Natural Information
and Conversational
Implicatures
Anton Benz
Overview
Conversational Implicatures
 Lewis (1969) on Language Meaning
 Lewisising Grice
 Applications

Conversational
Implicatures
The Standard Theory
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

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 B’s response: Solve A’s
problem of finding petrol for his car.
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.
Problem: We can exchange H and
H* and still get a valid inference:
1.
2.
3.
4.
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*.
Lewis (1969) on
Language Meaning
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.

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 M=M’.
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 = id|M

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)
Two possibilities to define meaning.
 Coincide for signalling conventions in
semantic interpretation games.
 Lewis defines truth conditions of signals F
as S1(F).

Lewisising Gricean
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.
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.
Idea of Explanation of Implicatures
1.
2.
3.
Start with all signalling conventions (S,H)
such that H(F) = [F].
Impose additional pragmatic constraints.
Implicature F +>  is explained if for all
remaining (S,H): S1(F) |= 
Philosophical Motivation
Grice distinguished between
 natural meaning
 non-natural meaning
 Communicated meaning is non-natural
meaning.
Example
1.
2.


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

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.
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.
Coincides with S1(F) in case of semantic
interpretation games.
 Generalises to arbitrary games which
contain semantic interpretation games in
embedded form.

Applications
Example 1: Scalar Implicature
“Some of the boys came to the party”
said: at least two came
 implicated: not all came

Example 1: Scalar Implicature
The game defined by pure semantics

100%
50% >
50% <
“all”
“most”
50% >
“some”

1; 1
0; 0
0; 0
“most”
50% >
“some”

0; 0
“some”

1; 1
1; 1
Example 1: Scalar Implicature
The (pragmatically) restricted game
100%
“all”

1; 1
50% >
“most”
50% >
1; 1
50% <
“some”

In all branches that contain “some” the initial
situation is “50% < ”
1; 1
1.3 Parikh’s Explanation
¬
“some but
not all”
“some”
ρ'
silence
ρ > ρ'
-4,-3
¬
6,7

2,3
¬
-5,-4
“some”
ρ



¬
4,5
0,0
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.
The general situation
The situation where it is possible to book a hotel at the
tourist information, a place 2, and a place 3.
go-to tourist
office
1
s. a.
0
go-to pl. 2
“place 2”
1
“tourist
office”
“place 3”
s. a.
0
go-to pl. 3
1/2
s. a.
0
s. a. : search
anywhere
“tourist
office”
booking
possible at
tour. off.
go-to t. o.
“place 2” go-to pl. 2
“place 3”
go-to pl. 3
go-to t. o.
“tourist
office”
booking
not
possible
“place 2”
“place 3”
go-to pl. 2
go-to pl. 3
1st Step
1
0
1/2
-1
1
1/2
2nd Step
booking
possible at
tour. off.
booking
not
possible
“tourist
office”
go-to t. o.
“place 2”
go-to pl. 2
1
1
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 +>  B
Situation where AB holds true:
“A & B”
“A”
go-to station
1
go-to palace
1
go-to s
go-to p
“B”
go-to s
go-to p
1
1
1
1