ESSLLI Day3

Information about ESSLLI Day3

Published on September 28, 2007

Author: DC_Cloepatra

Source: authorstream.com

Content

Two Theories of Implicatures (Parikh, Jäger):  Two Theories of Implicatures (Parikh, Jäger) Day 3 – August, 9th Overview:  Overview Prashant Parikh: A disambiguation based approach Gerhard Jäger: A dynamic approach A disambiguation based approach :  A disambiguation based approach Prashant Parikh (2001) The Use of Language Repetition: The Standard Example:  Repetition: The Standard Example Every ten minutes a man gets mugged in New York. (A) Every ten minutes some man or other gets mugged in New York. (F) Every ten minutes a particular man gets mugged in New York. (F’) How to read the quantifiers in a)? Abbreviations:  Abbreviations : Meaning of `every ten minutes some man or other gets mugged in New York.’ ’: Meaning of `Every ten minutes a particular man gets mugged in New York.’ θ1: State where the speaker knows that . θ2: State where the speaker knows that ’. A Representation:  A Representation General Characteristics:  General Characteristics There is a form A that is ambiguous between meanings  and ’. There are more complex forms F, F’ which can only be interpreted as meaning  and ’. The speaker but not the hearer knows whether  (type θ1) or ’ (type θ2) is true. Slide8:  It is assumed that interlocutors agree on a Pareto Nash equilibria (S,H). The actual interpretation of a form is the meaning assigned to it by the hearer’s strategy H. Implicatures:  Implicatures Classification of Implicatures:  Classification of Implicatures Parikh (2001) distinguishes between: Type I implicatures: There exists a decision problem that is directly affected. Type II implicatures: An implicature adds to the information of the addressee without directly influencing any immediate choice of action. Examples of Type I implicatures:  Examples of Type I implicatures A stands in front of his obviously immobilised car. A: I am out of petrol. B: There is a garage around the corner. +>The garage is open and sells petrol. Assume that speaker S and hearer H have to attend a talk just after 4 p.m. S utters the sentence: S: It’s 4 p.m. (A) +> S and H should go for the talk. () A model for a type I implicature:  A model for a type I implicature The Example:  The Example Assume that speaker S and hearer H have to attend a talk just after 4 p.m. S utters the sentence: S: It’s 4 p.m. (A) +> S and H should go for the talk. () The possible worlds:  The possible worlds The set of possible worlds Ω has elements: s1: it is 4 p.m. and the speaker wants to communicate the implicature  that it is time to go for the talk. s2: it is 4 p.m. and the speaker wants to communicate only the literal content . The Speaker’s types:  The Speaker’s types Assumption: the speaker knows the actual world. Types: θ1= {s1}: speaker wants to communicate the implicature . θ2 = {s2}: speaker wants to communicate the literal meaning . Hearer’s expectations about speaker’s types:  Hearer’s expectations about speaker’s types Parikh’s model assumes that it is much more probable that the speaker wants to communicate the implicature . Example values: p(θ1) = 0.7 and p(θ2) = 0.3 The speaker’s action set:  The speaker’s action set The speaker chooses between the following forms: A  It’s 4 pm. ([A] = ) B  It’s 4 pm. Let’s go for the talk. ([B] = )   silence. The hearer’s action set:  The hearer’s action set The hearer interprets utterances by meanings. Parikh’s model assumes that an utterance can be interpreted by any meaning  which is stronger than its literal meaning . The Game Tree:  The Game Tree The Utility Functions:  The Utility Functions Parikh decomposes the utility functions into four additive parts: A utility measure that depends on the complexity of the form and processing effort. A utility measure that depends on the correctness of interpretation. A utility measure that depends on the value of information. A utility measure that depends on the intrinsic value of the implicated information. Utility Value of Information :  Utility Value of Information Derived from a decision problem. Hearer has to decide between: going to the talk stay Utility Value of Information :  Utility Value of Information Before learning ‘It’s 4 p.m.’: EU(leave) = 0.2×10 + 0.8×(-2) = 0.4 EU(not-leave) = 0.2×(-10) + 0.8×10 = 6 After learning ‘It’s 4 p.m.’(A), hence that it is time to leave: EU(leave|A) = 1×10 = 10 EU(not-leave|A) = 1×(-10) = -10 Utility value of learning ‘It’s 4 p.m.’ (A): UV(A) = EU(leave|A) - EU(not-leave) = 10 – 6 = 4 Other Utilities:  Other Utilities Intrinsic Value of Implicature: 5 Cost of misinterpretation -2 In addition, Parikh assumes that in case of miscommunication the utility value of information is lost (*) Various costs due to complexity and processing effort. Higher for speaker than hearer. The Game Tree:  The Game Tree Some Variations of the Payoffs:  Some Variations of the Payoffs -4 -5 -(4+5) without (*) minus utility value minus intr. val. of implic. minus both Result:  Result In all variations it turns out that the strategy pair (S,H) with S(θ1) = It’s 4 p.m., S(θ2) = silence, and H(It’s 4 p.m) = [It’s 4 p.m]  [Let’s go to the talk] is Pareto optimal. A Dynamic Approach :  A Dynamic Approach Gerhard Jäger (2006) Game dynamics connects semantics and pragmatics General:  General Jäger (2006) formulates a theory of implicatures in the framework of Best Response Dynamic (Hofbauer & Sigmund, 1998), which is a variation of evolutionary game theory. We will reformulate his theory using Cournot dynamics, a non–evolutionary and technically much simpler learning model. Overview:  Overview An Example: Scalar Implicatures The Model Other Implicatures An Example:  An Example Scalar Implicatures The Example:  The Example We consider the standard example: Some of the boys came to the party. +> Not all of the boys came to the party. Possible Worlds:  Possible Worlds Possible Forms and their Meanings:  Possible Forms and their Meanings Complexities:  Complexities F1, F2, and F3 are about equally complex. F4 is much more complex than the other forms. It is an essential assumption of the model that F4 is so complex that the speaker will rather be vague than using F4. The first Stage:  The first Stage Hearer’s strategy determined by semantics. Speaker is truthful, else the strategy is arbitrary. The second Stage:  The second Stage Hearer’s strategy unchanged. Speaker chooses best strategy given hearer’s strategy. The third Stage:  The third Stage Speaker’s strategy unchanged. Hearer chooses best strategy given speaker’s strategy. Result:  Result The third stage is stabile. Neither the speaker nor the hearer can improve the strategy. The form F1: `Some of the boys came to the party.’ is now interpreted as meaning that some but not all of them came. This explains the implicature. The Model:  The Model The Signalling Game:  The Signalling Game Ω = {w1,w2,w3} the set of possible worlds. Θ = {θ1,θ2,θ3} = {{w1},{w2},{w3}} the set of speaker’s types. (Speaker knows true state of the world) p(θi)=1/4: hearer’s expectation about types. A1 = {F1,F2,F3,F3} the speaker’s action set. A2 = (Ω) the hearer’s action set. (Speaker chooses a Form, hearer an interpretation) Slide41:  The payoff function divides in two additive parts: c(.): measures complexity of forms: c(F1) = c(F2) = c(F3) = 1; c(F4) = 3. inf(θ,M): measures informativity of information M  Ω relative to speaker’s type θ = {w}: Slide42:  The game is a game of pure coordination, i.e. speaker’s and hearer’s utilities coincide: Additional Constraints:  Additional Constraints It is assumed that the speaker cannot mislead the hearer; i.e. if the speaker knows that the hearer interprets F as M, then he can only use F if he knows that M is true, i.e. if θ  M. The Dynamics:  The Dynamics The dynamic model consists of a sequence of synchronic stages. Each synchronic stage is a strategy pair (Si,Hi), i = 1,…,n In the first stage (i=1), the hearer interprets forms by their (literal) semantic meaning. the speaker’s strategy is arbitrary. The Second Stage (S2,H2):  The Second Stage (S2,H2) The hearer’s strategy H2 is identical to H1. The speaker’s strategy S2 is a best response to H1: EU(S2,H2) = maxS EU(S,H2) with EU(S,H) = θΘ u(θ,S(θ),H(S(θ))) The Third Stage (S3,H3):  The Third Stage (S3,H3) The speaker’s strategy S3 is identical to S2. The hearer’s strategy H3 is a best response to S3: EU(S3,H3) = maxH EU(S3,H) Slide47:  This process is iterated until choosing best responses doesn’t improve strategies. The resulting strategy pair (S,H) must be a weak Nash equilibrium. Remark: Evolutionary Best Response would stop only if strong Nash equilibria are reached. Implicatures:  Implicatures An implicature F +>  is explained if in the final stable state H(F) = . Other Implicatures:  Other Implicatures I-Implicatures What is expressed simply is stereotypically exemplified.:  I-Implicatures What is expressed simply is stereotypically exemplified. John’s book is good. +> The book that John is reading or that he has written is good. A secretary called me in. +> A female secretary called me in. There is a road to the right. +> There is a hard-surfaced road to the right. An Example:  An Example There is a road to the right. w1: hard surfaced road. w2: soft surfaced road. F1: road F2: hard surfaced road F3: soft surfaced road The first Stage:  The first Stage Hearer’s strategy determined by semantics. Speaker is truthful, else the strategy is arbitrary. The second Stage:  The second Stage Hearer’s strategy unchanged. Speaker chooses best strategy given hearer’s strategy. The third Stage:  The third Stage Speaker’s strategy unchanged. Hearer chooses best strategy given speaker’s strategy. Any interpretation of F2 below yields a best response. M-implicatures What is said in an abnormal way isn’t normal.:  M-implicatures What is said in an abnormal way isn’t normal. Bill stopped the car. +> He used the foot brake. Bill caused the car to stop. +> He did it in an unexpected way. Sue smiled. +> Sue smiled in a regular way. Sue lifted the corners of her lips. +> Sue produced an artificial smile. An Example:  An Example Sue smiled. +> Sue smiled in a regular way. Sue lifted the corners of her lips. +> Sue produced an artificial smile. w1: Sue smiles genuinely. w2: Sue produces artificial smile. F1: to smile. F2: to lift the corners of the lips. The first Stage:  The first Stage Hearer’s strategy determined by semantics. Speaker is truthful, else the strategy is arbitrary. The second Stage:  The second Stage Hearer’s strategy unchanged. Speaker chooses best strategy given hearer’s strategy. The third Stage:  The third Stage Speaker’s strategy unchanged. Hearer chooses best strategy given speaker’s strategy. Any interpretation of F2 below yields a best response. The third Stage continued:  The third Stage continued There are three possibilities: A fourth Stage:  A fourth Stage Speaker’s optimisation can then lead to: A fifth Stage:  A fifth Stage Speaker’s optimisation can then lead to: Horn Anti-Horn

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