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- what is probabilistic pragmatics?
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- example: vanilla rational speech act model
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- extensions & applications:
- individual differences
- embedded scalars
\[ \definecolor{firebrick}{RGB}{178,34,34} \newcommand{\red}[1]{{\color{firebrick}{#1}}} \] \[ \definecolor{green}{RGB}{107,142,35} \newcommand{\green}[1]{{\color{green}{#1}}} \] \[ \definecolor{blue}{RGB}{0,0,205} \newcommand{\blue}[1]{{\color{blue}{#1}}} \] \[ \newcommand{\den}[1]{[\![#1]\!]} \] \[ \newcommand{\set}[1]{\{#1\}} \]
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Franke & JÃ¤ger (2016), Probabilistic pragmatics, ZfS 35(1):3-44
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\(\Rightarrow\) 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 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!]
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)
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