On Status and Form of the Relevance Principle

1
On Status and Form of the Relevance Principle

• Anton Benz, ZAS Berlin
• Centre for General Linguistics, Typology and
  Universals Research

2
Overview

• Background Relevance and Conversational
  Implicatures
• Frameworks and Definitions of Relevance
• Relevance and Definitions of Implicatures
• Relevance and Calculability of Implicatures

3
Relevance and Conversational Implicatures
4
Communicated meaning

• Grice distinguishes between
• What is said.
• What is implicated.
• Some of the boys came to the party
• said at least two came
• implicated not all came

5
Assumptions about Conversation

• Conversation is a cooperative effort.
• Each participant recognises in the talk exchanges
  a common purpose.
• 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 Bs response Solve As problem
  of finding petrol for his car.

6
The Conversational Maxims(short, without Manner)

• 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.

7
The Conversational Maxims

• Be truthful (Quality) and say as much as you can
  (Quantity) as long as it is relevant (Relevance).

8
Relevance Scale Approach(Hirschberg, van Rooij)

• A theory about relevance implicatures is a
  relevance scale approach iff it defines or
  postulates a linear pre-order on propositions
  such that an utterance of proposition A
  implicates a proposition H iff A is less relevant
  than ? H

9
Examples

• Job Interview J interviews E
• J Do you speak Spanish?
• E I speak some Portugese.
• gt E doesnt speak Spanish.
• A in front of his obviously immobilised car.
• A I am out of petrol.
• B There is a garage around the corner. (G)
• gt The garage is open. (H)

10
An Explanation of the Out of Petrol Example

• 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.

11
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.

12
Guiding Questions

• What is the proper definition of relevance that
  makes the first but not the second inference
  valid?
• What is the status of this notion of relevance
  with respect to the other maxims?

13
Optimal Assertions
14
General Situation

• We consider situations where
• A person I, called inquirer, has to solve a
  decision problem ((O, P),A,u).
• A person E, called expert, provides I with
  information that helps to solve Is decision
  problem.
• PE represents Es expectations about O at the
  time when she answers.

15
The general situation
16
Game and Decision Theory

• Decision theory Concerned with decisions of
  individual agents
• Game theory Concerned with interdependent
  decisions of several agents.

17
Measures of Relevance I

• New information A is relevant if
• it leads to a different choice of action, and
• it is the more relevant the more it increases
  thereby expected utility.

18
Measures of Relevance I

• Let ((O, P),A,u) be a given decision problem.
• Let a be the action with maximal expected
  utility before learning A.
• Possible definition of Relevance of A
• (Sample Value of Information)

19
Measures of Relevance II

• New information A is relevant if
• it increases expected utility.
• it is the more relevant the more it increases it.

20
Measures of Relevance III

• New information A is relevant if
• it changes expected utility.
• it is the more relevant the more it changes it.

21

• Previous Result No decision theoretically
  defined relevance measure can account for choice
  of best answers. (Benz 2006)
• ? First Negative Result about Relevance.
• Is it possible to acount for Implicatures of
  answers ( assertions subordinated to a decision
  problem of the addressee)?

22
Implicatures and Relevance Scales

• Second Negative Result about Relevance

23
Relevance Scale Approach

• Let M be a set of propositions.
• Let ? be a linear well-founded pre-order on M
  with interpretation
• A ? B ? B is at least as relevant as A.
• then A gt B iff A lt B.

24
Lemma
25
(No Transcript)
26
An Example(Argentine wine)

• Somewhere in Berlin... Suppose J approaches the
  information desk at the entrance of a shopping
  centre.
• He wants to buy Argentine wine. He knows that
  staff at the information desk is very well
  trained and know exactly where you can buy which
  product in the centre.
• E, who serves at the information desk today,
  knows that there are two supermarkets selling
  Argentine wine, a Kaisers supermarket in the
  basement and an Edeka supermarket on the first
  floor.
• J I want to buy some Argentine wine. Where can I
  get it?
• E Hm, Argentine wine. Yes, there is a Kaisers
  supermarket downstairs in the basement at the
  other end of the centre.

27
Propositions
28

• No Relevance scale approach can explain this
  example.

29
Calculating Implicatures and Relevance

• Third Negative Result about Relevance

30
The Out of Patrol Example

• A stands in front of his obviously immobilised
  car.
• A I am out of petrol.
• B There is a garage around the corner. (G)
• gt The garage is open (H)

31
The correct explanation

• 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.

32

• Is there a relevance measure that makes the
  argument valid?

33

• The previous result shows that this is not
  possible if the relevance measure defines a
  linear pre-order on propositions.

34
The Posterior Sample Value of Information

• Let O(a) be the set of worlds where action a is
  optimal.
• If
• the speaker said that A
• it is common knowledge that ?a PE(O(a)) 1
• for all K ? H UVI(KA) gt 0,
• then H is true.
• Where UVI(KA) is the sample value of information
  posterior to learning A.
• UVI(KA) EUI(aA?KA?K) ? EUI(aAA?K)

35
Application to Out-of-Petrol Example

• Let K ? H the garage is closed
• A there is a garage round the corner
• We assume that the inquirer has a better
  alternative than going to a closed garage.
• It follows then that UVI(KA) gt 0, and our
  criterion predicts that
• H the garage is open
• is true.

36
Relevance and Answers

• Relevance
• is presumed to be maximised by the answering
  person.
• defines a linear pre-order on the set of possible
  answers.
• is definable from the receivers perspective.
• makes the standard explanation in the
  out-of-patrol example valid.

37
Relevance and Answers

• Relevance
• is presumed to be maximised by the answering
  person.
• defines a linear pre-order on a set of possible
  answers.
• is definable from the receivers perspective.
• makes the standard explanation in the
  out-of-patrol example valid.

38
Relevance and Conversational Maxim

• Conversational Maxim
• presumed to be followed by the speaker.
• Necessary for calculating appropriate answers and
  implicatures.
• The relevance measure defined by the posterior
  sample value of information does not define a
  conversational maxim.

39
THE END
40
Relevance and Best Answers
41
The Italian Newspaper Example

• Somewhere in the streets of Amsterdam...
• J Where can I buy an Italian newspaper?
• E At the station and at the Palace but nowhere
  else. (SE)
• E At the station. (A) / At the Palace. (B)

42
Answers

• (A) There are Italian newspapers at the station.
• (B) There are Italian newspapers at the Palace.
• With sample value of information Only B is
  relevant.
• With utility value A, B, and A?B are equally
  relevant.

43

• Assume now that E learned that
• (A) there are no Italian newspapers at the
  station.
• With sample value of information A is relevant.
• With utility value the uninformative answer is
  the most relevant answer.

44

• Need Uniform definition of relevance that
  explains all examples.

45
No relevance based approach can avoid non-optimal
answers.

• First Negative Result about Relevance

46
The Conversational Maxims

• Maxim of Quality
• Do not say what you believe to be false.
• Do not say that for which you lack adequate
  evidence.
• Maxim of Quantity
• Make your contribution to the conversation as
  informative as is required for he current talk
  exchange.
• Do not make your contribution to the conversation
  more informative than necessary.

47

• Maxim of Relevance
• Make your contributions relevant.
• Maxim of Manner
• Be perspicuous, and specifically
• Avoid obscurity.
• Avoid ambiguity.
• Be brief (avoid unnecessary wordiness).
• Be orderly.