Natural Information and Conversational Implicatures

1
Natural Information and Conversational
Implicatures

• Anton Benz

2
Overview

• Conversational Implicatures
• Lewis (1969) on Language Meaning
• Lewisising Grice
• Applications

3
Conversational Implicatures

• The Standard Theory

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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

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Assumptions about Conversation

• Conversation is a cooperative effort.
• Each participant recognises in their 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.

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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.

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Problem We can exchange H and H and still get a
valid inference

1. B said that G but not that H.
2. H is relevant and G ? H ? G.
3. Hence if G ? H, then B should have said G ? H
   (Quantity).
4. Hence H cannot be true, and therefore H.

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Lewis (1969) on Language Meaning
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Lewis Conventions (1969)

• Lewis Goal Explain the conventionality of
  language meaning.
• Method Meaning is defined as a property of
  certain solutions to signalling games.
• Ultimately a reduction of meaning to a regularity
  in behaviour.

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Semantic Interpretation Game

• Communication poses a coordination problem for
  speaker and hearer.
• The speaker wants to communicate some meaning M.
  In order to communicate this he chooses a form F.
• The hearer interprets the form F by choosing a
  meaning M.
• Communication is successful if MM.

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Lewis Signalling Convention

• Let F be a set of forms and M a set of meanings.
• A strategy pair (S,H) with
• S M ? F and H F ? M
• is a signalling convention if
• H?S idM

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Meaning in Signalling Conventions

• Lewis (IV.4,1996) distinguishes between
• indicative signals
• imperative signals
• applied to semantic interpretation games
• a form F signals that M if S(M)F
• a form F signals to interpret it as H(F)

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• Two possibilities to define meaning.
• Coincide for signalling conventions in semantic
  interpretation games.
• Lewis defines truth conditions of signals F as
  S?1(F).

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Lewisising Gricean
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• Assumption speaker and hearer use language
  according to a semantic convention.
• Goal Explain how implicatures can emerge out of
  semantic language use.
• Non-reductionist perspective.

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Representation of Assumption

• Semantics defines interpretation of forms.
• Let F denote the semantic meaning.
• Hence, assumption H(F)F, i.e.
• H(F) is the semantic meaning of F
• F ? Lewis imperative signal.

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Idea of Explanation of Implicatures

1. Start with all signalling conventions (S,H) such
   that H(F) F.
2. Impose additional pragmatic constraints.
3. Implicature F gt ? is explained if for all
   remaining (S,H) S?1(F) ?

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Philosophical Motivation

• Grice distinguished between
• natural meaning
• non-natural meaning
• Communicated meaning is non-natural meaning.

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Example

• I show Mr. X a photograph of Mr. Y displaying
  undue familiarity to Mrs. X.
• I draw a picture of Mr. Y behaving in this manner
  and show it to Mr. X.
• The photograph naturally means that Mr. Y was
  unduly familiar to Mrs. X
• The picture non-naturally means that Mr. Y was
  unduly familiar to Mrs. X

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• Taking a photo of a scene necessarily entails
  that the scene is real.
• Every branch which contains a showing of a photo
  must contain a situation which is depicted by it.
  
• The showing of the photo means naturally that
  there was a situation where Mr. Y was unduly
  familiar with Mrs. X.
• The drawing of a picture does not imply that the
  depicted scene is real.

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Natural Information of Signals

• Let G be a semantic interpretation game.
• Let S be a set of strategy pairs (S,H).
• The we identify the natural information of a form
  F in G with respect to S with
• The set of all branches of G where the speaker
  chooses F.

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• Coincides with S?1(F) in case of semantic
  interpretation games.
• Generalises to arbitrary games which contain
  semantic interpretation games in embedded form.

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Applications
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Example 1 Scalar Implicature

• Some of the boys came to the party
• said at least two came
• implicated not all came

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Example 1 Scalar Implicature
The game defined by pure semantics
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Example 1 Scalar Implicature
The (pragmatically) restricted game
all
?
100
1 1
most
50 gt
50 gt
1 1
some
?
1 1
50 lt
In all branches that contain some the initial
situation is 50 lt
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1.3 Parikhs Explanation
??
4,5
some but not all
-4,-3
?
??
some
6,7
?
??
2,3
?
?
some
?'
-5,-4
??
silence
?
0,0
? gt ?'
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Example 2 Relevance Implicature

• H approaches the information desk at the city
  railway station.
• H I need a hotel. Where can I book one?
• S There is a tourist office in front of the
  building.
• implicated It is possible to book hotels at the
  tourist office.

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The general situation
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The situation where it is possible to book a
hotel at the tourist information, a place 2, and
a place 3.
1
go-to tourist office
s. a. search anywhere
0
s. a.
tourist office
1
go-to pl. 2
place 2
s. a.
0
1/2
place 3
go-to pl. 3
s. a.
0
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go-to t. o.
1st Step
1
tourist office
booking possible at tour. off.
place 2
go-to pl. 2
0
place 3
go-to pl. 3
1/2
go-to t. o.
-1
tourist office
booking not possible
place 2
go-to pl. 2
1
place 3
go-to pl. 3
1/2
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2nd Step
tourist office
booking possible at tour. off.
go-to t. o.
1
booking not possible
place 2
go-to pl. 2
1
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Example 3 Italian Newspaper

• Somewhere in the streets of Amsterdam
• H Where can I buy an Italian newspaper?
• S (A) At the station. / (B) At the palace.
• Not valid A gt ? B

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Situation where A?B holds true
1
go-to station
1
go-to palace
A B
1
go-to s
A
1
go-to p
B
1
go-to s
go-to p
1