Maria Bittner, Rutgers http://www.users.cloud9.net/~mbittner NASSLLI 2016 Rutgers, New Brunswick NJ LANGUAGE TYPE: tense-based temporal reference ! q Mainstream view: English tenses are temporal anaphors § anaphora to an aforementioned reference point, construed either as a time (e.g. Reichenbach 1947) or as an event (e.g. Kamp 1981, Webber 1988). § parallels with nominal anaphora o tense ~ pronoun (e.g. Partee 1973, 1984, Stone 1997, Kratzer 1998) o tense ~ anchored (in)definite (e.g. Webber 1988, Moens & Steedman 1988;

see also Kamp & Reyle 1993) q Competing view: English tenses are temporal indefinites § tenses (introduce new times) ~ indefinites (introduce new individuals) § indexical anchor to speech act only, no discourse anaphora § possible pragmatic enrichment to establish coherence may lead to additional inferences about temporal relations (e.g. Comrie 1981, Lascarides & Asher 1993, Kehler 1994, 2002) LANGUAGE TYPE: aspect-based temporal reference, no grammatical tense q Mainstream view (formal syntax & semantics): Temporal reference in Mandarin can be analyzed in terms of English-based categories, including: § English-style syntactic sentences (e.g. Huang 1982, Huang et al. 2009) § English-based aspectual classes (e.g. achievement, accomplishment), grammatical aspects (e.g. perfective, progressive), reference times, ...

(see Li & Thompson 1981, Smith 1991/7, Smith & Erbaugh 2005, Wu 2003, 2009,

Xiao & McEnery 2004, Lin 2006, and many others). q Competing view (a few Mandarin scholars, Chinese language textbooks) Proper analysis of Mandarin discourse requires Mandarin-based categories, including: § Mandarin-based pragmatic 'sentences' ('。'), zero anaphora, topic chains, ... (e.g. Tsao 1979, 1990, Chu 1998, Li 2005) § Mandarin-based aspectual classes (e.g. dur. 'action' v. pnc. 'resultative action') (e.g. Chao 1968, Henne et al. 1977, Tai 1984, DeFrancis, J. ed. 2003)

Main goal: Unified approach to temporal reference that factors out semantic universals while allowing for different language types and contextual variation (Bittner 2014) q Basic idea: Universally, temporal reference relies on grammatical centering systems of obligatory grammatical categories that keep track of top-ranked temporal drefs (events, states, times). Within this space, there is room for linguistic diversity, e.g.: § English has a grammatical system of tense markers (TNS, e.g. past PST v. present PRS) which introduce or refer to top-ranked times (usually topic time, sometimes background time) and may anchor them to input background event. § Mandarin has a grammatical system of aspect features (ASP, e.g. eventive E/ v. stative S/) which introduce background eventualities (events or states) and anchor them to input topic state or input background eventuality (event or state). q Universal logic: Nobody's categories are universal; but all can be analyzed in terms of universal primitives (e.g. event, state, time, consequent state, dref hierarchy, etc). To represent temporal reference, extend UCε to UCτ, with time drefs and generalized temporal dref algebra (building on Bach 1986, Moens & Steedman 1988).

Ø English: TNS-based temporality Ø Mandarin: ASP-based temporality Ø Implementation in UCτ Ø Conclusion

Ø English: TNS-based temporality Ø Mandarin: ASP-based temporality Ø Implementation in UCτ Ø Conclusion

Indefinite npx ~ TNSt (Comrie 1981, Lascarides & Asher 1993, Kehler 1994)! (N) An indefinite np (e.g. a manx) introduces a new individual into discourse

(possibly restricted by a pragmatic coherence relation) (T) An indefinite TNS marker (e.g. PSTt, FUTt) introduces a new time into discourse

(possibly restricted by a pragmatic coherence relation) e.g.! (1) i. Al went (PSTt1 goe1) into a florist shopx.

ii. He promised (PSTt2 promisee2) his wife fresh flowers. EXPLANATION: e2 < e

iii. He bought (PSTt3 buye3) somey beautiful roses. RESULT : e1 < e3 But problems with negation & quantification (see Partee 1973), e.g.: (2) i. Al went (PSTt1 goe1) into a florist shop.

ii. He didn't buy (PSTt2 not buye2) anything.

q {indexical, anaphoric} pronoun ~ TNS (Partee 1973, Stone 1997, etc)

(N) A pronoun refers to an individual that satisfies its presuppositions about the relation

to the speaker (e.g. I) or to an antecedent individual (e.g. hex in (3ii))

(T) A TNS marker refers to a time that satisfies its presuppositions about the relation to

the speech time (e.g. PRS) or to an antecedent time (e.g. PSTt1 in (3ii)). e.g.!

(3) i. Once upon a timet there was (PSTt1 bes1) an old kingx. t1 ⊆ s

ii. Hex was (PSTt1 bes2) very rich. ELABORATION: t1 ⊆ s2 q But pn ≁ TNS in discourse-initial contexts (e.g. ü(4a) v. #(4b))

(4) Entering a store, Customer addresses an unfamiliar Shop Assistant:

a. I bought (PSTt1 go) something here and I want (PRS want) to exchange it. (~ 'dog' in langs. w/o articles, e.g. anaphoric 'dogx' ⇒ 'dogx' if no antecedent)

b. # Hex bought (PST go) something here and he wants (PRS want) to exchange it.

q anchored np ~ tns (Webber 1988, building on Moens & Steedman 1988)

(N) An anchored np (e.g. npxy in (5)) introduces a new individual (...y) that is

anaphorically anchored to a salient antecedent individual (...x).

(T) An anchored TNS (e.g. TNSet in (5)–(7)) introduces a new time (...t) that is

anaphorically anchored to a salient antecedent event (...e).! q event algebra (Moens & Steedman 1988 in MB notation):

▷e = consequent state of event e, ◀︎e = preparatory process of event e, ...! q (5) i. A busx drove up (PSTt1 drive.upe1). θe1 ⊆ t

ii. The driverxy1 opened (PSTe1t2 opene2) the doorsxy2. RESULT: θe2 ⊆ t2 ⊆ θ▷e

iii. A passengerxz got off (PSTe2t3 get.offe3). RESULT: θe3 ⊆ t3 ⊆ θ▷e

(6) i. Alx went into (PSTt1 go.intoe1) a florist shop. θe1 ⊆ t

ii. He promised (PSTe1t2 promisee2) Bea fresh flowers. EXPLANATION: θe2 ⊆ t2 ⊆ θ◀e

(7) i. Alx went into (PSTt1 go.intoe1) a florist shop. θe1 ⊆ t

ii. He did not buy (PSTe1t not buye) anything. RESULT: ¬∃t, e: θe ⊆ t ⊆ θ▷e1...

q Generalized event algebra (M&S + Bach + Bittner): ⟨Dε ∪ Dσ, ⊑, ▷, ◀, s, p, x, y⟩

INPUT OPERATION OUTPUT GRAPHIC REP.

point, e ●

point, e ▷e = s consequent state, s ––––– M&S

point, e ◀︎e = e′ preparatory process, e′ ●●●● M&S

process, e′ se′ = s′ state equivalent, s′ ––––– Bach

process, e′ pe′ = e′′ point equivalent, e′′ ●●●● Bach

state, s′ xs′ = e′′′ start point, e′′′ ● Bittner

state, s′ ys′ = e c(ulmination-)point, e ● Bittner 2014 q grinding: vp[process ➝ state] ~ np[object ➝ mass] (modified Bach 1986)

(8) vp. Al iss {workinge′ , leavinge}. {s ⊑ se′ , s ⊑ s(te) }

np. Al added _y {oily′ , eggx} to the salad. {y ⊑ y′ , y ⊑ sx } q packaging: vp[pl ➝ atomic event] ~ np[pl ➝ atomic object] (modified Bach 1986)

(9) vp. Al did a bite′′ of {worke′, *leavinge}. {e′′ = pe′ , no pe for atomic e}

np. Al ate a portionx′′ of {eggsx′, *an eggx}. {x′′ = px′ , no px for atomic x}

q Top-level reference by English TNS!

⊤-reference: speech event topic time

⊥-reference: background event background time

e.g. relation 1: relation 2 (& 3) ! time–⊤ε situation–time(–⊥ε) source coherence relation! (1) i. Al went into (PST⊤t go.intoe) a florist shop.

ii. He promised (PST⊤⊥t promisee) his wife fresh flowers.

t2 < θe0 θe2 ⊆ t2 ⊆ θ◀e1 PST⊤⊥t EXPLANATION (i-ii)

iii. He asked (PST⊤⊤ aske) the assistant for some roses.

q Top-level reference by English TNS!

⊤-reference: speech event topic time

⊥-reference: background event background time e.g. time–⊤ε situation–time(–⊥ε) source coherence relation! (10) i. Al played chess (PST⊤t play.chesse) today.

ii. He started (PST⊤⊥t start⊥εe) badly ...

t2 < θe0 θe2 ⊆ t2 ⊆ θse1 PST⊤⊥t ELABORATION (i-ii)

e2 = xse1 start⊥e

ii′. ... but in the end⊥′εt ...

t′2 ⊆ θyse1 but in the end⊥′εt CONTRAST (ii-ii′)

... he won (PST⊤⊤ win⊥′εe).

t′2 < θe0 θe3 ⊆ t′2 PST⊤⊤ ELABORATION (i-ii′)

e3 = yse1 win⊥′εe

Ø English: TNS-based temporality Ø Mandarin: ASP-based temporality Ø Implementation in UCτ Ø Conclusion

q Mandarin discourse consists of topic chains (Tsao 1979, Chu 1998, Li 2005, etc), i.e. chains of 1+ open stop 'sentences' (units marked by ) about a topical individual. ! (11) i. Xiăoli niánqīng piàoliang , gōnzuò yĕ hăo

Xiaoli⊤ young pretty , ⊤job also good

Xiaoli⊤ is young and pretty. She⊤ has a good job, too.

ii. Suīrán yŏu ge nánpéngyou , kĕshì bù xiăng jiéhūn

although ⊤have CL boyfriend , but not ⊤wish get.married

Although she⊤ has a boyfriend, she⊤ doesn't wish to get married. (12) i. Nà-liàng chē , jiàqián tài guì , yánsè yĕ bù hăo , Lisi bù xĭhuan

that-CL car⊤ , ⊤price too high , ⊤color also not good , Lisi⊥ not like⊤

That car⊤ is too expensive and it⊤ has an ugly color. Lisi⊥ doesn't like it⊤.

ii. Zuótiān qù kàn-le , hái kāi-le yíhuìr , háishì bù xĭhuan , ...

yesterday ⊥go look⊤-PNC , even ⊥drive⊤-PNC Ma.while , still not ⊥like⊤ , ...

Yest. he⊥ went to look at it⊤ and even ⊥took it⊤ for a spin. He⊥ still didn't like it⊤, ...

q A MANDARIN VERB is compositionally built out of: § an ASP feature (eventive E/ or stative S/), which introduces an eventuality (event or state) and relates it to the input topic state (E⊤/ or S⊤) or bckground eventuality (E⊥/ or S⊥/) § an eventuality predicate, which specifies the eventuality introduced by ASP

q Hence ASP-PROMINENCE at every level: § lexicon: o compound verb = ASP feature + complex eventuality predicate of compositionally predictable type o reduplicated verb = ASP feature + complex eventuality predicate of compositionally predictable type § syntax: o serial verb construction (SVC) = ASP feature + compositional series of eventuality predicates which all co-specify the eventuality introduced by ASP o grammatical aspect markers (e.g. punctual le 'PNC', durative zhe 'DUR') form anaphoric chains with antecedent ASP features (e.g. E/ ... PNC) § discourse: o aspectual topic chain ('。'): topic state update (terminating in topic-setting pause |s) followed by 1+ comment clauses with ⊤σ-anaphors (ASP⊤/, PNC⊤). o (individual) topic chain (zero anaphora): 1+ aspectual topic chains about topic states that are (a) centered on the same individual, and (b) related closely enough for zero anaphora (e.g. central-part as in (11i–ii)).

E/ (ün-ci 'n-events') S/ (*n-ci 'n-events')! combines with: combines with: vε: event predicate (üzài 'be in prg') vσ: state predicate (ühěn 'very') vε: xué 'study/learn', măi 'shop/buy', vσ: qīng1 'clean/clear', qīng2 'light/low', lèi 'tired'

dă 'beat/hit', kàn 'look/see/read', duŏ 'many/much', tèng 'ache', ài 'love',

xiăngε 'think', zuòε 'sit down' xiăngσ 'wish/miss', yŏu 'have' vε-vε: gòu-măi (purchase-buy) 'buy' vσ-vσ: gān-zào (dry-arid) 'dry' vε-n: kàn-shū (read-book) 'read' vσ-n: ài-guó (love-country) 'patriotic' vσ-vε: àn-shā (dark-kill) 'assassinate' n-vσ: tóu-téng (head-ache) 'have a headache' vε•: pt event predicate (*zài 'be in prg') vσ•: pt scale state predicate (*hěn 'very') vε•: lái 'come', qù 'go', dào 'get to', vσ•: zuòσ• 'seated', zhànσ• 'stand', cuò 'wrong',

wán 'finish', yíng 'win', sĭ 'die' zài 'be in/on/at/in prg', méiyǒu 'have no' vε~vε: kànkàn 'take a look, read a bit' vσ~vσ: qīngqīngchŭchŭ 'perfectly clear' vε-vε•: dă-sĭ (beat-die) 'beat to death' vσ-vε•: lèi-si (tired-die) 'dead tired' vε-vσ(•): xiĕ-cuò 'write wrong' vε-vσ•: zhù-zài (live-be.in) 'live in' vε•-n: dào-jiā (arr-home) 'come home' vε⟨vσ•⟩vε•: kāi⟨buσ•⟩guò 'unable to drive across'

q serial verb construction (SVC) = ASP feature + compositional series of eventuality predicates which all co-specify the eventuality introduced by ASP § in (13i), E⊤/ introduces a process (e1) whose progress state (se1) starts with Xiaoli going to town (xse1) and culminates in her buying something (yse1) § in (13ii), E⊥/ introduces a point (e2) whose preparatory process (t ︎e2) is Xiaoli's walk (part of process e1) and whose consequent state is a state of her being tired (we2) § in (13ii), E⊤/ introduces a point (e3) in which Xiaoli sits down (with the intention that) the consequent state culminate in her resting a bit (ywe3)

(13) i. Xiǎoli jīntiān jìn.chéng qù mǎi dōngxi le 。

Xiaoli⊤ today |s E⊤/enter.town go buy things PNC⊤ 。

Xiaoli⊤ went shopping in town today.

ii. Tā zǒu lèi le , zuò.xiàlai xiūxi~xiūxi 。

s/he⊤ E⊥/walk tired PNC⊤ ,|s E⊤/sit.down rest.a.bit 。

When she⊤ got tired of walking, she⊤ sat down to rest a bit.

q punctual aspect marker (-)le 'PNC' (a.k.a 'perfective') highlights a verifiable point

INPUT e•. point event e. (n-atom) event s•. pt scale state s. (n-degree) state

OUTPUT e• pe s•, xs, ys xs, ys ! (14) e•. Wŏ xiĕ-wán-le xìn。

SG E/write-finish-PNC letter

e•. I finished writing a letter (verifiable pt event, e•). e. Wŏ xiĕ-le xìn kěshì mei xiĕ-wán。

SG E/write-PNC letter but not writee-finish•

pe. I did a bit of letter writing but didn't finish. (verifiable pt equivalent, pe)

s•. Chènshān xiăo-le yi.diăn。

shirt [S/small-PNC a.Mbit•]

s•. The shirt is a bit small. (verifiable scalar pt, s•).

xs•. The shirt got a bit smaller. (verifiable start pt, xs•)

s. Tā bìng-le sān-tiān。

SG [S/sick-PNC three-Mday]

xs, ys. He was sick for three days (verifiable start pt, xs; 3 days from xs to ys)

q The minimal unit of Mandarin discourse is an open stop sentence ('。'). § It begins with the introduction of a topic state (terminating in topic-setting pause |s) followed by one or more comments about this topic state (terminating in '。'). § Each comment is a clause with an ASP-feature, which introduces a background eventuality and relates it to the current topic state, either directly (E⊤σ/ or S⊤σ/) or via an anaphoric chain with a dependent aspect marker (e.g. S/... PNC⊤σ) q The next larger unit is an (individual) topic chain (zero anaphora) § It begins with the introduction of a topical individual as part of topic state update, and consists of one or more open stop sentences whose topic states are: o centered on that topical individual! o related closely enough for zero anaphora (e.g. 'central part' as in (11i–ii))

(Individual) topic chain (11i–ii) (zero anaphora) consists of 2 aspectual topic chains ('。'): (11) i. [Xiaoli is young and pretty. She has a good job too.]

topic state ⊤s1: e0-present state of ⊤Xiaoli

Xiaoli⊤ |s ...

comment 1: ⊤s1 is a central part of a state s11 of ⊤Xiaoli being young and pretty

S⊤σ/⊤young S⊤σ/⊤pretty , ...

comment 2: ⊤s1 is also a central part of a state s12 of ⊤Xiaoli having a good job

⊤job also S⊤σ/good 。(end of comments about ⊤s1)

ii. [Although she has a boyfriend, she doesn't wish to marry.]

topic state ⊤s2: larger state of ⊤Xiaoli (s1 ⊑↑ s2), extended to current boyfriend⊥

although S⊤σ/⊤have CL boyfriend ,|s ...

comment 1: ⊤s2 is a central part of a state s21 of Xiaoli not wanting to marry

but not S⊤σ/⊤wish E/marry 。(end of comments about ⊤s2)

q Tsao's (1990) experiment

Native English speakers, and native Mandarin speakers learning English, were shown

English and Mandarin texts with capitalization and full stops removed. They were

asked to restore the full stops. Native English speakers were mostly in agreement on

English sentence boundaries ('.'). Native Mandarin speakers were found to ... ... mostly agree with English speakers on English sentence boundaries ('.') ... but not with other Mandarin speakers on Mandarin sentence boundaries ('。') q Explanation! § English sentences are units of syntax. Their boundaries are usually recoverable from syntactic markers (e.g. TNS). § Mandarin sentences are units of information structure, not syntax. A topic state update (terminating in a topic-setting pause, |s) is followed by n comment(s) (clauses with topic state anaphors E⊤/, S⊤/, or PNC⊤). Since states do not have visible boundaries, speakers may disagree where one topic state ends and the next one begins (e.g. whether the Mandarin discourse (11i–ii) is about two topic states (⊤s1 and ⊤s2, as on the previous slide), or one (⊤s′1, present state of Xiaoli).

Ø English: TNS-based temporality Ø Mandarin: ASP-based temporality Ø Implementation in UCτ Ø Conclusion

Typed dref entities

dref entity: x (individual) e (event) s (state) t (time)

UCτ variable: x e s t Centering-based anaphora, e.g.!

center of attn. backgr. of attn.

⊤τ ⊤σ ⊤δ ⊤ε ⊥ε ⊥′ε ⊥σ ⊥τ typed anaphors Start-up update! Speaking up (e0) focuses attention, giving rise to (e0-)minimal info-state: {⟨⟨e0⟩, ⟨⟩⟩}

Reference to ƒ-values (á la Moens & Steedman 1988, see also next slide)

θe time of event e θs time of state s

↑e central individual in event e ↑s central individual in state s

↓e background individual in event e ↓s background individual in state s

Figure 3. UCτ event algebra: ⟨Dε ∪ Dσ, ⊑ε, ⊑σ, w, t, s, p, x, y, ...⟩ INPUT OPERATION OUTPUT GRAPHIC REP.

point, e ●

point, e we = s consequent state, s ––––– M&S 1988 point, e te = e′ preparatory process, e′ ●●●● M&S 1988 process, e′ se′ = s′ state equivalent, s′ ––––– Bach 1986 process, e′ pe′ = e′′ point equivalent, e′′ ●●●● Bach 1986 state, s′ xs′ = e′′′ start point, e′′′ ● Bittner 2014 state, s′ ys′ = e culmination point, e ● Bittner

(13) i. Xiǎoli jīntiān jìn.chéng qù mǎi dōngxi le 。

Xiaoli⊤ today |s E⊤/enter.town go buy things PNC⊥⊤ 。

Xiaoli⊤ went shopping in town today. Model for Mandarin (13i) Dref Symbol: Description Temp. conds. Source

● ⊤e0: ↑e0 speaks up e0 ■■■■■■■ t1: part of e0-day t1 ⊆ e0-day todayt –––– ⊤s1: ⊤Xiaoli x1 within t1 s1 ⊆ t1 ⊥τ|s ●●● e1: x1 goes to town (xse1) se1 ⊑↑ s1 E⊤/vε• vε• vε

& buys things (yse1) y(se1) = ys1 < e0 PNC⊥⊤

(13') i. Xiǎoli went shopping in town today.

Xiaoli⊤ PSTt goe

shopping in town today⊤ Model for English (13'i) Dref Symbol: Description Temp. conds. Source

● ⊤e0: ↑e0 speaks up e0 ■■■■■■■ ⊤t1: e0-past, t1 < θe0 PSTt part of e0-day t1 ⊆ e0-day today ●●● e1: Xiaoli x1 goes shopping θe1 ⊆ t1 PSTt Ve

(13) ii. Tā zǒu lèi le , zuò.xiàlai xiūxi~xiūxi 。

s/he⊤ E⊥/walk tired PNC⊥⊤ ,|s E⊤/sit.down rest.a.bit 。

When she⊤ got tired of walking, she⊤ sat down to rest a bit. Model for Mandarin (13i–ii) Dref Symbol: Description Temp. conds. Source

● ⊤e0: ↑e0 speaks up e0 ■■■■■■■ t1: part of e0-day t1 ⊆ e0-day todayt –––– ⊤s1: ⊤Xiaoli x1 within t1 s1 ⊆ t1 ⊥τ|s ●●● e1: x1 goes to town (xse1) se1 ⊑↑ s1 E⊤/vε• vε• vε

& buys things (yse1) y(se1) = ys1 < e0 PNC⊥⊤

● e2: x1 gets tired (we2) e2 ⊑↑ e1 E⊥/vε vσ

from walking (te2) e2 = xs2 < e0 PNC⊥⊤

––––– ⊤s2: ⊤Xiaoli x1 within t1 after e2 s2 ⊆ t1 ⊥τ|s

●● e3: x2 sits down (xse3) se3 ⊑↑ s2 E⊤/vε• vε•

to rest a bit (yse3)

(13') ii. When she got tired of walking, she sat down to rest a bit.

[whent [she⊤ PST⊥⊥ gete tired of walking]]t, she⊤ PST⊤⊥ sit.downe to rest a bit Model for English (13'i–ii) Dref Symbol: Description Temp. conds. Source

● ⊤e0: ↑e0 speaks up e0 ■■■■■■■ ⊤t1: e0-past, t1 < θe0 PSTt part of e0-day t1 ⊆ e0-day today⊤ ●●● e1: Xiaoli x1 goes shopping θe1 ⊆ t1 PSTt Ve ■■ t2: e0-past, part of e1-prg.time t2 < θe0, t2 ⊆ θse1 whent PST⊥⊥ ● e2: x1 gets tired (we2) θe2 ⊆ t2 PST⊥⊥ Ve

of walking (te2)

■■■ ⊤t3: e0-past, part of e2-con.time t3 < θe0, t3 ⊆ θwe2 [when ]t PST⊤⊥ ●● e3: x1 sits down (xse3) θe3 ⊆ t3 PST⊤⊥ Ve

to rest a bit (yse3)

Moens & Steedman (1988) idea implemented in UCτ (15) When they built that bridge, a famous architect drew up the plans .

[whent [ PST⊥ builde that bridge]]t PST⊤⊥ draw.upe the plans⊥ ●●● e2: they build that bridge θe2 ⊆ t2 PST⊤ Ve

■■ t3: e0-past, part of e2-pre.time t3 < θe0, t3 ⊆ θte2 [when ]t PST⊤⊥ (16) ... , they used the best materials .

PST⊤⊥ usee the best materials⊥

●●● e2: they build that bridge θe2 ⊆ t2 PST⊤ Ve

■■ t3: e0-past, part of e2-prg.time t3 < θe0, t3 ⊆ θse2 [when ]t PST⊤⊥ (17) ... , my commute got a lot easier .

PST⊤⊥ gete a lot easier

●●● e2: they build that bridge θe2 ⊆ t2 PST⊤ Ve

■■ t3: e0-past, part of e2-con.time t3 < θe0, t3 ⊆ θwe2 [when ]t PST⊤⊥

Ø English: TNS-based temporality Ø Mandarin: ASP-based temporality Ø Implementation in UCτ Ø Conclusion

q UCτ has logical tools for a unified analysis of temporal reference, which factors out semantic universals while allowing for linguistic diversity & coherence-driven variation q Universally, temporal reference relies on grammatical centering systems of obligatory gramm. categories that keep track of top-ranked temp. drefs (events, states, times). q Linguistic diversity, e.g. § English has a grammatical system of tense markers (TNS, e.g. PST v. PRS) which introduce or refer to the topic time or background time and may anchor this dref to the input background event. § Mandarin has a grammatical system of aspect features (ASP, e.g. E/ v. S/) which introduce background eventualities (events or states) and anchor them to the input topic state (either directly or via anaphorically linked aspect markers) or to the input background eventuality (event or state). q Coherence-driven semantic variation § lexical meaning adjustments ~ phonological adjustments (e.g. assimmilation) § accommodation (e.g. discourse-initial PST⊤ → (PST⊤)t or coherence (e.g. ▷︎ v. ◀)

q Basic ideas! § In discourse, plurals and quantifiers can function as antecedents or anaphors, because they can introduce or refer to ranked drefs for sets. § Logical representation in UC0 extended with drefs and anaphors for sets of individuals (UCδ||) q Suggested readings § Berg, M. van den. 1993. Full Dynamic Plural Logic. Proceedings of the 4th

Symposium on Logic and Language. § Berg, M. van den, 1994. A direct definition of generalized dynamic quantifiers.

Proceedings of the 9th Amsterdam Colloquium.

Bach, E. 1986. The algebra of events. Linguistics and Philosophy 9:5–16. Bittner, M. 2014. Temporality: Universals and Variation. Wiley-Blackwell. Chao, Y. R. 1968. A Grammar of Spoken Chinese. University of California Press. Chu, Ch. 1998. A Discourse Grammar of Mandarin Chinese. Peter Lang. Comrie, B. 1981. On Reichenbach's approach to tense: CLS 17, 24–30.

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