Sorites project

Motivation

We consider the following argument:

Premise 1: The Sears Tower is tall.

Premise 2: A building that is 1m shorter than a tall building is tall.

Conclusion: Every building in Chicago is tall.

When people hear this argument, they tend to think that premise 1 (the “concrete” premise) and premise 2 (the “inductive” premise) are both clearly true, but that the conclusion – which would naturally follow from the premises according to first order logic – is clearly false.

We explain people’s reactions to statements of this kind with a formal model of scalar adjective interpretation and show that their reactions are sensitive to the prior distribution on building heights and to the change in height ε given in the inductive premise (in this case, 1 meter).

We do all of this in the domain of prices.

Directory structure

Files

• data_summary.Rmd
  • ☐ shows data collected so far and fit of log-normal curves
  • summarizes ☑ results from sorites judgments collected so far, with a ☑ clear indication of the precise wording used for each.
• data/: contains data from all experiments
  • sorites/: data from experiments where we elicit ratings for "goodness" of sorites premises
  • priors/: data from experiments where we elicit prior probabilities of items costing different amounts
  • each experiment is labeled with a unique number as an identifier.
  • data filenames are data_exp{NUMBER}_{YEAR}_{MONTH}_{DATE}_{HOUR}.csv
• experiments: A copy of the HTML and JavaScript files for running each of the experiments is in experiments directory. This directory also includes a subdirectory detailing many of the prior experiments using an old naming scheme.
• models/: contains webppl models
• model/: An older attempt at a webppl model of adjectives taking in some fit parameters for the prior. Really, the prior parameters should be inferred from the prior elicitation experiments results within the webppl model.
• paper: Draft of the paper for this project
• writeups: Brief .Rmd summaries and graphs for each experiment. These contain more details about the design of experiments.

Main Experiments

• Priors: Actual source of prior data: Experiment 9 (or Experiment 6?)
  • Experiment 6 prior elicitation has all 5 items, but only 10 Ss.
  • Experiment 9 prior elicitation has only 3 items, but 36 Ss.
• Final sorites experiments: Experiments 10 and 11
  • Experiment 10 uses a conditional statement for the inductive premise ("If a laptop is expensive, then another laptop that costs $E less is also expensive.")
  • Experiment 11 uses a relative clause for the inductive premise ("A laptop that costs $E less than an expensive laptop is also expensive.")
  • Both experiments used relative clauses for the concrete premise ("A laptop that costs $V is expensive.")

All Experiments

• Pilot experiments
  • Experiment 0: sorites premises where the dollar amounts were not etreme enough to get a variety of judgments (first 30 Ss in file)
  • Experiment 1: sorites premises with more extreme values but still not full range of ratings
  • Experiment 2: binned free response prior experiment
  • Experiment 3: binned sliders prior experiment with 10 bins per item
  • Experiment 4: binned sliders prior experiment with 20 bins per item
  • Experiment 5: binned sliders prior experiment with 40 bins per item
  • Experiment 6: binned sliders prior experiment with varied bin numbers, prior and posterior. this is the experiment that insipired the dollar amounds in the next sorites premises experiments
  • Experiment 7: sorites premises experiment with new dollar amounts
  • Experiment 8: a prior elicitation experiment where in one condition, we asked about bins individually
• Sorites priors experiments
  • ONE PRIOR ELICITATION EXPT Experiment 9: 3 domain bins prior elicitation experiment
• Sorites premises experiments
  • ACTUAL SORITES EXPT Experiments 10 & 11: sorites premises experiment with full range of responses, two different ways of phrasing the inductive premise. Also within this directory is a folder older-writeups which contains descriptions of many of the experiments as well as some old model results.

To do

• Document nicely give a number
• add in concrete premise
  • figure out binning
    • compare model to empirical for concrete
    • compare prior dist params with and without joint inference
• Model comparison with unlifted L1 and L0 versions of speaker models
  • use webppl AIS (use sherlock)
  • could run into variance issues. if so, we could simplify prior param inference (e.g. outside of AIS, empirical, MAP)
• pin down semantics of inductive premise