\[ \definecolor{firebrick}{RGB}{178,34,34} \newcommand{\red}[1]{{\color{firebrick}{#1}}} \] \[ \definecolor{green}{RGB}{107,142,35} \newcommand{\green}[1]{{\color{green}{#1}}} \] \[ \definecolor{blue}{RGB}{0,0,205} \newcommand{\blue}[1]{{\color{blue}{#1}}} \] \[ \newcommand{\den}[1]{[\![#1]\!]} \] \[ \newcommand{\set}[1]{\{#1\}} \]

overview

 

  • what is probabilistic pragmatics?

 

  • example: vanilla rational speech act model

 

  • extensions & applications:
    • individual differences
    • embedded scalars

probabilistic pragmatics

what is probabilistic pragmatics?

  • definitely one thing: a piece of bad terminology
    • probabilities play a role, but they are not the main thing

 

  • blunt umbrella term for a set of approaches unified by family resemblance
    • game theoretic pragmatics, "Bayesian pragmatics"
    • modern post-Grice (Geurts, Lauer, Optimality or Relevance Theory)

 

  • gradient concept characterized by a property cluster

Franke & Jäger (2016), Probabilistic pragmatics, ZfS 35(1):3-44

key properties

  1. probabilistic
    • language users are usually uncertain about relevant contextual elements
    • probabilities are a good tool to capture uncertainty
  2. interactive
    • pragmatics is not only about readings of sentences
    • explicitly consider speaker and listener perspectives
  3. rationalistic
    • language use as goal-oriented, purposeful behavior
  4. computational
    • formally precise, implementable (likely: quantitative) formulations
  5. data-oriented
    • pragmatic theory feeds full data-generating model for experimental data

 

\(\Rightarrow\) Bayesian as a consequence of particular implementations of 1-3

levels of analysis

LoA

rational analysis

A rational analysis is an explanation of an aspect of human behavior based
on the assumption that it is optimized somehow to the structure of the 
environment. ... [T]he term does not imply any actual logical deduction in 
choosing optimal behavior, only that the behavior will be optimized. 
                                                    (Anderson 1991, p. 471)

example: reference game paradigm

  • speaker and listener observe a fixed set \(T\) of referents, e.g.:

    RSAstim

  • speaker knows which referent \(t \in T\) she wants to talk about

  • speaker can choose a message \(m\) from set \(M = \{ \text{blue}, \text{green}, \text{square}, \text{circle} \}\)

  • listener tries to recover intended referent based on message

  • communication is successful if guess matches intended referent

[signaling game!]

rational speech act model

dummy

literal listener picks literal interpretation (uniformly at random):

\[ P_{LL}(t \mid m) \propto P(t \mid [\![m]\!]) \]

dummy

Gricean speaker approximates informativity-maximization (with parameter \(\lambda\)):

\[ P_{S}(m \mid t \, ; \, \lambda) \propto \exp(\lambda \cdot \log P_{LL}(t \mid m)) \]

dummy

pragmatic listener uses Bayes' rule to infer likely world states:

\[ P_L(t \mid m \, ; \, \lambda) \propto P(t) \cdot P_S(m \mid t \, ; \, \lambda) \]

(c.f., Benz 2006, Frank & Goodman 2012)

individual variation

simple & complex reference games