• what is probabilistic pragmatics?

• example: vanilla rational speech act model

• extensions & applications:
  • individual differences
  • embedded scalars

• 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

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

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)

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

  

• 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

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:

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