Editing Pragmatics (section)

==Formalization==
There has been a great amount of discussion on the boundary between semantics and pragmatics<ref>{{cite web| url = https://web.stanford.edu/group/cslipublications/cslipublications/site/9781575866673.shtml| title = see for instance F.Domaneschi. C. Penco, What is Said and What is Not, CSLI Publication, Stanford}}</ref> and there are many different formalizations of aspects of pragmatics linked to context dependence. Particularly interesting cases are the discussions on the semantics of indexicals and the problem of referential descriptions, a topic developed after the theories of [[Keith Donnellan]].<ref>see for instance S. Neale, Descriptions, 1990</ref> A proper logical theory of formal pragmatics has been developed by [[Carlo Dalla Pozza]], according to which it is possible to connect classical semantics (treating propositional contents as true or false) and intuitionistic semantics (dealing with illocutionary forces). The presentation of a formal treatment of pragmatics appears to be a development of the Fregean idea of assertion sign as formal sign of the act of assertion.

=== 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<ref>{{Cite journal |last1=Goodman |first1=Noah D. |last2=Frank |first2=Michael C. |date=November 2016 |title=Pragmatic Language Interpretation as Probabilistic Inference |url=https://doi.org/10.1016/j.tics.2016.08.005 |journal=Trends in Cognitive Sciences |volume=20 |issue=11 |pages=818–829 |doi=10.1016/j.tics.2016.08.005 |pmid=27692852 |issn=1364-6613}}</ref> framework developed by Noah Goodman and [[Michael C. Frank]], which has already seen much use in the analysis of metaphor,<ref>{{Cite journal |last1=Kao |first1=Justine T. |last2=Bergen |first2=Leon |last3=Goodman |first3=Noah D. |date=2014 |title=Formalizing the Pragmatics of Metaphor Understanding |journal=Cognitive Science|s2cid=13623227 }}</ref> hyperbole<ref>{{Cite journal |last1=Kao |first1=Justine T. |last2=Wu |first2=Jean Y. |last3=Bergen |first3=Leon |last4=Goodman |first4=Noah D. |date=2014-08-04 |title=Nonliteral understanding of number words |journal=Proceedings of the National Academy of Sciences |volume=111 |issue=33 |pages=12002–12007 |doi=10.1073/pnas.1407479111 |doi-access=free |pmid=25092304 |pmc=4143012 |bibcode=2014PNAS..11112002K |issn=0027-8424|hdl=1721.1/95752 |hdl-access=free }}</ref> and politeness.<ref>{{cite report | last1=Yoon | first1=Erica J. | last2=Frank | first2=Michael C. | last3=Tessler | first3=Michael Henry | last4=Goodman | first4=Noah D. | title=Polite speech emerges from competing social goals | date=2018-12-29 | doi=10.31234/osf.io/67ne8}}</ref> 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 <math>L_1</math> will reason about the pragmatic speaker <math>S_1</math>, and will then infer the likely world state <math>s</math> taking into account that <math>S_1</math> has deliberately chosen to produce utterance <math>u</math>, while <math>S_1</math> chooses to produce utterance <math>u</math> by reasoning about how the literal listener <math>L_0</math> will understand the literal meaning of <math>u</math> and so will attempt to maximise the chances that <math>L_0</math> will correctly infer the world state <math>s</math>. As such, a simple schema of the Rational Speech Act reasoning hierarchy can be formulated for use in a reference game such that:<ref>{{Cite web |last1=Scontras |first1=Gregory |last2=Tessler |first2=Michael Henry |last3=Franke |first3=Michael |access-date=17 February 2024 |title=Introducing the Rational Speech Act framework |url=https://www.problang.org/chapters/01-introduction.html |url-status=live |archive-url=https://web.archive.org/web/20231001163525/https://www.problang.org/chapters/01-introduction.html |archive-date=October 1, 2023 |website=Probabilistic language understanding: An introduction to the Rational Speech Act framework}}</ref>

<math>\begin{align}
& 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 [\![ u ]\!](s) \cdot P(s)
\end{align}</math>