structural:expansion
Rational Speech Act and Probabilistic Pragmatics

Over the past decade, many probabilistic and Bayesian methods have become very popular in the modelling of pragmatics, of which the most successful framework has been the Rational Speech Act framework developed by Noah Goodman and Michael C. Frank, which has already seen much use in the analysis of metaphor, hyperbole and politeness. In the Rational Speech Act, listeners and speakers both reason about the other's reasoning concerning the literal meaning of the utterances, and as such, the resulting interpretation depends, but is not necessarily determined by the literal truth conditional meaning of an utterance, and so it uses recursive reasoning to pursue a broadly Gricean co-operative ideal.

In the most basic form of the Rational Speech Act, there are three levels of inference; Beginning from the highest level, the pragmatic listener L 1 {\displaystyle L_{1}} will reason about the pragmatic speaker S 1 {\displaystyle S_{1}}, and will then infer the likely world state s {\displaystyle s} taking into account that S 1 {\displaystyle S_{1}} has deliberately chosen to produce utterance u {\displaystyle u}, while S 1 {\displaystyle S_{1}} chooses to produce utterance u {\displaystyle u} by reasoning about how the literal listener L 0 {\displaystyle L_{0}} will understand the literal meaning of u {\displaystyle u} and so will attempt to maximise the chances that L 0 {\displaystyle L_{0}} will correctly infer the world state s {\displaystyle s}. As such, a simple schema of the Rational Speech Act reasoning hierarchy can be formulated for use in a reference game such that:

L 1: P L 1 (s | u) ∝ P S 1 (u | s) ⋅ P (s) S 1: P S 1 (u | s) ∝ exp (α U S 1 (u; s)) L 0: P L O (s | u) ∝ ] (s) ⋅ P (s) {\displaystyle {\begin{aligned}&L_{1}:P_{L_{1}}(s|u)\propto P_{S_{1}}(u|s)\cdot P(s)\\&S_{1}:P_{S_{1}}(u|s)\propto \exp(\alpha U_{S_{1}}(u;s))\\&L_{0}:P_{L_{O}}(s|u)\propto \!](s)\cdot P(s)\end{aligned}}}