Convention and Communication

Lewis - Convention

Convention vs. Communication

Convention• Problem of coordination• Agents• Equilibrium• Action

Communication• Signaling problem• Communicator and audience• Signal Plan• Signal

Signaling Problem

• A signaling problem is a situation S involving an agent called communicator and one or more agents called audience, such that it is true and it is common knowledge for the communicator and audience that:

Signaling Problem

• 1) Exactly one of several alternative states of affaires s1….sn holds. The communicator, but not the audience is in the good position to tell which one is it.

Signaling Problem

• 2) Each member of the audience can do any one of several actions r1…rn called responses. Everyone involved want the audience’s responses to depend in a certain way upon the state of affairs that holds. There is certain one-to-one function F from {s1} on {r1} such that everyone prefers that each member of the audience do F(s1) on condition that s1 holds, for each s1.

Signaling Problem

• 3) The communicator can do any one of several alternative actions σ1… σn called signals. The audience is in a good position to tell which one he does.

Cowboys vs. Indians

• Possible states of affairs:1) s1 – Cowboys are attacking from the west2) s2 – Cowboys are attacking from the east3) s3 – Cowboys are attacking from both sides

Cowboys vs. Indians

• Responses:1) r1 – Men are going on the west. Women are

going on the east.2) r2 – Men are going on the east. Women are

going on the west.3) r3 – 50% of men are going on the west and

50% of men are going on the east. Women are staing at tipi.

Cowboys vs. Indians

• Signals:1) σ 1 =2) σ 2 = 3) σ 3 =

Functions in communication

• Communicator’s function (Fc):From {s1…sn} on {σ1… σn}

Functions in communication

• Communicator’s function (Fc):From {s1…sn} on {σ1… σn}

• Audience’s function (Fa):From {σ1… σn} on {r1…rn}

Functions in communication

• Communicator’s function (Fc):From {s1…sn} on {σ1… σn}

• Audience’s function (Fa):From {σ1… σn} on {r1…rn}

<Fc, Fa> = System of signals

Signaling Convention

Signaling convention = any convention whereby members of population P, who are involved as communicators or audience in a certain signaling problem S do their respective contingency plan. If so convention exists we also call <Fc, Fa> a conventional signaling system.

Meanings of Signals

• σ1 is a conventional signal that s1 holds

Meanings of Signals

• σ1 is a conventional signal that s1 holds

• σ1 conventionaly means that s1 holds

Meanings of Signals

• σ1 is a conventional signal that s1 holds

• σ1 conventionaly means that s1 holds

• σ1 is a conventional signal to do r1

Meanings of Signals

• σ1 is a conventional signal that s1 holds

• σ1 conventionaly means that s1 holds

• σ1 is a conventional signal to do r1

• σ1 conventionaly means to do r1

Meanings of Signals

• Signal-that = indicative signal• Signal-to do = imperative signal

Meanings of Signals

• Fa’:• 1) If is observed, do whatever seems best on the

assumption that cowboys were observed attacking from the west

• 2) If are observed do whatever seems on assumption that cowboys were observed attacking from the east

• 3) If are observed do whatever seems on assumption that cowboys were observed attacking from both sides

Meanings of Signals

• Fc’:• 1) If it seems the best that Indians in villige do

r1 do• 2) If it seems the best that Indians in villige do

r2 do• 3) If it seems the best that Indians in villige do

r3 do

Meanings of Signals

• σ is indicative = σ means in <Fc, Fa> that s holds

Meanings of Signals

• σ is indicative = σ means in <Fc, Fa> that s holds

• σ is imperative = σ means in <Fc, Fa> to do r

Meanings of Signals

• Meaning of the signal-that is a state of affairs which is truly (according to system of signals <Fc, Fa>) described by the signal σ

Meanings of Signals

• Meaning of the signal-that is a state of affairs which is truly (according to system of signals <Fc, Fa>) described by the signal σ

• Meaning of the signal-to do is a response which (according to system of signals <Fc, Fa>) should be taken in virtue of signal σ. σ is true in an instance of S if almost every member of the audience does do r in that instance

Meanings of Signals

• If <Fc, Fa> is any signaling system with indicative or imperative signals, we can identify <Fc, Fa> by scpecifing three things:

• 1) set of signals, which is to be range of Fc and the domain of Fa

• 2) whether given signal is indicative or imperative

• 3) for every signal the state of affairs in which it is true

Meanings of Signals

• The domain of L is to be set of signals <Fc, Fa>• Given any signal σ, L is to assign it on

interpretation <μ, τ>• μ = mood• τ = truth condition

Summary

• 1) communication is based on convention• 2) three types of signals (indicative,

imperative, neutral)• 3) L might be interpreted as a language