Resume

Research

Learning

Blog

Teaching

Jokes

Kernel Papers

by Tessler and Goodman (PsyArXiv 2019)

Previous work showed that boolean concepts can be accurately and quickly transmitted using language, and that two language constructs (generics and qualifiers) play a central role in transmitting conceptual knowledge. The immediate follow-up question is: how do generics actually work? Generics have been studied for a long time, and a specific model describing how generics function has eluded linguists, arguably because generics seem to be too flexible. Consider the four following generics, which all have the same syntactic structure:

- Mosquitoes fly
- Mosquitoes lay eggs
- Mosquitoes are female
- Mosquitoes carry malaria

Most would agree that 1, 2 and 4 are true, but 3 seems odd if not outright false. However, when we think about each statement, peculiarities emerge. 100% of mosquitoes fly whereas <1% of mosquitoes carry malaria, but both statements seem true, whereas the exact same percentage (50%) of mosquitoes lay eggs and are female, but we think of laying eggs as true but being female as false. I think these examples show at least two peculiarities. First, how prevalent a property is for a class (i.e. in what fraction of the instances of a class does the property hold true) doesn’t seem to determine our agreement with whether the class has the property. Second, there appears to be implicit type checking: particular properties (i.e. gender) are properties of instances, not properties of classes (i.e. laying eggs).

In a previous paper, these two authors proposed a model to explain how humans probabilistically interpret/evaluate generics. In this paper, they test their model’s predictions against human behavioral data.

The model posits that humans attempt to infer, from an exemplar \(x\) in concept class \(k\), whether exemplar \(x\) possess feature \(f\), denoted \(f(x)\):

\[P(f(x) = True | x \in k) := r_{kf}\]The authors posit that whether \(f(x)\) evaluates to true depends on an unknown, feature-specific threshold \(\theta\). The joint probability of the truth-value and the threshold is given by

\[P(r_{kf}, \theta | generic, k, f) \propto \delta_{r_{kf} > \theta} P(\theta) P(\r_{kf})\]where \(P(\theta)\) is a prior probability over thresholds and \(P(r_{kf})\) is the prior probability of feature \(f\) across all classes \(k\). As an aside, I feel like thresholds should be feature-specific.

Because no clear baseline models exist in the literature, the authors posit 3 baseline models themselves, all of which differ only in the likelihood:

- Fixed threshold likelihood