Game Theory And Grice’ Theory Of Implicatures
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Game Theory And Grice’ Theory Of Implicatures

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Game Theory And Grice’ Theory Of Implicatures Game Theory And Grice’ Theory Of Implicatures Presentation Transcript

  • Game Theory and Grice’ Theory of Implicatures Anton Benz
  • Anton Benz: Game Theory and Grice’ Theory of Implicatures
    • Grice’ approach to pragmatics
        • Assumptions about communication
        • The Cooperative Principle and the Maxims
    • Scalar Implicatures
        • The `standard explanation’
        • A game theoretic reconstruction
    • Where can game theory improve pragmatic theory?
        • A problem for the standard theory: predictive power
        • An example of contradicting inferences
    • The game theoretic approach at work
        • Implicatures of answers
  • A simple picture of communication
    • The speaker encodes some proposition p
    • He sends it to an addressee
    • The addressee decodes it again and writes p in his knowledgebase.
    • Problem: We communicate often much more than we literally say!
      • Some students failed the exam.
      • +> Most of the students passed the exam.
  • Gricean Pragmatics
    • Grice distinguishes between:
    • What is said .
    • What is implicated .
      • “Some of the boys came to the party.”
        • said: At least two of the boys came to the party.
        • implicated: Not all of the boys came to the party.
    • Both part of what is communicated .
  • Assumptions about Conversation
    • Conversation is a cooperative effort . Each participant recognises in their talk exchanges a common purpose .
    • Example: A stands in front of his obviously immobilised car.
      • A: I am out of petrol.
      • B: There is a garage around the corner.
      • Joint purpose of B’s response : Solve A’s problem of finding petrol for his car.
  • The Cooperative Principle
    • Conversation is governed by a set of principles which spell out how rational agents behave in order to make language use efficient.
    • The most important is the so-called cooperative principle :
    • “Make your conversational contribution such as is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged.”
  • The Conversational Maxims
    • Maxim of Quality :
    • 1. Do not say what you believe to be false. 2. Do not say that for which you lack adequate evidence.
    • Maxim of Quantity :
    • 1. Make your contribution to the conversation as informative as is required for he current talk exchange. 2. Do not make your contribution to the conversation more informative than necessary.
    • Maxim of Relevance : make your contributions relevant.
    • Maxim of Manner : be perspicuous, and specifically:
    • 1. Avoid obscurity. 2. Avoid ambiguity. 3. Be brief (avoid unnecessary wordiness). 4. Be orderly.
  • The Conversational Maxims
    • Maxim of Quality : Be truthful.
    • Maxim of Quantity :
    • Say as much as you can.
    • Say no more than you must.
    • Maxim of Relevance : Be relevant.
  • The Conversational Maxims
    • Be truthful (Quality) and say as much as you can (Quantity) as long as it is relevant (Relevance).
  • An example: Scalar Implicatures
    • Let A(x)  “x of the boys came to the party”
    • It holds A(all)  A(some).
    • The speaker said A(some).
    • If all of the boys came, then A(all) would have been preferred (Maxim of Quantity).
    • The speaker didn’t say A(all), hence it cannot be the case that all came.
    • Therefore some but not all came to the party.
  • Game Theory
    • In a very general sense we can say that we play a game together with other people whenever we have to decide between several actions such that the decision depends on:
      • the choice of actions by others
      • our preferences over the ultimate results.
    • Whether or not an utterance is successful depends on
      • how it is taken up by its addressee
      • the overall purpose of the current conversation.
  • The Game Theoretic Version (For a scale with three elements: <all, most, some>) “ all” “ some” “ most” “ most” “ some” “ some” 100% 50% > 50% <     50% > 50% > 0; 0 1; 1 0; 0 0; 0 1; 1 1; 1
  • The Game Theoretic Version (Taking into account the speaker’s preferences) 100% 50% > 50% < “ all” “ some” “ most”   50% > 1; 1 1; 1 1; 1 In all branches that contain “some” the initial situation is “50% < ” Hence: “some” implicates “50% < ”
  • General Schema for explaining implicatures
    • Start out with a game defined by pure semantics.
    • Pragmatic principles define restrictions on this game.
    • Semantics + Pragmatic Principles explain an implicature of an utterance if the implicated proposition is true in all branches of the restricted game in which the utterance occurs.
  • An example of contradicting inferences I
    • Situation: A stands in front of his obviously immobilised car.
      • A: I am out of petrol.
      • B: There is a garage around the corner. (G)
      • Implicated: The garage is open. (H)
    • How should one formally account for the implicature?
    • Set H*:= The negation of H
    • B said that G but not that H*.
    • H* is relevant and G  H*  G.
    • Hence if G  H*, then B should have said G  H* (Quantity).
    • Hence H* cannot be true, and therefore H.
  • An example of contradicting inferences II
    • Problem: We can exchange H and H* and still get a valid inference:
    • B said that G but not that H.
    • H is relevant and G  H  G.
    • Hence if G  H, then B should have said G  H (Quantity).
    • Hence H cannot be true, and therefore H*.
    • Missing: Precise definitions of basic concepts like relevance .
  • The Utility of Answers
    • Questions and answers are often subordinated to a decision problem of the inquirer.
    • Example: Somewhere in Amsterdam
      • I: Where can I buy an Italian newspaper?
      • E: At the station and at the palace.
      • Decision problem of A: Where should I go to in order to buy an Italian newspaper.
  • The general situation
  • Decision Making
    • The Model:
    • Ω: a (countable) set of possible states of the world.
    • P I , P E : (discrete) probability measures representing the inquirer’s and the answering expert’s knowledge about the world.
    • A : a set of actions.
    • U I , U E : Payoff functions that represent the inquirer’s and expert’s preferences over final outcomes of the game.
    • Decision criterion: an agent chooses an action which maximises his expected utility :
    • EU(a) =  v  Ω P(w)  U(v,a)
  • An Example
    • John loves to dance to Salsa music and he loves to dance to Hip Hop but he can't stand it if a club mixes both styles. It is common knowledge that E knows always which kind of music plays at which place .
      • J: I want to dance tonight. Where can I go to?
      • E: Oh, tonight they play Hip Hop at the Roter Salon.
      • implicated: No Salsa at the Roter Salon.
  • A game tree for the situation where both Salsa and Hip Hop are playing both play at RS “ Salsa” 1 go-to RS stay home 0 1 go-to RS stay home 0 1 go-to RS stay home 0 “ both” “ Hip Hop” RS = Roter Salon
  • The tree after the first step of backward induction both Salsa Hip Hop “ both” “ Salsa” “ Hip Hop” “ Salsa” “ Hip Hop” stay home go-to RS go-to RS go-to RS go-to RS 1 0 0 2 2
  • The tree after the second step of backward induction both Salsa Hip Hop “ both” “ Salsa” “ Hip Hop” stay home go-to RS go-to RS 1 2 2 In all branches that contain “Salsa” the initial situation is such that only Salsa is playing at the Roter Salon. Hence: “Salsa” implicates that only Salsa is playing at Roter Salon
  • General method for calculating implicatures (informal)
    • Describe the utterance situation by a game (in extensive form, i.e. tree form).
        • The game tree shows:
      • Possible states of the world
      • Utterances the speaker can choose
      • Their interpretations as defined by semantics.
      • Preferences over outcomes (given by context)
    • Simplify tree by backward induction.
    • ‘Read off’ the implicature from the game tree that cannot be simplified anymore.
  • Another Example
    • J approaches the information desk at the city railway station.
      • J: I need a hotel. Where can I book one?
      • E: There is a tourist office in front of the building.
      • (E: *There is a hairdresser in front of the building.)
      • implicated: It is possible to book hotels at the tourist office.
  • The situation where it is possible to book a hotel at the tourist information, a place 2, and a place 3. “ place 2” 1 0 1 s. a. go-to tourist office 0 1/2 0 “ tourist office” “ place 3” go-to pl. 2 go-to pl. 3 s. a. s. a. s. a. : search anywhere
  • The game after the first step of backward induction booking possible at tour. off. 1 0 1/2 -1 1 1/2 booking not possible “ place 2” “ tourist office” “ place 3” “ place 2” “ tourist office” “ place 3” go-to t. o. go-to pl. 2 go-to pl. 3 go-to t. o. go-to pl. 2 go-to pl. 3
  • The game after the second step of backward induction booking possible at tour. off. 1 1 booking not possible “ tourist office” “ place 2” go-to t. o. go-to pl. 2
  • Conclusions
    • Advantages of using Game Theory:
    • provides an established framework for studying cooperative agents;
    • basic concepts of linguistic pragmatics can be defined precisely;
    • extra-linguistic context can easily be represented;
    • allows fine-grained predictions depending on context parameters.
  • Scalar implicatures: The standard explanation
    • The ‘Standard Explanation’ for a scale with two elements:
    • It holds p 1  p 2 but not p 2  p 1 .
    • There are two expression e 1 , e 2 of comparable complexity.
    • e 1 means p 1 and e 2 means p 2 .
    • The speaker said e 2 .
    • If p 1 is the case, then the use of e 1 is preferred (by 1. and Quantity).
    • The speaker didn’t say e 1 , hence p 1 is not the case.
    • Therefore p 2  ¬ p 1 is the case.
  • A Schema for Inferring Implicatures
    • S has said that p;
    • it is mutual knowledge that S and H play a certain (signalling) game G;
    • in order for S to say that p and be indeed playing G, it must be the case that q;
    • (hence) it is mutual knowledge that q must be the case if S utters p;
    • S has done nothing to stop H, the addressee, thinking that they play G;
    • therefore in saying that p S has implicated that q.