Collective Predication

This repo contains work relevant to plural/collective predication

Stubborn distributivity

1. The boxes are heavy
   • the boxes each are heavy (distributive)
   • the boxes together are heavy (collective
2. The boxes are big
   • the boxes each are big (distributive)
   • the boxes together are big (NO collective)

Heavy and other "complaisantly collective" predicates names a collective property that is maximally predictable in context

• to change the collective weight of a set, one would need to change the weight of an individual member

Big and other "stubbornly distributive" predicates (i.e., predicates of physical extent) names a collective property that is variable, or unstable across contexts; the property is defintionally dependent on physical arrangement, which is variable

• to change the collective size/height/shape of a set, one needs only to rearrange its members (without a change to individual properties)

Experiment 1: accessing interpretations

A reference task to check whether each and together reliably disambiguate between distributive and collective interpretations for big/heavy/tall:

http://cocolab.stanford.edu/experiments/collective/expt1/expt1.html

Conclusion: each and together are reliable disambiguators.

Experiment 2: naturally-occurring examples from corpora

Expt. 2a: 40 most frequent plural predications

Extracted 40 most frequent sentences from the BNC:

• the NOUNs were ADJECTIVE

Participants rated distributive (with each) and collective (with together) paraphrases.

http://cocolab.stanford.edu/experiments/collective/expt2a/expt2a.html

• No clear grouping for "stubborn distributivity;"
• sig. effect of subject noun for at least 3 predicates.
• Numbers yields the highest rate of collective interpretations for stubbornly distributive small; numbers do not physically instantiate/vary by arrangement.

Expt. 2b: big, heavy, tall

Extracted 5 most frequent subject nouns from the Google Books:

• the NOUNs were BIG/HEAVY/TALL

http://cocolab.stanford.edu/experiments/collective/expt2b/expt2b.html

• heavy does get more collective interpretations
• BUT: the difference between predicates disappears at the sentence level
• waves gets greatest rates of collective interpetation for big
• heavy gets more collective interpretations as object size decreases (i.e., potential for collective knowledge increases)

Experiment 3: manipulating predictability and speaker knowledge

Hypothesis:

1. more predictable -> more collective interpretations
2. less distributive knowledge -> more collective interpretations

http://cocolab.stanford.edu/experiments/collective/expt3/expt3.html

• Significant effect of contextual predictability for big and tall
• No effect of predictability for heavy (it is already maximally predictable)
• Significant effect of speaker knowledge for heavy

Modeling speaker knowledge and contextual predictability in ambiguity resolution

Bayesian Rational Speech-Act (RSA) model:

• Language understanding as social reasoning

  • Treat ambiguity resolution as a lifted variable to be inferred by the pragmatic listener

• Standard truth-functional semantics parameterized to gradable thresholds, interpretation-resolving variables, and properties of context:

  • [[dist]]^θ_d = λs. ∀ x ∈ s [d(x) > θ_d]
  • [[coll]]^c,θ_c = λs. [c + ∑_x∈s d(x) > θ_c]
  • [[amb]]^{v,c,θ_d,θ_c} = if v [[coll]]^c,θ_c, else [[dist]]^θ_d

• Speakers and listeners coordinate on utterance and interpretation most likely to correctly resolve QUD (i.e., the state of the world)

• Speaker observes world with either full or sum access

• Estimates of collective properties (i.e., total size/weight/height) susceptible to varying amounts of contextual noise, an additive factor drawn from the prior over contextual noise P(c):

  

• Literal listener updates beliefs about world given utterance and prior knowledge:

  • P_L0(s | u,v,θ_d,θ_c) ∝ [[u]]^{v,c,θ_d,θ_c}(s) · P(c) · P(s)

• Speaker choses utterance to communicate about observed state in accordance with her utility (minimizing surprisal and cost)

  • U_S1(u; s,v,θ_d,θ_c) = log(L₀(s|u,v,θ_d,θ_c)) − C(u)
  • P_S1(u | o,v,θ_d,θ_c) ∝ exp(𝝰 · 𝔼_Pa(s|o)[U_S1 (u; s,v,θ_d,θ_c)])

• Pragmatic listener jointly infers interpretation and state given utterance

  • P_L1(s,v,θ_d,θ_c | u,a) ∝ P_S1(u | o(a,s),v,θ_d,θ_c) · P(s) · P(v) · P(θ_d,θ_c)

http://forestdb.org/models/plural-predication.html

1. More predictable (less noise) -> more collective
2. Less distributive knowledge (sum access) -> more collective

A noisier collective interpretation is less useful at effectively resolving the QUD, which makes it less likely.