Game Theoretic Pragmatics Session 6: Neo … ImplicatureDivision of pragmatic labourLevinson’s 3 heuristics Game Theoretic Pragmatics Session 6: Neo-Gricean Pragmatics

Scalar Implicature Division of pragmatic labour Levinson’s 3 heuristics

Game Theoretic PragmaticsSession 6: Neo-Gricean Pragmatics

<1>

Roland Muhlenbernd, Michael Franke, Jason Quinley

Game Theoretic Pragmatics Session 6: Neo-Gricean Pragmatics <1>


Introduction

1. Status Quo: Basic knowledge of game theoretic toolsI to model language use (signaling games)I to analyse emerging phenomena (Solution concepts: Nash

Equilibrium, Iterated Strict Dominance, Rationalizability)

2. But now?I How do I know, how a model for a particular Implicature

should look like? (what kind of parameters?)I Which solution concept is appropriate for Implicatures?

3. Outstanding Work:I More formal concepts of Implicatures: Neo-Gricean PragmaticsI Solution concept with an adequate epistemic interpretation,

which at best gives the right results: IBR-Model



Table of Contents

Scalar Implicature

Division of pragmatic labour

Levinson’s 3 heuristics



Definition

A Scalar Implicature is a...

I ...Generalized Quantity Implicature based on the use of aninformationally weak term in an implication scale like〈all , some〉

I It’s use implicates that all similar utterances using aninformationally stronger term are not true, because thespeaker would use this more informative utterance(Q1: ”Make your contribution as informative as required.”)

Example:

A farmer says: ”Some horses jumped over the fence.” Accordingscalar Implicature you would derive the information, that not allhorses jumped over the fence.



Implication scale

An implicational scale is a set of lexical items that are

I of the same constituent category

I ordered in terms of their informativeness.

Examples

I 〈 all, most, some 〉I 〈 always, often, sometimes 〉I 〈 succeed in, try to, want to 〉I 〈 hot, warm 〉I 〈 certain, probable, possible 〉I 〈 n, ... 4, 3, 2, 1 〉



Definition

Formal Definition of Scalar Implicature:

Given an implication scale 〈e1, e2...en〉: If a speaker uses theutterance U(ei ), he implicit means¬U(ei−1) ∧ ¬U(ei−2) . . . ∧ ¬U(e1).

Example: 〈all , most, some〉U(some) = Some horses jumped over the fence.# ¬U(most) ∧ ¬U(all)

Questions:How does this account help us for choosing parameters for oursignaling game model? How does it help us for finding an adequatesolution concept?



Signaling game parameter 〈{S , R}, T , Pr , M, J·K, A, US , UR〉Model procedure:

I M corresponds to a given implication scale 〈e1, e2...en〉I T contains states te1 , te2¬e1 , . . . ten¬en−1...¬e1

I A substantially matches with T

I US,R(t, m, a) =

{> 0 if (t, a) is a match

0 else

Pr(t) a∀ a`¬∀ a∃¬`¬∀ mall mmost msome

t∀ 1/n 1,1 0,0 0,0√ √ √

t`¬∀ 1/2− 1/n 0,0 1,1 0,0 −√ √

t∃¬`¬∀ 1/2 0,0 0,0 1,1 − −√

Tabelle: Parameters of a signaling game for 〈all , most, some〉



Solution concept benchmarkLiteral production/interpretation strategy:

t∀

t`¬∀

t∃¬`¬∀

mall

mmost

msome

a∀

a`¬∀

a∃¬`¬∀

Pragmatic production/interpretation strategy:

t∀

t`¬∀

t∃¬`¬∀

mall

mmost

msome

a∀

a`¬∀

a∃¬`¬∀



”In order to understand how and why a language changes, the lin-guist must keep in mind two ever-present and antinomic factors:First, the requirements of communication, the need for the spea-ker to convey his message, and second, the principle of least effort,which makes him restrict his output of energy, both mental and phy-sical, to the minimum compatible with achieving his ends.” (Marinet1962)



Two basic and competing forces of linguistic realm

The force of unification (Speaker’s economy) is a direct leasteffort correlate, a drive toward simplification whichwould result in the evolution of exactly one totallyunmarked infinitely ambigous vocable.

The force of diversification (Auditor’s economy) is anantiambiguity principle leading toward theestablishment of as many different expressions asthere are messages to communicate.

”The two opposing economies are in extreme conflict.”(Zipf, 1949)



Horn’s two principles

Q-Principle: Make your contribution sufficient (Q1)Say as much as you can (given R-Principle)

R-Principle: Make your contribution necessary (Q2, R, M)Say no more than you must (given Q-Principle)



Q- vs. R-Principle

ts : Batman saved Gotham City.

1. ⇒ tp: It was possible for Batman to save Gotham City.

2. ⇒ ta: Batman was able to save Gotham City.

Q-Principle

mp: ”It was possible for Batman to save Gotham City!”# ¬ts : Batman didn’t save Gotham City.

R-Principle

ma: ”Batman was able to save Gotham City!”# ts : Batman saved Gotham City.



Tannen’s example

First exchange

Wife: Bob’s having a party. You wanna go?Husband: Okay.

Second exchange (later)

Wife: Are you sure you want to go?Husband: Okay. Let’s not go. I’m tired anyway.

Third exchange (post-mortem)

Wife: We didn’t go to the party because you didn’t want to.Husband: I wanted to. You didn’t want to.(Tannen, 1975)

Question: Who is right? OR What is the source of thismisunderstanding?





A unmarked message describes the prototypical case (R-Principle).A marked message excludes the prototypical case, thus describes arare case (Q-Principle).

Example

”Black Bart killed the sheriff.”# Murder in a prototypical way.(R)”Black Bart caused the sheriff to die.”# Murder in a non-prototypical way.(Q)



Signaling game parameter 〈{S , R}, T , Pr , M, J·K, A, US , UR , C 〉Model procedure:

I T = {tp, tr}, M = {mu, mm}, A = {ap, ar}I Prototypical case defined by Pr : Pr(tp) > Pr(tr )

I Introduce message cost function C : M → RI Marked message defined by C : C (mm) > C (mu)

I US(t, m, a) = TS(t, a)− C (m);

Pr(t) ap ar mu mm

tp 3/4 1,1 0,0√ √

tr 1/4 0,0 1,1√ √

.1 .2

Tabelle: Parameters of the game ’Division of pragmatic labour’



Solution concept benchmarkSome possible strategies:

Horn:

tp

tr

mu

mm

ap

ar

Anti-Horn:

tp

tr

mu

mm

ap

ar

Smolensky:

tp

tr

mu

mm

ap

ar

Nash Equilibria

RH RAH RS RAS

SH .875, 1 −.125, 0 .625, .75 .125, .25SAH −.175, 0 .825, 1 .575, .75 .075, .25SS .65, .75 .15, .25 .65, .75 .15, .25SAS .05, .25 .55, .75 .55, .75 .05, .25



Levinson’s Theory

I ”According to the standard line, there are just two levels to atheory of communication. A level of sentence meaning(grammar theory) and a level of speaker meaning (classicalpragmatics).”

I ”What is omit is a third layer, what we may call the level ofutterance meaning.”

I ”It is also at this level, naturally, that we can expect thesystematicity of inference that might be deeply interconnectedto linguistic structure and meaning...”(Levinson, 2000)



The 3 Heuristics

Utterance meaning is a result of Default-Interpretations appliedaccording 3 heuristics:

I Q-Heuristic: What isn’t said to be the case, isn’t the case.

I I-Heuristic: What is said in a simple (unmarked) wayrepresents a stereotypical situation.

I M-Heuristic: What is said in an abnormal (marked) wayrepresents an abnormal situation.

Corresponding terminologies:Levinson Q-Heuristic M-Heuristic I -Heuristic

Grice Q1-Implicature M1&M3-Implicature Q2-Implicature

Horn Q-Principle Q-Principle R-Principle



I-Heuristic

What is said in a simple (unmarked) way represents a stereotypicalsituation.

I What is communicated is more precise than what is said.

I Inference to the best interpretation.

I Restriction of a more general predicate to a stereotypicalinstance.

Examples

”The secretary smiled.” # The female secretary smiled.”John had a drink.” # John had an alcoholic drink.”I like to drink milk.” # I like to drink cows milk.



Signaling game parameter 〈{S , R}, T , Pr , M, J·K, A, US , UR , C 〉

Model procedure:

I T = {tc , tg}, M = {mm, mc , mg}, A = {ac , ag}I Prototypical case defined by Pr : Pr(tc) > Pr(tg )

I General predicate defined by C : C (mm) < C (mc) = C (mg )

Pr(t) ac ag mc mg mm

tc 3/4 1,1 0,0√

−√

tg 1/4 0,0 1,1 −√ √

.2 .2 .1

Tabelle: Parameters of the game ’I-Heuristic’



Solution concept benchmark

tc

tg

mc

mm

mg

ac

ag

tc

tg

mc

mm

mg

ac

ag

tc

tg

mc

mm

mg

ac

ag

tc

tg

mc

mm

mg

ac

ag

tc

tg

mc

mm

mg

ac

ag

tc

tg

mc

mm

mg

ac

ag

I all these strategies are distinguishingI all these strategies depict successful communicationI all these strategies are strict Nash EquilibriaI the first three strategies depict trustful sender behaviourI only one strategy depicts pragmatic language use



Homework:

I 3rd homework sheet (due June 9)

Next Session:

I IBR-Model Part 1

References:I Atlas, J. and S. Levinson (1981), It-clefts, informativeness, and logical form: radical pragmatics. In: Radical

pragmatics, pp 1-61, New York.

I Grice, P. (1975), Logic and conversation. In: Speech Acts, pp 41-58, New York: Academic Press.

I Horn, L. (1984), Toward a new taxonomy for pragmatic inference: Q-based and R-based implicature. InMeaning, form, and use in context: Linguistic appications, pp 11-42, Georgetown University Press.

I Levinson, S. (1983), Pragmatics. Cambridge University Press.

I Levinson, S. (2000), Presumptive Meaning. The MIT Press.


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Game Theoretic Pragmatics Session 6: Neo … ImplicatureDivision of pragmatic labourLevinson’s 3 heuristics Game Theoretic Pragmatics Session 6: Neo-Gricean Pragmatics