST-T=EV-T UT-T

AST-T ASP’ ——[—————]——|——>3 3AST-Ti PP ASP° VP d. Modification

2 2 AST-T=EV-T UT-T

P° ZEIT-P EV-T VP —[—[—————]———|—]——> ∅ 2 TODAY

Z° NP

(THE) 2SIT-Ti NP

today

The AST-T is directly ordered in the past by Tense (31b). Temporal modification of the AST-T,itself co-temporal with the EV-T (31C), yields the ordering in (31d): the past AST-T is ordered bythe null P° of central coincidence within the SIT-T of its internal argument today. Since todaypicks out an interval containing subintervals that both precede and follow UT-T, a subinterval ofthe time designated by today can fall in the past. The EV-T is thus indirectly ordered (viacovaluation with the AST-T) within a past subinterval of the day of utterance.9

The ordering relation between the time designated by a temporal modifier and UT-T is thusnever directly established by Tense, but rather indirectly via modification of the AST-T, itselfdirectly ordered by Tense relative to UT-T. The claim that Tense does not determine the timereference of temporal modifiers explains why a present time adverb can modify a past tensesentence.

4.2. Time Adverbs and Perfect Aspect

As is well known, adding a temporal adverb to a perfect sentence can yield two distinct readings.(32), for instance, is ambiguous. It can be used to assert that Terri's lunch culminated either at orprior to noon

9In contrast, (i) cannot be uttered felicitously on the day of utterance. The construal in (ii) is ruled out becausecalendar nouns such as Sunday cannot be used to designate a day containing the UT-T, as extensively discussed byKamp & Reyle (1993).i. Terri cried Sunday. ii. * AST-T=EV-T UT-T

—[—[—————]——|———]——>SUNDAY

See D&UE (in progress) for discussion of the interaction of Tense with (quantified) time adverbs.

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32. Terri had eaten lunch at noon

We have analyzed time adverbs as modifiers restricting the reference of a time span projected inthe syntax as an argument of either T° or ASP°. There are two time arguments that can inprinciple be modified: the AST-T and the EV-T. When these intervals are covalued (e.g. with thesimple past; see (30-31)), modification of the AST-T and the EV-T yield temporallyundistinguishable construals. In contrast, in a (past) perfect sentence (see the phrase-structure in(20)), these two time spans are temporally distinct, restrictive temporal modification will thusinduce distinct construals.

Modification of the EV-T in (33a), where the adverb is base-generated adjoined to the EV-T,yields the so-called event-time reading in (33a’). The predicate AT establishes a relation of centralcoincidence between its external argument, the EV-T, and the SIT-T of its internal argument. ThePP thus restricts the reference of the EV-T to the time denoted by the Zeit-P [(THE) noon].

33a. Terri's lunch culminates at noon. b. Terri's lunch culminates before noon.2 2

EV-T PP AST-T PP2 2P° ZEIT-P P° ZEIT-P

AT 2 AT 2Z° NP Z° NP

(THE) 2 (THE) 2SIT-T NP SIT-T NP

noon noon

a’. EV-T AST-T UT-T b’. EV-T AST-T UT-T

—[——]——[——]———|——> —[——]——[——]———|——> NOON NOON

In contrast, modification of the AST-T in (33b), where the adverb is base-generated adjoined to theAST-T, yields a temporally distinct construal, the so-called reference-time reading in (33b’). Thetime of Terri's lunch is understood has having culminated prior to a past reference-time, our AST-T, which itself coincides with the SIT-T of the NP noon.

We have argued that temporal interpretation involves computing ordering relations andanaphoric dependencies between time intervals. We now argue that temporal computation issubject to economy conditions governing the representations generated at each step of thecomputation.

5. Economy/Optimality Constraints on Temporal Computation10

D&U-E (2005) propose that economy principles govern the steps in —and the representationsgenerated by— the temporal computation of a given sentence. This proposal aims at uniformlyexplaining a broad set of empirical facts: (i) restrictions on the complexity of tenses and aspects(that is, on the iteration of temporal heads); (ii) cooccurrence restrictions in complex structuresinvolving subordination; and (iii) the typology of temporal construals in subordinate clauses —beit complement, relative or adjunct clauses. 10The term optimality should not be understood as referring to optimality theory. The two conditions we formulateare optimality conditions merely because they require the output of a temporal derivation to be optimal in a sense tobe defined below in the text.

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The proposal is that temporal derivations are governed by the two principles stated below.

34. Temporal Computation Economy (TC-economy)A given temporal construal must be achieved in an optimal manner.That is, no step in the temporal derivation may be semantically vacuous, temporallyuninformative. Each step must yield a temporally distinct construal.

TC-economy requires that each step in a temporal derivation effectively contribute to the calculus—that is, no step may be vacuous. This condition is inspired by Fox (2000) who defines economyconditions applying at the syntax-semantic interface, governing both the steps in a derivation andthe representations generated at each step of the derivation. These principles are economyprinciples in the sense that they are designed to guarantee that a given semantic interpretation isachieved in an optimal manner —in Fox' own words, «with no more effort than is necessary».

We first show how TC-economy restricts iteration of temporal heads by excludingcombinations that are logically possible but remain unattested. We then show how TC-economyinteracts with the constraint in (35) to derive the distribution of dependent vs. independenttemporal construals in event reporting subordinate clauses.

35. Temporal Constraint on Semantic Subordination (TCSS)The anchoring of a subordinate clause via a temporal head must yield an optimal output.The output is optimal when the times for which the speaker makes a statement —that is, thematrix and subordinate Assertion-Times— end up intrinsically ordered relative to eachother.

5.1. Restrictions on the Iteration of Temporal Heads

We have presented an analysis of two aspectual viewpoints: progressive and retrospective. Note,however, that not all logical combinations of these viewpoints are possible: although the perfectof the progressive is grammatical (36a), both the progressive of the perfect and the progressive ofthe progressive are ungrammatical (36b-c).

36a. Kim has/had been working.b. *Kim is/was having worked.c. *Kim is/was being working.

The ungrammaticality of the aspectual patterns in (36b-c) will follow automatically from TC-economy. The intuition underlying this proposal is that aspect recursion is licit iff it is temporallyinformative. That is, if each aspectual viewpoint focuses a temporally distinct time span, thusproviding a new (distinct) viewpoint on the described situation. This will not be the case witheither the progressive of the perfect or the progressive of the progressive.

Recursive aspect in (36) will have the following phrase structure.

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37. Progressive of a Progressive Progressive of a Perfect Perfect of a ProgressiveASP-P2 ASP-P2 ASP-P22 2 2

AST-T2 ASP’ AST-T2 ASP’ AST-T2 ASP’2 2 2 ASP° ASP-P1 ASP° ASP-P1 ASP° ASP-P1

WITHIN 2 WITHIN 2 AFTER 2AST-T1 ASP’ AST-T1 ASP’ AST-T1 ASP’2 2 2

ASP° VP ASP° VP ASP° VP

WITHIN 2 AFTER 2 WITHIN 2EV-T EV-T EV-T

We run through in (38) the derivation of the progressive of the progressive. Each aspectualviewpoint focuses a time span. The lowest head (PROG1) orders AST-T1 within the EV-T and, thus,picks out a subinterval of the EV-T, as in (38a). The highest head (PROG2) takes this time span(AST-T1) as its internal argument and orders AST-T2 within AST-T1, yielding (38b). The timefocused by PROG2 (that is, AST-T2) is thus itself an interval properly contained within the timefocused by PROG1 (that is, AST-T1).

38. *Kim is being working.a. PROG1 WORK b. *PROG2 PROG1 WORK

AST-T2—[———[————————]———]——> —[———[———[———]——]——]——>

EV-T AST-T1 EV-T AST-T1

Now consider the derivation of the progressive of the perfect in (39). The lowest aspect (PERF)orders AST-T1 after the EV-T, yielding (39a). The highest aspect (PROG) orders AST-T2 within AST-T1, yielding (39b). As the resulting output (39b) shows, the time focused by the highest aspect(PERF) –that is, AST-T2– is itself once again properly contained within the interval focused by thelowest aspect (PERF) –that is, AST-T1.

39. *Kim is having worked.a. PERF WORK b. *PROG PERF WORK

AST-T2—[——]——[————————]——> —[——]——[———[———]———]——>

EV-T AST-T1 EV-T AST-T1

Our model thus generates outputs that are formally identical for these illicit aspectualcombinations: AST-T2 is exhaustively contained within AST-T1, be it in (38b) or (39b). This is not atrivial result: it allows us to formulate a generalization that can uniformly explain theungrammaticality of theses aspectual combinations. Recall that the role of grammatical aspect isto convey a viewpoint on the described event. The first aspect in either (38a) or (39a) provides aviewpoint by focusing an interval either contained within the EV-T (38a), or subsequent to the EV-T (39a). The addition of an aspect to either (38a) or (39a), however, does not provide a new(temporally distinct) viewpoint on the situation since the interval picked out by the additionalaspect (AST-T2) is itself exhaustively included within —and, as such, non-distinct from— theinterval already picked out by the lowest aspect (AST-T1). In sum, iteration of aspect in either (38)or (39) is semantically vacuous: it does not shift the viewpoint —that is, it does not focus a timespan itself distinct from the time focused by the first viewpoint. The following descriptive

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generalization emerges: aspect recursion is illicit if the addition of a viewpoint does not shift theviewpoint or, alternatively, vacuously shifts the viewpoint. This generalization followsautomatically from TC-economy: (34) bans any temporally vacuous step in a temporal derivation.

Finally, the perfect of a progressive will not violate TC-economy, as illustrated in (40).

40. Kim has been working.a PROG WORK b. PERF PROG WORK

AST-T1 AST-T1 AST-T2 AST-T1 AST-T2—[——[——]——]——> —[—[——]—]——[——]——> —[—[——]——[—]—]——>

EV-T EV-T EV-T

The lowest aspect (PROG) orders AST-T1 within the EV-T and, thus, focuses a subinterval of theEV-T (40a). The highest aspect (PERF) orders AST-T2 after AST-T1, yielding different possibletemporal construals, illustrated in (40b). The perfect in (40b) provides a distinct viewpoint on thedescribed event since it picks out an interval (AST-T2) subsequent to —and thus temporallydistinct from— the interval picked out by the progressive (AST-T1). Adding a perfect to aprogressive is thus temporally/semantically informative. TC-economy is thereby satisfied.

Finally, the last logically possible combination —the perfect of a perfect— will likewisenot violate TC-economy, as the highest occurrence of the perfect focuses an interval subsequentto the interval focused by the lowest occurrence of the perfect. We thus predict iteration of theperfect, in contrast to iteration of the progressive, to be in principle a licit aspectual combination.

This predication is empirically valid. The perfect of a perfect is attested, for instance, inFrench. This so called ‘passé surcomposé’ is productive in certain dialects of French (itsconditions of use are, however, poorly understood).

41. Quand j'ai eu dansé, je me suis désaltéré.When HAVE-PRES-1SG HAVE.PAST-PART DANSE.PAST-PART I quenched my thirst.’

Compound perfect tenses are further attested in Breton. Indeed, not only does Bretonproductively make use of the perfect of a perfect (42a), but it also allows both a pluperfect of aperfect (42b) and a future perfect of a perfect (47c). The glosses are those provided by a Frenchgrammar of Breton and bilingual French-Breton speakers –see Léon (2001).11

42a. Lennet em eus bet ul levr da deir eur.READ.PAST-PART 1SG HAVE.PRES BE.PAST-PART a book at three o'clock ‘J'ai eu lu un livre à trois heures.’

b. Lennet em boa bet ul levr da deir eur . READ.PAST-PART 1SG HAVE.PAST BE.PAST-PART a book at three o'clock

‘J'avais eu lu un livre à trois heures.’

11The Breton equivalent of auxiliary have in (42) it itself a synthetic form created by morphological merger of theverb Be with a locative preposition (Jouitteau 2005). The derivational relationship between be and have shouldexplain why main verb be can itself combine either with auxiliary be or auxiliary have, yielding a perfect:i. ul levr em bo bet ii. en Naoned on bet

a book 1SG HAVE.PRES BE.PAST-PART in Nantes 1SG BE.PRES BE.PAST-PART

‘I have had a book.’ (‘J'ai eu un livre.’) ‘I have been/gone to Nantes.’

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c. Lennet em bo bet ul levr da deir eur. READ.PAST-PART 1SG HAVE.FUT BE.PAST-PART a book at three o'clock

‘J'aurai eu lu un livre à trois heures.’

We conclude that the perfect of a perfect is a licit aspectual combination that can surface cross-linguistically. We leave open the question of why recursion of the perfect is attested in certainlanguages but not others.

We will show that TC-economy together with the TCSS (35) have a wide empiricalcoverage. These constraints go a long way in explaining restrictions on the distribution andinterpretations of tenses in subordinate clauses —be it a complement, a relative or a temporaladverbial clause. We confine ourselves here to event reporting sentences.

5.2. Independent vs. Dependent Construals in Subordinate Clauses

In an independent or matrix clause, the external argument of T° (REF-T in (7)) denotes UT-T. Wenow turn to the setting of this reference-time in a subordinate clause. We take the null hypothesisto be that temporal anchoring of a (finite) subordinate clause into a matrix clause can in principlebe either deictic or anaphoric. Deictic anchoring (henceforth D-anchoring) of a subordinateclause is illustrated in (43a): the external argument of the subordinate TP —henceforth, theanchor-time— is identified with UT-T. The embedded AST-T is thus anchored directly to speech-time. D-anchoring yields an independent temporal construal of the subordinate clause.

43a. D-anchoring of AST-T2 b. A-anchoring of AST-T2TP1 TP12 2

REF-T = UT-T T’ REF-T = UT-T T’2 2T° ASP-P1 T° ASP-P1

2 2 AST-T1 ASP’ AST-T1 ASP’2 2

ASP° VP ASP° VP2 2EV-T1 VP EV-T1 VP2 2

V° TP2 V° TP22 2Anchor-time REF-T = UT-T T’ Anchor-time REF-T = AST-T1/EV-T1 T’2 2

T° ASP-P2 T° ASP-P22 2AST-T2 AST-T2

Anaphoric-anchoring (henceforth A-anchoring) of a subordinate clause is illustrated in (43b): theexternal argument of the embedded TP is bound by the matrix AST-T1/EV-T1. The embedded AST-T isthus anchored with respect to a time argument in the matrix. A-anchoring yields a dependenttemporal construal of the subordinate clause.12

12Recall from section 3 that anaphora between time intervals is established via either covaluation or (semantic)binding. A-anchoring of a subordinate clause will involve binding of the embedded anchor-time by the matrix AST-T/EV-T. This assumption allows us to analyze dependant construals in stative subordinate clauses (simultaneous anddouble access) as involving A-anchoring of the subordinate clause into the matrix. To illustrate, the sentence Kimsaid Terri was in Boston allows a simultaneous reading where the time of Terri's saying coincides with the time of

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We freely allow either D-anchoring or A-anchoring as long the resulting derivation satisfiesTC-economy (no step in the derivation is vacuous, temporally uninformative) and the TCSS (thederivation ultimately yields an intrinsic temporal ordering of the matrix and embedded AST-T s).

5.2.1.Anchoring Complement Clauses

We have argued that the anchor-time in a subordinate clause can be freely set to UT-T (D-anchoring) or to the matrix AST-T/EV-T (A-anchoring). For concreteness, we assume the defaultsetting for the anchor-time to be UT-T. We assume resetting of the anchor-time to the matrix AST-T to be free —as long as the resulting derivation/output satisfies our two optimality conditions:TC-economy and TCSS. This proposal yields three scenarios for complement clauses:obligatory/optional/vacuous resetting of the subordinate anchor-time, which we discuss in turn.

5.2.1.1. Obligatory Resetting of the Anchor-Time to the Matrix AST-T

As is well known, the dependent construal of a complement clause is enforced with either a past(eventive) verb under a past in the matrix (44a), or with a future (eventive) verb under a future inthe matrix (44b). If the anchor-time could be freely set to UT-T, then (44a) should allow thetemporal construal in (44ii).

44a PAST-PAST: Kim said that Marty left.i. Dependent construal ii. Independent construal

AST-T2 AST-T1 UT-T * AST-T1 AST-T2 UT-T —[———]———[———]———|——> —[———]———[———]———|——>DEPARTURE SAYING SAYING DEPARTURE

b. FUTURE-FUTURE: Kim will say that Marty will leave

In (44ii), the external argument of the subordinate T° has been D-anchored to UT-T. Theembedded past Tense thus orders the UT-T after the subordinate AST-T (AST-T2), itself covalued(and, hence, cotemporal with) the subordinate EV-T (EV-T2). AST-T2 (= EV-T2), is thus ordered inthe past relative to UT-T —but remains unordered relative to the past matrix AST-T (AST-1). Thetemporal construal in (44ii) is thereby freely generated. This reading, however, is unavailable:Marty's departure cannot be understood as temporally subsequent to the time of Kim's saying.

In contrast, A-anchoring of the external argument of the subordinate T° to the matrix AST-T

(AST-T1) yields the only grammatical temporal construal of (44a): the time of Marty's departure isback-shifted with respect to the past time of saying (44i).

Kim's being Boston. It makes no sense to say that these two intervals corefer/are covalued —as one interval must belarger than the other. If however, the anaphoric dependency between the two clauses is established via semanticbinding (i), then we obtain the correct interpretation: (i) states that the matrix EV-T (the interval at which Kim'ssaying occurs) has the property of being an interval at which Terri's being in Boston holds.i. EV-T1 λi [BE IN BOSTON (TERRI) (i)]Dependent construals with stative sentences thus provide strong support for the claim in section 3 that anaphorabetween time-denoting arguments (just like anaphora between individual-denoting arguments) is either binding orcovaluation. This much said about dependent construals with stative subordinate clauses, we confine ourselves toevent reporting sentences in the rest of this paper. Simultaneous and double access readings (see footnote 13) raiseintricate issues which cannot receive an adequate treatment within the scope of this paper. See D&U-E (in progress).

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Why is the dependent construal of a complement clause enforced with either past underpast or future under future? We contend that past/future shifted readings obligatorily arise whenmerging a complement clause into the matrix requires resetting the anchor from its default value(UT-T) to the matrix AST-T in order to satisfy the TCSS. To illustrate, we run through the temporalcomputation of (44a) and (44b) in parallel below.

45. D-anchoringa. PAST UNDER PAST b. FUTURE UNDER FUTURE

Compute the temporal construal of the matrix:PAST SAY FUT SAY

i. AST-T1 (=EV-T1) ___UT-T i’. UT-T___AST-T1 (= EV-T1)Compute the temporal construal of the complement Anchor-time set to UT-T:

PAST LEAVE FUT LEAVE

ii. AST-T2 (= EV-T2) ___ UT-T ii’. UT-T___AST-T2 (= EV-T2)Non-optimal output:

iii/iii’. No ordering relation established between AST-T1 & AST-T2 TCSS violated

The temporal derivations in (45) with D-anchoring of the embedded anchor-time do not yield anintrinsic ordering —subsequence, precedence, or inclusion— of the matrix and embedded AST-Times. Resetting the embedded anchor-time from its default value to the matrix AST-T isconsequently required in order to achieve a relative ordering of the AST-Ts. The resultingderivation (46i-ii’) converges: it yields the optimal output in (46iii) where the AST-Ts end upordered relative to each other. A dependent past/future-shifted reading is thus enforced.

46. A-anchoringa. PAST UNDER PAST b. FUTURE UNDER FUTURE

Compute the temporal construal of the matrix:PAST SAY FUT SAY

i. AST-T1 (=EV-T1) ___UT-T i’. UT-T___AST-T1 (=EV-T1)

Compute the temporal construal of the complement Anchor-time set to AST-T1:PAST LEAVE FUT LEAVE

ii. AST-T2 (=EV-T2) ___AST-T1 ii’. AST-T1___AST-T2 (=EV-T2)

Optimal output:iii. AST-T2___AST-T1___UT-T iii’. UT-T___AST-T1___AST-T2

The temporal anchoring of a complement clause —with either a past eventive verb under a matrixpast, or a future eventive verb under a matrix future— must be anaphoric. Identifying theembedded anchor-time with the matrix AST-T is the only way of ensuring temporal orderingbetween the matrix and embedded AST-Times, as required by the TCSS.

5.2.1.2. Optional Resetting of the Anchor-Time to the Matrix AST-T

Resetting the embedded anchor-time from its default value (UT-T) to the matrix AST-T is notalways enforced. With the following combinations of matrix and subordinate tenses, resetting is alegitimate (that is, temporally informative) step —but remains optional/free.

47a. PAST-FUTURE: Kim will say that Marty cheated.

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b. PRESENT-FUTURE: Kim will say that Marty is cheating.c. will/would alternation under PAST: Kim said that Marty will/would cheat.

Consider first the temporal derivation of past under future (47a) in (48). For simplicity, wehenceforth simplify the schemas representing the temporal construal of simple tenses: we do notrepresent the EV-T when it is cotemporal with the AST-T (perfective aspect). (48i), for example,should be understood as shorthand for: UT-T__AST-T1(=EV-T1).

48. Kim will say that Marty cheated.Compute TP1: FUT SAY

i. UT-T___AST-T1Compute TP2: PAST CHEAT

Anchor-time set to UT-T Anchor-time reset to AST-1ii. AST-T2___UT-T ii’. AST-T2___AST-T1

Output of (i-ii/ii’) optimaliii. AST-T2___UT-T___AST-T1 iii’. UT-T___AST-T2___AST-T1

AST-T2___UT-T___AST-T1

D-anchoring in (48i-ii) yields a well-formed output where the matrix and embedded AST-Ts endup ordered relative to each other. Resetting of the anchor-time is thus not enforced. Resetting,however, is free as long as the resulting output satisfies both TC-economy and the TCSS. Now,the TCSS is satisfied in (48iii’) since resetting yields an ordering of the matrix and subordinateAST-Ts. TC-economy is also satisfied since resetting the anchor-time is temporally informative.That is, the alternative derivations in (48i-ii) and (48i-ii’) yield temporally distinct construals: thetime of cheating is a past time in (48iii) but could be a future time in (48iii’). In sum, resetting theanchor-time is legitimate (since it is temporally informative) —but optional/free.

Consider next the temporal derivation of present under future (47b) sketched in (49).

49. Kim will say that Marty is cheating.Compute TP1: FUT SAY

i. UT-T___AST-T1Compute TP2: PRES CHEAT

Anchor-time set to UT-T Anchor-time reset to AST-1ii. UT-T ii’. AST-T1

AST-T2 AST-T2

Output of (i-ii/ii’) optimaliii. UT-T___AST-T1 iii’. UT-T___AST-T1

AST-T2 AST-T2

D-anchoring in (49i-ii) yields a well-formed output (49iii) where the AST-Ts end up intrinsicallyordered relative to each other. Resetting of the embedded anchor-time (49ii’) is allowed as ityields a well-formed output (49iii’). The TCSS is satisfied (resetting yields an ordering of theAST-Ts). TC-economy is also satisfied since resetting the anchor-time is informative: it yields analternative temporal construal. In particular, whereas D-anchoring generates a reading where thetime of Marty's cheating is simultaneous with UT-T, A-anchoring generates a reading where the

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time of Marty's cheating is simultaneous with the future time of Kim's saying. In sum, resettingthe anchor-time is once again legitimate —but optional/free.13

We now argue that the will/would alternation under a matrix past (47c) is an overtmorphological reflex of the resetting of the anchor-time to the matrix AST-T. Consider thetemporal derivation of future under past sketched below.

50. Kim said that Marty will/would cheatCompute TP1: PAST SAY

i. AST-T1___UT-T

Compute TP2: FUT CHEAT

Anchor-time set to UT-T Anchor-time reset to AST-1ii. UT-T___AST-T2 ii’. AST-T1___AST-T2

Output of (i-ii/ii’) optimaliii. AST-T1 ___UT-T___AST-T2 iii’. AST-T1___AST-T2___UT-T

AST-T1___UT-T___AST-T2

The derivation in (50i-ii) converges since its yields the relative ordering of AST-Ts in (50iii),where the time of saying is past relative to both UT-T and the time of cheating. Resetting theanchor-time to AST-T1 also yields an intrinsic ordering of the AST-Ts (AST-T1 before AST-T2), thussatisfying the TCSS. This alternative derivation is informative (thus satisfying TC-economy)since it yields a temporally distinct construal where the time of cheating (in the future relative tothe time of saying) remains unordered relative to UT-T. That is, the time of cheating could eitherprecede or follow UT-T (50iii’).

Now, assuming will and would are derived from the abstract predicate WOLL (Ogihara 1989and references therein), then resetting the anchor-time from UT-T to the matrix AST-T has an overtmorphological reflex. When the anchor-time is set to UT-T, then the embedded future is spelledout as will. In contrast, when the anchor-time is set to the past matrix AST-T, the embedded futureis spelled out as would (see Uribe-Etxebarria 1994).

5.2.1.3. Vacuous resetting of the Anchor-Time to the Matrix AST-T.

Finally, when the tense in the matrix is present (51), dependent and independent construals canno longer be distinguished. That this, the embedded AST-Ts will end up anchored to UT-T whetherthe anchoring is deictic or anaphoric, as the temporal derivation in (52) illustrates.

51. Kim says that Marty will cheat/cheated/is cheating.

13Kim will say that Marty is cheating further allows a Double Access reading where the time of cheating overlapswith both UT-T and the matrix past time of saying. D&U-E (in progress) analyze DA readings as involving both D-anchoring to the UT-T and A-anchoring to the matrix EV-T via semantic binding (see (i) footnote 12). Note that theDA reading of (49) satisfies both TC-economy (it represents a construal temporally distinct from both (49iii) and(49iii’)) and the TCSS (the AST-Ts end up ordered relative to each other).

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52. Kim says that Marty will leave Paris.Compute TP1: PRES SAY

i. UT-T

AST-T1Compute TP2: FUT LEAVE

Anchor-time set to UT-T Anchor-time reset to AST-1ii. UT-T___AST-T2 ii’. AST-T1___AST-T2

Output of (i-ii/ii’) optimaliii. UT-T___AST-T2 iii’. UT-T

AST-T1 AST-T1___AST-T2

The alternative derivations in (51i-ii) and (51i-ii’) yield temporally identical outputs. The step in(52ii’) at which the anchor-time is reset is thus illicit: it violates TC-economy since it issemantically vacuous, temporally uninformative.

5.2.2. Anchoring Relative Clauses

As is well-known, relative clauses allow temporally independent readings (Abusch 1988, 1993,Enç 1987, Stowell 1995a-b among others). The relative clause in (53) thus allows the twoconstruals in (53a-b).

53. Marty met the man who left Paris.a. Forward-shifted b. Backward-shifted

AST1 AST-T2 UT-T AST-T2 AST1 UT-T—[————]——[————]——[———]—> —[————]——[————]——[———]—>

MEETING LEAVING LEAVING MEETING

Notice in particular that (53) allows a forward-shifted reading where the past EV-T of the relativefollows the past EV-T of the matrix. This reading was unavailable in a past complement clauseembedded under a matrix past (see (44) above). To generate the ambiguity in (53), we have toassume that relative clauses are anchored directly to UT-T. D-anchoring of the embedded past tothe UT-T yields no intrinsic ordering relation, as shown in (54iii). The ordering relation betweenAST-T1 and AST-T2 can thus be freely construed as either precedence (AST-T1 before AST-T2)yielding (53a), or subsequence (AST-T1 after AST-T2) yielding (53b).

54i. Matrix: PAST MEET AST-T1___UT-T

ii. Relative: PAST LEAVE anchor-time is set to UT-T: AST-T2___UT-T

iii. Output of (i-ii): no ordering established between AST-T1 & AST-T2

Relative clauses do however allow A-anchoring as the paradigm in (55) from Uribe-Etxebarria(1994: 147) illustrates. Recall that the will/would alternation under a matrix past is an overtmorphological reflex of the setting of the subordinate anchor-time. When the anchor-time is set toUT-T, the embedded future surfaces as will. When the anchor-time is set to the past matrix AST-T,the embedded future surfaces as would. We give the respective temporal derivations for (55) inparallel in (56).

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55a. I didn't find a linguist who will chair a session.b. I didn't find a linguist who would chair a session.

56. I didn't find a linguist who WOLL chair a sessionCompute TP1: PAST FIND

i. AST-T1___UT-T

Compute TP2: FUT CHAIR

Anchor-time set to UT-T Anchor-time reset to AST-1ii. UT-T___AST-T2 ii’. AST-T1___AST-T2

Output of (i-ii/ii’) optimaliii. AST-T1 ___UT-T___AST-T2 iii’. AST-T1___AST-T2___UT-T

AST-T1___UT-T___AST-T2

Uribe-Etxebarria points out that (55) displays a contrast in the scope construal of the head of therelative. In (55a), the indefinite is interpreted outside the scope of negation, as the paraphrase(57a) illustrates. Consequently, a Negative Polarity Item (NPI) is not licensed inside the relative(57b). In contrast, in (55b), the indefinite is interpreted under the scope of negation, as theparaphrase (58a) illustrates. Consequently, an NPI is licensed inside the relative clause (58b).

57a. There is linguist who will chair a session and I didn't find himb. *I didn't find a linguist who will chair any sessions.

58a. I didn't find a single linguist who would chair a session.b. √I didn't find a linguist who would chair any sessions.

Uribe-Etxebarria concludes that there is a structural difference in (55). In (55a), the indefinite hasbeen scoped out at LF outside the c-command domain of negation, whereas in (55b), theindefinite remains within the scope of negation at LF.

Now suppose we interpret scoping out in (55a) as yielding an LF where the matrix and therelative clause are conjoined —that is, as yielding precisely the interpretation in (57a). In otherwords, the relative clause in (55a) is scoped out and interpreted as an independent clausecoordinated with the matrix. The anchor-time of the relative clause can no longer be reset to thematrix AST-T: A-anchoring is achieved via semantic binding (see footnote 12) which requires c-command. The anchor-time can thus only be set to UT-T. This yields the temporal construal in(56iii), the abstract predicate WOLL necessarily surfaces as will.14

Generalizing this scoping out/conjunction analysis of relative clauses explains whyrelatives generally allow free temporal construals. Recall from (54) that D-anchoring of theembedded past into the matrix past yields no intrinsic ordering relation. Now, the TCSS will notapply to exclude the output in (54iii), since this condition was explicitly stated as a temporalconstraint on semantic/LF subordination. The ordering between AST-T1 and AST-T2 is thus freelyinterpreted as either precedence (AST-T1 before AST-T2) yielding the forward-shifted reading(53a), or subsequence (AST-T1 after AST-T2) yielding the backward-shifted reading (54b).

14This analysis of temporally free construals with relative clauses is very close to Stowell (1993) in that it imputesthe freedom of temporal interpretation that relatives exhibit to scoping out at LF and, hence, to the structural positionof the relative at LF. See footnote 16 for an alternative analysis of the temporally free construals with relatives.

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We must, however, enforce A-anchoring in (55b) where the indefinite is construed ashaving narrow scope with respect to negation —else we incorrectly predict that WOLL couldsurface as will with the narrow scope reading of the indefinite. This correlation between the scopeconstrual of an indefinite and the dependent vs. independent construal of a relative clause(modifying it) also holds in intensional contexts. Abusch (1988:4) points out that (59) isambiguous between an extensional (de-re) construal where John looked for a specific womanwho married him, and an intensional (de-dicto) construal where John looked for any woman whomarried him. Crucially, the intensional reading excludes the forward shifted reading of therelative. Once again, this means that when an indefinite has narrow scope (this time, with respectto an intensional verb), A-anchoring must be enforced.

59. John looked for a woman who married him.

How do we capture the correlation between the narrow scope construal of an indefinite, undernegation or an intensional verb, and A-anchoring of the relative clause?15 Abusch (1988) suggeststhat it is the temporal argument of the head noun itself which is responsible for the dependentconstrual of the relative clause on the matrix tense. Adapting this proposal, we enforce A-anchoring of the relative (when the head noun has narrow scope relative to negation/intensionalverb) via semantic binding of the situation-time of the noun by the matrix AST-T/EV-T (cotemporalin (55b)/(59)). We refer the reader to D&UE (in progress) for a detailed analysis.16

5.2.3. Anchoring Adverbial Temporal Clauses

We now turn to the question of the anchor-time in adjunct temporal clauses. We first provide anargument to establish that temporal adjunct clauses —unlike both complement and relativeclauses— are never A-anchored into the matrix.

Recall, however, the premise underlying our analysis of temporal subordination: anchoringof a (finite) subordinate clause into a matrix can in principle be either deictic or anaphoric. Wefreely allow D-anchoring and A-anchoring as long the resulting derivation satisfies TC-economyand the TCSS. We will show that D-anchoring of temporal adjunct clauses need not be stipulated:it falls out automatically from the interaction of these two conditions.

Consider the minimal pair below. We run through the temporal derivation of (60a) in (61).Past perfect in the matrix yields the ordering in (61i) and Past in the adjunct, the ordering in(61ii). (AST-T2 and EV-T2 are covaluated since we have null/perfective aspect in the adjunct.) Theconnective WHEN then orders the matrix AST (AST-T1) within the AST-T of the adjunct (AST-T2).17

15Stechow (1995) interprets Abusch's (1993) analysis of relative and complement clauses embedded underintensional verbs to mean that the tenses that occur in intensional contexts are ‘bound tenses’ —they can be neitherdeictic nor free. This analysis of tense in intensional contexts, however, does not extend to the dependent temporalconstrual arising in (55b) when the indefinite is construed under the scope of negation.16This proposal suggests an alternative analysis (to the one given in the text above) of temporally free construalswith relatives. The source of temporally free/bound construals should be uniformly imputed to the time-argument ofthe head noun. In a nutshell, free readings arise when the latter is not bound by the matrix tense (as is the case whenthe indefinite has wide scope with respect to negation/intensional verb). In contrast, anaphoric readings arise whenthe latter is bound by the matrix tense (as is the case when the indefinite has narrow scope with respect tonegation/intensional verb). See Demirdache (1997) for related discussion.17 See (13b) for the syntax of temporal adjunct clauses, and D&U-E (2002, 2004b) for a detailed analysis.

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60a. √Kim had left when Terri finished.b. *Kim had left when Terri has finished.

61. D-anchoring (√Kim had left when Terri finished)Compute TP1: PAST PERF LEAVE Compute TP2: PAST FINISH

i. EV-T1___AST-T1___UT-T ii. EV-T2=AST-T2___UT-T anchor-time = UT-T

Output of steps (i-ii) AST-T1 & AST-T2 unordered relative to e.o.Compute the temporal contribution of the connective

iii. WHEN: EV-T1____AST-T1_____UT-T

AST-T2=EV-T2

D-anchoring of the adjunct thus yields the correct construal for (60a): Kim's departure (EV-T1) isunderstood as having culminated prior to Terri's finishing (EV-T2), as shown in (61iii).

Now, consider the alternative derivation in (62) with the anchor-time set to AST-T1.

62. A-anchoring (√Kim had left when Terri finished)Compute TP1: PAST PERF LEAVE Compute TP2: PAST FINISH

i. EV-T1___AST-T1___UT-T ii. EV-T2=AST-T2___AST-T1 anchor-time = AST-T1

Output of steps (i-ii)iii. EV-T2=AST-T2___EV-T1___AST-T1___UT-T

EV-T1___EV-T2=AST-T2___AST-T1___UT-T

Compute the temporal contribution of the connectiveiv. WHEN: AST-T1

AST-T2

The derivation crashes as it yields contradictory ordering requirements: AST-T1 must besubsequent to AST-T2 at step (iii), but simultaneous with AST-T2 at step (iv). We conclude that A-anchoring fails to generate the temporal construal of the grammatical sentence (60a).

We now show that A-anchoring fails to filter the temporal construal of the ungrammaticalsentence (60b). We first run through the derivation of (60b) with the anchor-time set to UT-T:

63. D-anchoring (*Kim had left when Terri has finished)Compute TP1: PAST PERF LEAVE Compute TP2: PRES PERF FINISH

i. EV-T1___AST-T1___UT-T ii. EV-T2___UT-T anchor-time = UT-T

AST-T2Compute the temporal contribution of the connective

iii. WHEN: AST-T1

AST-T2

The derivation crashes since it yields orderings requirements that cannot be simultaneouslysatisfied: AST-T1 must precede UT-T (step (i)), but overlap with AST-T2=UT-T (steps (ii-iii)). Weconclude that D-anchoring correctly excludes the ungrammatical (60b).

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We now turn to the derivation of (60b) with the anchor-time anaphorically set to the matrixAST-T. Crucially, the derivation does not yield contradictory orderings: the resulting output (64iv) is perfectly interpretable. (64b) is nonetheless an ungrammatical sentence. A-anchoring musttherefore be excluded.

64. A-anchoring (*Kim had left when Terri has finished)Compute TP1: PAST PERF LEAVE Compute TP2: PRES PERF FINISH

i. EV-T1___AST-T1___UT-T ii. AST-T1 anchor-time =AST-T1

EV-T2___AST-T2Compute the temporal contribution of the connective

iii. WHEN: AST-T1

AST-T2Output of (i-iii):

iv. EV-T1___AST-T1___UT-T

EV-T2___AST-T2

Summarizing, A-anchoring of the adjunct clause fails to generate the temporal construal of thegrammatical sentence (60a), and incorrectly generates a well-formed temporal construal for theungrammatical (60b). We conclude that the anchor-time in a temporal adjunct clause —incontrast to either complement or relative clauses— must be speech-time. That is, temporaladjuncts always yield independent construals.

Now, the unavailability of A-anchoring with temporal adjuncts need not be stipulated: itfalls out automatically from our economy conditions. To see why, lets reconsider the derivationsinvolving anaphoric anchoring.

A-anchoring in (62) is automatically filtered by the TCSS since the derivation yieldscontradictory orderings of the AST-Ts. A-anchoring in (64) is likewise automatically filtered. Inparticular, step (64iii) in the derivation is temporally uninformative, as it yields an output (64iv)non-distinct from the output of steps (64i-ii) combined. The connective is thus temporallyvacuous. TC-economy is thereby violated.

We moreover explain why the ungrammatical (60b) cannot be generated: TC-economyrules out A-anchoring in (64), and the TCSS rules out D-anchoring in (63).

The generalization that emerges is simple. When a temporal adjunct is merged into amatrix, the ordering relation between the AST-Ts must be established by the temporal connectiveitself, since the role of the connective is precisely to order the matrix and adjunct AST-Ts. Thederivation in (64) crashes because the ordering relation between the AST-Ts (inclusion) is alreadyestablished at step (ii) of the derivation by present Tense in the adjunct. At step (iii), theconnective WHEN then fails to determine the temporal ordering of the AST-Ts. It is thus temporallyuninformative, vacuous and TC-economy is violated.

We started off this last section by discussing the backward/forward shifted readings thatobligatory arise with the complement clauses in (65a/66a). We argued that A-anchoring isenforced in (65a/66a) to ensure an intrinsic ordering of the matrix and subordinate AST-Ts, asrecapitulated in (67).

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65. Backward-shifted readings 66. Forward-shifted readingsa. Kim said that Terri left the party. a. Kim will say that Terri will leave the party.b. Kim arrived after Terri left the party. b. Kim arrived before Terri left the party.

67i. Kim PAST SAY: AST-T1___UT-T

ii. Terri PAST LEAVE: AST-T2___UT-T

Output of (i-ii) no ordering of the AST-Tsiii. Resetting the anchor-time to AST-T2 AST-T1 AFTERTENSE AST-T2

In contrast, adjunct clauses are always D-anchored into the matrix. D-anchoring ensures thatbackward/forward shifted construals in after/before clauses (65b/66b) are established via thetemporal connective itself:

68i. Kim PAST ARRIVE: AST-T1___UT-T

ii. Terri PAST LEAVE: AST-T2___UT-T

Output of (i-ii) no ordering of the AST-Tsiii. Temporal contribution of the connective AFTER AST-T1 AFTERCONNECTIVE AST-T2

A-anchoring of the adjunct (at step (68ii)) would have violated TC-economy because past Tensein the adjunct would itself determine the ordering relation (subsequence) between the AST-Ts:AST-T1 AFTERTENSE AST-T2. Step (68iii) would thereby be temporally vacuous. The connective willhave failed to determine the ordering of the AST-Ts.

We hope to have shown that the proposal that temporal computation is governed byoptimality conditions covers a broad range of empirical facts. In particular, restrictions on theiteration of temporal heads, and the distribution of dependent vs. independent temporal construalsin subordinate —be it complement, relative or adjunct— clauses with eventive verbs.

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