Rationalizing Evaluativity Dylan Bumford and Jessica Ret UCLA - - PowerPoint PPT Presentation

Rationalizing Evaluativity

Dylan Bumford and Jessica Ret

UCLA

August 20, 2020

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evaluativity: an overview

a construction is evaluative iff it implies that some degree exceeds a contextual standard.

• canonical evaluativity: positive constructions like Jane is tall.
• canonical non-evaluativity: explicit comparatives like Jane is taller

than Keisha.

• the Bierwisch (1989) Test: evaluative constructions entail the negation
• f their antonymic positive counterpart

(1) a. Jane is tall. → Jane is not short. b. Jane is taller than Keisha. Jane is not short.

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evaluativity: the challenge

• the problem (Kamp 1975, Cresswell 1976): if the meaning of a

comparative is compositionally derived in part from that of a positive construction, why isn’t the comparative evaluative too?

• the canonical solution: a null operator POS which contributes

evaluativity only in the absence of overt degree morphology (2) a. tallw = λx. heightw(x) b. Jane is POS tallw = heightw(j) ≥ s c. Jane is taller than Keishaw = heightw(j) > heightw(k)

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Lassiter & Goodman (2013)

• instead, Lassiter & Goodman (2013) argue the evaluativity of positive

constructions can be derived from pragmatic reasoning effects

• gradable adjectives like tall denote relations between individuals, degrees

(3) a. tallw = λdλx. heightw(x) ≥ d b. Jane is ∅d tallw = heightw(j) ≥ d

• in positive constructions, the degree argument is unsaturated
• evaluativity emerges when listeners are forced to estimate a value for the

degree argument d in addition to estimating a subject’s height w

• they use a Rational Speech Act model (Frank & Goodman 2012)
• not knowing which threshold d the speaker has in mind, the listener

assumes the speaker has made a rational choice to uter the sentence

• the speaker must think the sentence is reasonably informative (worth saying)
• but at the same time, highly informative sentences are relatively likely
• so the listener takes a weighted average of hypotheses about possible

values the speaker may have had in mind, resulting in a degree argument value that is higher (but not by much) than the relevant standard

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evaluativity: a typology

• the L&G and POS approaches both assume that evaluativity surfaces

in the absence of overt degree morphology

• but there is in fact no such correlation (Bierwisch 1989, Ret 2015)
• what’s more, evaluativity can depend on antonymy

(4) non-evaluativity a. Jane is 5 f. tall. measure phrase b. Jane is taller/shorter than Keisha. comparative (5) antonym-insensitive evaluativity a. Jane is tall/short. positive construction b. Is Jane tall/short? polar degree question (6) antonym-sensitive evaluativity a. How tall/short is Jane? degree question b. Jane is as tall/short as Keisha. equative c. Jane is that tall/short too. degree demonstrative

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evaluativity: a typology

• the L&G and POS approaches both assume that evaluativity surfaces

in the absence of overt degree morphology

• but there is in fact no such correlation (Bierwisch 1989, Ret 2015)
• what’s more, evaluativity can depend on antonymy

(4) non-evaluativity a. Jane is 5 f. tall. measure phrase b. Jane is taller/shorter than Keisha. comparative (5) antonym-insensitive evaluativity a. Jane is tall/short. positive construction b. Is Jane tall/short? polar degree question (6) antonym-sensitive evaluativity a. How tall/short is Jane? degree question b. Jane is as tall/short as Keisha. equative c. Jane is that tall/short too. degree demonstrative

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the open argument problem

• in RSA, the listener’s reasoning is driven by uncertainty
• but, in the traditional degree-semantic account (and L&G’s), when a

speaker asserts Jane is as short as Keisha, or Jane is that short, there isn’t anything uncertain to reason about (7) a. Jane is (exactly) thatc shortw = htw(j) ≤

(=) dc

b. Jane is (exactly) as short as Keishaw = {d : htw(j) ≤ d} ⊇

(=) {d : htw(k) ≤ d}

• these adjectival constructions have degree arguments, like Jane is tall

does, but those arguments are bound or valued overtly

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markedness in RSA

• the evaluativity contrast in (8) is due to the relative markedness of

the negative adjective (Lehrer 1985, Ret 2015) (8) a. Jane is (exactly) as tall as Keisha. non-eval. equative b. Jane is (exactly) as short as Keisha.

• eval. equative
• in fact, RSA models of markedness-driven Manner implicature have

been proposed

• Bergen et al. 2016 (see also Pots et al. 2016) model the difference

between synonymous short (i.e. unmarked) and long (i.e. marked) messages using a similar paradigm centered around lexical uncertainty

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Bergen et al. 2016

• two messages are denotationally equivalent, but one is more costly

marked = {w1,w2} unmarked = {w1,w2}

• listener is uncertain of exactly what propositions the messages

express, so they consider various strengthenings of the literal meaning marked unmarked L0 {w1,w2} {w1,w2} L1 {w1} {w1,w2} L2 {w1,w2} {w1} L3 {w1} {w2} . . . . . . . . .

• some of these possible denotations are a priori more likely than others

w1 w2 0.0 0.5 1.0

Prob

Prior over worlds

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Bergen et al. 2016

• listeners interpret uterances based on their prior beliefs and

speakers’ choices

• speakers choose uterances based on their cost and listeners’

interpretations n(w | u, L) ∝ P(w) · n(u | w, L)

[greatly simplifying]

n(u | w, L) ∝ n−1(w | u, L) − C(u)

• under these conditions, marked messages are rationally interpreted

as describing less likely scenarios, despite literal equivalence

0.0 0.5 1.0 marked w1 w2 0.0 0.5 1.0 unmarked

L0

0.0 0.5 1.0 w1 w2 0.0 0.5 1.0

L1

0.0 0.5 1.0 w1 w2 0.0 0.5 1.0

L2

0.0 0.5 1.0 w1 w2 0.0 0.5 1.0

L3

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LU doesn’t help with the open argument problem

• does this help L&G with the anytonym-sensitive evaluativity

contrast? (9) a. Jane is (exactly) as tall as Keisha. non-eval. equative b. Jane is (exactly) as short as Keisha.

• eval. equative
• these messages are plausibly denotationally equivalent, and (9b) more

marked than (9a)

• but as things stand, they’re both maximally informative with respect

to the parameters under discussion; consider:

• tall =

L0 L1 L2 L3 · · ·

• as tall/short as Keisha =

L0

• so there are no strengthenings to consider; the use of the negative

antonym in (9a) is simply inexplicable

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the new normal

• if the use of short (rather than tall) introduces evaluativity in

certain constructions, there must be more to think about in these messages than the subject’s height

• we propose that, in addition to reasoning about an adjective’s

degree argument, listeners reason about the distribution of that value within the relevant comparison class (Barker 2002)

• an individual’s height may be unknown within a known

distribution

• an individuals’ height may be known within an unknown

distribution

1 3 5 7 9 11 1 3 5 7 9 11 1 3 5 7 9 11 1 3 5 7 9 11 1 3 5 7 9 11

• in other words, there are many ways to be tall, and even many

ways to be 5 f tall

1 3 5 7 9 11

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model assumptions, priors

• to model this, we assume
• height is known to be normally distributed, though the center of the

distribution is unknown

• worlds are thus distinguished by both the height of the subject and the

center of the comparison class

• worlds where the subject’s height is far from the mean are a priori unlikely

10 20 Prob 1.2 2.5 1.2 3.9 2.5 1.2 4.6 3.9 2.5 1.2 3.9 4.6 3.9 2.5 1.2 2.5 3.9 4.6 3.9 2.5 1.2 2.5 3.9 4.6 3.9 1.2 2.5 3.9 4.6 1.2 2.5 3.9 1.2 2.5 1.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 Prob

Prior over subject heights and comparison classes

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positive construction: semantic assumptions

• positive constructions are tautologies ≈ Jane has a height (Ret 2015)
• strengthened interpretations place subject’s height in various upper

(resp. lower) percentile of comparison class Jane is tall Jane is short . . . . . . . . . L−1 λw. htw(j) ≥ µw − 1 λw. htw(j) ≤ µw − 1 L0 λw. htw(j) ≥ µw + 0 λw. htw(j) ≤ µw + 0 L1 λw. htw(j) ≥ µw + 1 λw. htw(j) ≤ µw + 1 . . . . . . . . .

mu 2 2 2 2 2 1 2 3 4 5 6 7 8 9 10 11 ht

[[Tall]] := ht ≥ mu - 2

2 2 2 2 2 1 2 3 4 5 6 7 8 9 10 11 ht

[[Tall]] := ht ≥ mu - 1

2 2 2 2 2 1 2 3 4 5 6 7 8 9 10 11 ht

[[Tall]] := ht ≥ mu + 0

2 2 2 2 2 1 2 3 4 5 6 7 8 9 10 11 ht

[[Tall]] := ht ≥ mu + 1

2 2 2 2 2 1 2 3 4 5 6 7 8 9 10 11 ht

[[Tall]] := ht ≥ mu + 2

false true denotation

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positive simulation: Jane is tall

10 20 Prob 1.2 2.5 1.2 3.9 2.5 1.2 4.6 3.9 2.5 1.2 3.9 4.6 3.9 2.5 1.2 2.5 3.9 4.6 3.9 2.5 1.2 2.5 3.9 4.6 3.9 1.2 2.5 3.9 4.6 1.2 2.5 3.9 1.2 2.5 1.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 Prob

L0 literal listener

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positive simulation: Jane is tall

10 20 Prob 0.3 1.3 0.3 3 1.3 0.3 4.6 3 1.3 0.3 4.9 4.6 3 1.3 0.3 3.8 4.9 4.6 3 1.3 2.1 3.8 4.9 4.6 3 2.1 3.8 4.9 4.6 2.1 3.8 4.9 2.1 3.8 2.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L0 + lex. uncertainty

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positive simulation: Jane is tall

10 20 Prob 0.2 0.6 0.2 1.6 0.6 0.2 4.6 1.6 0.6 0.2 7.3 4.6 1.6 0.6 0.2 5.7 7.3 4.6 1.6 0.6 5.7 7.3 4.6 1.6 5.7 7.3 4.6 5.7 7.3 5.7 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L1 pragmatic listener

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positive simulation: Jane is tall

10 20 Prob 0.8 11.5 0.8 7.7 11.5 0.8 7.7 11.5 0.8 7.7 11.5 0.8 7.7 11.5 7.7 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L2 pragmatic listener

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positive simulation: Jane is tall

10 20 Prob 13.5 6.5 13.5 6.5 13.5 6.5 13.5 6.5 13.5 6.5 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L3 pragmatic listener

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positive construction simulation summary: Jane is tall

• As pragmatic iterations proceed, listeners become very confident that

Jane’s height exceeds the median, though they remain in the dark about what the median is

10 20 Prob 1.2 2.5 1.2 3.9 2.5 1.2 4.6 3.9 2.5 1.2 3.9 4.6 3.9 2.5 1.2 2.5 3.9 4.6 3.9 2.5 1.2 2.5 3.9 4.6 3.9 1.2 2.5 3.9 4.6 1.2 2.5 3.9 1.2 2.5 1.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 Prob

L0

10 20 Prob 0.2 0.6 0.2 1.6 0.6 0.2 4.6 1.6 0.6 0.2 7.3 4.6 1.6 0.6 0.2 5.7 7.3 4.6 1.6 0.6 5.7 7.3 4.6 1.6 5.7 7.3 4.6 5.7 7.3 5.7 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L1

10 20 Prob 0.8 11.5 0.8 7.7 11.5 0.8 7.7 11.5 0.8 7.7 11.5 0.8 7.7 11.5 7.7 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L2

10 20 Prob 13.5 6.5 13.5 6.5 13.5 6.5 13.5 6.5 13.5 6.5 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L3

• And as seen in the height marginal, even though the standard

remains unknown, the belief that Jane’s height exceeds it leads to a (positively skewed) evaluative distribution over worlds

• evaluativity: strong

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positive construction simulation: Jane is short

10 20 Prob 1.2 2.5 1.2 3.9 2.5 1.2 4.6 3.9 2.5 1.2 3.9 4.6 3.9 2.5 1.2 2.5 3.9 4.6 3.9 2.5 1.2 2.5 3.9 4.6 3.9 1.2 2.5 3.9 4.6 1.2 2.5 3.9 1.2 2.5 1.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 Prob

L0 literal listener

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positive construction simulation: Jane is short

10 20 Prob 2.1 3.8 2.1 4.9 3.8 2.1 4.6 4.9 3.8 2.1 3 4.6 4.9 3.8 2.1 1.3 3 4.6 4.9 3.8 0.3 1.3 3 4.6 4.9 0.3 1.3 3 4.6 0.3 1.3 3 0.3 1.3 0.3 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L0 + lex. uncertainty

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positive construction simulation: Jane is short

10 20 Prob 13.7 5.4 13.7 0.7 5.4 13.7 0.2 0.7 5.4 13.7 0.2 0.7 5.4 13.7 0.2 0.7 5.4 0.2 0.7 0.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L1 pragmatic listener

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positive construction simulation: Jane is short

10 20 Prob 19.8 0.2 19.8 0.2 19.8 0.2 19.8 0.2 19.8 0.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L2 pragmatic listener

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positive construction simulation: Jane is short

10 20 Prob 20 20 20 20 20 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L3 pragmatic listener

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positive construction simulation summary: Jane is short

• As pragmatic iterations proceed, listeners become absolutely certain

that Jane’s height falls below the standard, though they remain in the dark about what the standard is

10 20 Prob 1.2 2.5 1.2 3.9 2.5 1.2 4.6 3.9 2.5 1.2 3.9 4.6 3.9 2.5 1.2 2.5 3.9 4.6 3.9 2.5 1.2 2.5 3.9 4.6 3.9 1.2 2.5 3.9 4.6 1.2 2.5 3.9 1.2 2.5 1.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 Prob

L0

10 20 Prob 13.7 5.4 13.7 0.7 5.4 13.7 0.2 0.7 5.4 13.7 0.2 0.7 5.4 13.7 0.2 0.7 5.4 0.2 0.7 0.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L1

10 20 Prob 19.8 0.2 19.8 0.2 19.8 0.2 19.8 0.2 19.8 0.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L2

10 20 Prob 20 20 20 20 20 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L3

• Even though the center remains unknown, the belief that Jane’s

height falls below it leads to a (negatively skewed) evaluative distribution over worlds

• evaluativity: very strong

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degree demonstrative: semantic assumptions

• that tall/short both taken to denote that subject’s height is exactly 6
• strengthened interpretations again place subject’s height within

various upper/lower percentiles of comparison class Jane is that6 tall Jane is that6 short . . . . . . . . . L−1 λw. htw(j) = 6 ∧ 6 ≥ µw − 1 λw. htw(j) = 6 ∧ 6 ≤ µw − 1 L0 λw. htw(j) = 6 ∧ 6 ≥ µw + 0 λw. htw(j) = 6 ∧ 6 ≤ µw + 0 L1 λw. htw(j) = 6 ∧ 6 ≥ µw + 1 λw. htw(j) = 6 ∧ 6 ≤ µw + 1 . . . . . . . . .

mu 2 2 2 2 2 1 2 3 4 5 6 7 8 9 10 11 ht

[[Tall]] := ht = 6 & 6 ≥ mu - 2

2 2 2 2 2 1 2 3 4 5 6 7 8 9 10 11 ht

[[Tall]] := ht = 6 & 6 ≥ mu - 1

2 2 2 2 2 1 2 3 4 5 6 7 8 9 10 11 ht

[[Tall]] := ht = 6 & 6 ≥ mu + 0

2 2 2 2 2 1 2 3 4 5 6 7 8 9 10 11 ht

[[Tall]] := ht = 6 & 6 ≥ mu + 1

2 2 2 2 2 1 2 3 4 5 6 7 8 9 10 11 ht

[[Tall]] := ht = 6 & 6 ≥ mu + 2

false true denotation

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degree demonstrative simulation: Jane is that tall

10 20 Prob 14.5 22.5 26 22.5 14.5 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L0 literal listener

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degree demonstrative simulation: Jane is that tall

20 Prob 21.8 28.1 26 16.9 7.3 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L0 + lex. uncertainty

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degree demonstrative simulation: Jane is that tall

20 Prob 23.2 29.9 27.4 15.6 3.9 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L1 pragmatic listener

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degree demonstrative simulation: Jane is that tall

20 Prob 18.2 28.2 32.5 21 0.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L2 pragmatic listener

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degree demonstrative simulation: Jane is that tall

20 Prob 17.2 26.7 30.9 25.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L3 pragmatic listener

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degree demonstrative summary: Jane is that tall

• Jane’s height is of course fixed by the uterance, and since people are

usually normally-sized, a literal interpreter will assume 6 is the most likely center

10 20 Prob 14.5 22.5 26 22.5 14.5 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L0

20 Prob 23.2 29.9 27.4 15.6 3.9 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L1

20 Prob 18.2 28.2 32.5 21 0.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L2

20 Prob 17.2 26.7 30.9 25.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L3

• As iterations proceed, the listener’s belief does not move far from

where it is afer interpreting the sentence literally

• evaluativity: very weak

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degree demonstrative simulation: Jane is that short

10 20 Prob 14.5 22.5 26 22.5 14.5 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L0 literal listener

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degree demonstrative simulation: Jane is that short

20 Prob 7.3 16.9 26 28.1 21.8 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L0 + lex. uncertainty

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degree demonstrative simulation: Jane is that short

20 40 Prob 2.8 8.7 18.1 32.4 38 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L1 pragmatic listener

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degree demonstrative simulation: Jane is that short

50 Prob 0.4 28.1 71.4 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L2 pragmatic listener

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degree demonstrative simulation: Jane is that short

50 100 Prob 7.9 92.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L3 pragmatic listener

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degree demonstrative summary: Jane is that short

• Again, since the lexica all entail that a "6-short person" has height 6,

the distribution over Jane’s height is certain

10 20 Prob 14.5 22.5 26 22.5 14.5 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L0

20 40 Prob 2.8 8.7 18.1 32.4 38 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L1

50 Prob 0.4 28.1 71.4 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L2

50 100 Prob 7.9 92.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L3

• But now, the various strengthenings lead ultimately to a pragmatic

conclusion that 6 is almost certainly below the center

• evaluativity: very strong

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equative: semantic assumptions

• as tall/short as Keisha both taken to entail that subject’s height is

equal to Keisha’s height, which is unknown

• strengthened interpretations again place subject’s height within

various upper/lower percentiles of comp. class Jane is as tall as Keisha Jane is as short as Keisha . . . . . . . . . L−1 λw. htw(j) = k ∧ k ≥ µw − 1 λw. htw(j) = k ∧ k ≤ µw − 1 L0 λw. htw(j) = k ∧ k ≥ µw + 0 λw. htw(j) = k ∧ k ≤ µw + 0 L1 λw. htw(j) = k ∧ k ≥ µw + 1 λw. htw(j) = k ∧ k ≤ µw + 1 . . . . . . . . .

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equative simulation: Jane is as tall as Keisha

10 20 Prob 6.1 5.3 3.4 1.6 5.3 6.1 5.3 3.4 1.6 3.4 5.3 6.1 5.3 3.4 1.6 3.4 5.3 6.1 5.3 1.6 3.4 5.3 6.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L0 literal listener

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equative simulation: Jane is as tall as Keisha

10 20 Prob 6.1 4 1.7 0.4 6.6 6.1 4 1.7 0.4 5.1 6.6 6.1 4 1.7 2.9 5.1 6.6 6.1 4 2.9 5.1 6.6 6.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L0 + lex. uncertainty

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equative simulation: Jane is as tall as Keisha

10 20 Prob 6.6 4.2 1.3 7 6.5 4 1.1 5.4 7 6.4 3.6 0.9 3.1 5.4 7 6.3 3 3.1 5.5 7.1 5.7 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L1 pragmatic listener

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equative simulation: Jane is as tall as Keisha

20 Prob 4.7 1.2 8.4 4 0.9 9.6 7.9 3.7 0.6 7.1 9.8 8.1 3.7 0.3 7.3 10.4 9.1 3 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 20 Prob

L2 pragmatic listener

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equative simulation: Jane is as tall as Keisha

20 Prob 0.6 9.2 0.3 15.2 7.6 0.2 7.9 15.3 8.4 0.2 7.9 15.6 11.7 0.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 20 40 Prob

L3 pragmatic listener

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equative summary: Jane is as tall as Keisha

• Because Keisha’s height is unknown, the literal (and pragmatic)

posterior over worlds is spread out

10 20 Prob 6.1 5.3 3.4 1.6 5.3 6.1 5.3 3.4 1.6 3.4 5.3 6.1 5.3 3.4 1.6 3.4 5.3 6.1 5.3 1.6 3.4 5.3 6.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L0

10 20 Prob 6.6 4.2 1.3 7 6.5 4 1.1 5.4 7 6.4 3.6 0.9 3.1 5.4 7 6.3 3 3.1 5.5 7.1 5.7 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L1

20 Prob 4.7 1.2 8.4 4 0.9 9.6 7.9 3.7 0.6 7.1 9.8 8.1 3.7 0.3 7.3 10.4 9.1 3 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 20 Prob

L2

20 Prob 0.6 9.2 0.3 15.2 7.6 0.2 7.9 15.3 8.4 0.2 7.9 15.6 11.7 0.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 20 40 Prob

L3

• The various conceivable interpretations lead ultimately to a

conclusion that Jane is probably a bit above the median

• evaluativity: relatively weak

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equative simulation: Jane is as short as Keisha

10 20 Prob 6.1 5.3 3.4 1.6 5.3 6.1 5.3 3.4 1.6 3.4 5.3 6.1 5.3 3.4 1.6 3.4 5.3 6.1 5.3 1.6 3.4 5.3 6.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L0 literal listener

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equative simulation: Jane is as short as Keisha

10 20 Prob 6.1 6.6 5.1 2.9 4 6.1 6.6 5.1 2.9 1.7 4 6.1 6.6 5.1 0.4 1.7 4 6.1 6.6 0.4 1.7 4 6.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L0 + lex. uncertainty

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equative simulation: Jane is as short as Keisha

20 Prob 6.5 7.6 7.8 5.1 2 3.6 5.3 6.7 4.4 0.5 1.6 3.4 6.1 7.2 0.7 2.3 5 9.4 1.2 4.1 9.6 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L1 pragmatic listener

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equative simulation: Jane is as short as Keisha

20 40 Prob 1.4 4 16.8 26 0.1 0.9 8.1 12.8 0.1 1.6 10.8 0.5 9.5 0.3 7.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 20 40 Prob

L2 pragmatic listener

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equative simulation: Jane is as short as Keisha

20 40 Prob 25.5 36.7 1.9 28.7 5.8 1 0.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 Prob

L3 pragmatic listener

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equative summary: Jane is as short as Keisha

• Again, since Keisha’s height is unknown, the posterior probability

remains distributed across many heights

10 20 Prob 6.1 5.3 3.4 1.6 5.3 6.1 5.3 3.4 1.6 3.4 5.3 6.1 5.3 3.4 1.6 3.4 5.3 6.1 5.3 1.6 3.4 5.3 6.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L0

20 Prob 6.5 7.6 7.8 5.1 2 3.6 5.3 6.7 4.4 0.5 1.6 3.4 6.1 7.2 0.7 2.3 5 9.4 1.2 4.1 9.6 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L1

20 40 Prob 1.4 4 16.8 26 0.1 0.9 8.1 12.8 0.1 1.6 10.8 0.5 9.5 0.3 7.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 20 40 Prob

L2

20 40 Prob 25.5 36.7 1.9 28.7 5.8 1 0.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 Prob

L3

• But now, the various possible strengthenings lead to a pragmatic

conclusion that Jane is almost certainly below the median

• evaluativity: very strong

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results summary 1

positive form: both antonyms evaluative

• Jane is tall

10 20 Prob 1.2 2.5 1.2 3.9 2.5 1.2 4.6 3.9 2.5 1.2 3.9 4.6 3.9 2.5 1.2 2.5 3.9 4.6 3.9 2.5 1.2 2.5 3.9 4.6 3.9 1.2 2.5 3.9 4.6 1.2 2.5 3.9 1.2 2.5 1.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 Prob

L0

10 20 Prob 0.2 0.6 0.2 1.6 0.6 0.2 4.6 1.6 0.6 0.2 7.3 4.6 1.6 0.6 0.2 5.7 7.3 4.6 1.6 0.6 5.7 7.3 4.6 1.6 5.7 7.3 4.6 5.7 7.3 5.7 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L1

10 20 Prob 0.8 11.5 0.8 7.7 11.5 0.8 7.7 11.5 0.8 7.7 11.5 0.8 7.7 11.5 7.7 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L2

10 20 Prob 13.5 6.5 13.5 6.5 13.5 6.5 13.5 6.5 13.5 6.5 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L3

• Jane is short

10 20 Prob 1.2 2.5 1.2 3.9 2.5 1.2 4.6 3.9 2.5 1.2 3.9 4.6 3.9 2.5 1.2 2.5 3.9 4.6 3.9 2.5 1.2 2.5 3.9 4.6 3.9 1.2 2.5 3.9 4.6 1.2 2.5 3.9 1.2 2.5 1.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 Prob

L0

10 20 Prob 13.7 5.4 13.7 0.7 5.4 13.7 0.2 0.7 5.4 13.7 0.2 0.7 5.4 13.7 0.2 0.7 5.4 0.2 0.7 0.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L1

10 20 Prob 19.8 0.2 19.8 0.2 19.8 0.2 19.8 0.2 19.8 0.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L2

10 20 Prob 20 20 20 20 20 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L3

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results summary 2

degree demonstrative: antonym-sensitive evaluativity

• Jane is that tall

10 20 Prob 14.5 22.5 26 22.5 14.5 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L0

20 Prob 23.2 29.9 27.4 15.6 3.9 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L1

20 Prob 18.2 28.2 32.5 21 0.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L2

20 Prob 17.2 26.7 30.9 25.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L3

• Jane is that short

10 20 Prob 14.5 22.5 26 22.5 14.5 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L0

20 40 Prob 2.8 8.7 18.1 32.4 38 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L1

50 Prob 0.4 28.1 71.4 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L2

50 100 Prob 7.9 92.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 100 Prob

L3

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results summary 3

equative: antonym-sensitive evaluativity

• Jane is as tall as Keisha

10 20 Prob 6.1 5.3 3.4 1.6 5.3 6.1 5.3 3.4 1.6 3.4 5.3 6.1 5.3 3.4 1.6 3.4 5.3 6.1 5.3 1.6 3.4 5.3 6.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L0

10 20 Prob 6.6 4.2 1.3 7 6.5 4 1.1 5.4 7 6.4 3.6 0.9 3.1 5.4 7 6.3 3 3.1 5.5 7.1 5.7 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L1

20 Prob 4.7 1.2 8.4 4 0.9 9.6 7.9 3.7 0.6 7.1 9.8 8.1 3.7 0.3 7.3 10.4 9.1 3 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 20 Prob

L2

20 Prob 0.6 9.2 0.3 15.2 7.6 0.2 7.9 15.3 8.4 0.2 7.9 15.6 11.7 0.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 20 40 Prob

L3

• Jane is as short as Keisha

10 20 Prob 6.1 5.3 3.4 1.6 5.3 6.1 5.3 3.4 1.6 3.4 5.3 6.1 5.3 3.4 1.6 3.4 5.3 6.1 5.3 1.6 3.4 5.3 6.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L0

20 Prob 6.5 7.6 7.8 5.1 2 3.6 5.3 6.7 4.4 0.5 1.6 3.4 6.1 7.2 0.7 2.3 5 9.4 1.2 4.1 9.6 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 10 20 Prob

L1

20 40 Prob 1.4 4 16.8 26 0.1 0.9 8.1 12.8 0.1 1.6 10.8 0.5 9.5 0.3 7.1 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 20 40 Prob

L2

20 40 Prob 25.5 36.7 1.9 28.7 5.8 1 0.2 1 2 3 4 5 6 7 8 9 10 11 CC Center 11 10 9 8 7 6 5 4 3 2 1 Subj Height 50 Prob

L3

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conclusions

• evaluative inferences are not limited to positive constructions, so

cannot be driven only by the need to fill in a degree argument

• in demonstrative and equative constructions, positive and negative

antonyms compete semantically, so manner drives reasoning

• We adapted the schematic Bergen et al. (2016) model of lexical

competition under semantic uncertainty to derive evaluativity inferences in particular, given suitable semantic entries

• canonical degree constructions are not just vague, they’re

context-sensitive: unsaturated degree parameters model the former (L&G 2013), and background distribution parameters model the later (Barker 2002)

• in principle extendable to non-adjectival evaluative constructions

(Ret 2015) as well as context-sensitive phenomena writ large

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selected references

Barker, C. 2002. The dynamics of vagueness. Linguistics and Philosophy 25(1):1–36. Bergen, L., Levy, R., and Goodman, N. 2016. Pragmatic reasoning through semantic inference. Semantics and Pragmatics 9. Bierwisch, M. 1989. The semantics of gradation. In Dimensional Adjectives: Grammatical Structure and Conceptual Interpretation. Frank, M. and Goodman, N. 2012. Predicting pragmatic reasoning in language games. Science 336:998. Lassiter, D. and Goodman, N. 2013. Context, scale structure, and statistics in the interpretation of positive-form adjectives? In SALT 23. Lehrer, A. 1985. Markedness and antonymy. Journal of Linguistics 21(2): 397-429. Pots, C., Lassiter, D., Levy, R., and Frank, M. 2016. Embedded implicatures as pragmatic inferences under Compositional Lexical

• Uncertainty. Journal of Semantics 33:755–802.

Ret, J. 2015. The semantics of evaluativity. Oxford University Press. Tessler, M. H., Lopez-Brau, M., and Goodman, N. D. 2017. Warm (for winter): Comparison class understanding in vague language. In 15th International Conference on Cognitive Modeling.

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