Convention and Com m unication

1. Convention and Communication Lewis - Convention

2. Convention vs. Communication Convention Communication Signaling problem Communicator and audience Signal Plan Signal • Problem of coordination • Agents • Equilibrium • Action

3. Signaling Problem • A signaling problemis a situationSinvolvingan 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:

4. Signaling Problem • 1) Exactly one of several alternative states of affairess1….snholds. The communicator, but not the audience is in the good position to tell which one is it.

5. 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.

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

7. Cowboys vs. Indians • Possible states of affairs: • s1 – Cowboys are attacking from the west • s2 – Cowboys are attacking from the east • s3 – Cowboys are attacking from both sides

8. Cowboys vs. Indians • Responses: • r1 – Men aregoing onthe west. Womenare going onthe east. • r2 – Menare going onthe east. Womenare going onthe west. • r3 – 50% of menaregoing on thewestand 50% of men aregoing ontheeast. Womenare staing at tipi.

9. Cowboysvs. Indians • Signals: • σ 1 = • σ 2 = • σ 3 =

10. Functions in communication • Communicator’s function (Fc): From {s1…sn} on {σ1… σn}

11. Functionsincommunication • Communicator’s function (Fc): From {s1…sn} on {σ1… σn} • Audience’s function (Fa): From {σ1… σn} on {r1…rn}

12. Functionsincommunication • 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

13. 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.

14. Meanings of Signals • σ1is a conventionalsignalthat s1holds

15. Meanings of Signals • σ1is a conventionalsignalthat s1holds • σ1conventionalymeansthat s1holds

16. Meanings of Signals • σ1is a conventionalsignalthat s1holds • σ1conventionalymeansthat s1holds • σ1is a conventionalsignalto do r1

17. Meanings of Signals • σ1is a conventionalsignalthat s1holds • σ1conventionalymeansthat s1holds • σ1is a conventionalsignalto do r1 • σ1conventionalymeansto do r1

18. Meanings of Signals • Signal-that = indicativesignal • Signal-to do =imperativesignal

19. 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

20. Meanings of Signals • Fc’: • 1) Ifitseemsthe best that Indians in villige do r1do • 2) IfitseemsthebestthatIndiansinvilligedo r2do • 3) IfitseemsthebestthatIndiansinvilligedo r3do

21. Meanings of Signals • σisindicative = σmeansin <Fc, Fa> that s holds

22. Meanings of Signals • σisindicative = σmeansin <Fc, Fa> that s holds • σisimperative= σmeansin <Fc, Fa> to do r

23. Meanings of Signals • Meaning of thesignal-thatis a state of affairswhichistruly (according to system of signals <Fc, Fa>) described by thesignalσ

24. Meanings of Signals • Meaning of thesignal-thatis a state of affairswhichistruly (according to system of signals <Fc, Fa>) described by thesignalσ • Meaning of thesignal-to do is a responsewhich (according to system of signals <Fc, Fa>) should be takeninvirtue of signalσ. σistruein an instance of Sifalmosteverymember of theaudiencedoes do rinthatinstance

25. Meanings of Signals • If <Fc, Fa> isanysignaling system withindicativeorimperativesignals, we canidentify<Fc, Fa> by scpecifingthreethings: • 1) set of signals, whichis to be range of Fc and thedomain of Fa • 2) whethergivensignalisindicativeorimperative • 3) for everysignalthe state of affairsinwhichitistrue

26. Meanings of Signals • Thedomain of Lis to be set of signals <Fc, Fa> • Givenanysignalσ, Lis to assignit on interpretation <μ, τ> • μ = mood • τ = truthcondition

27. Summary • 1) communication is based on convention • 2) three types of signals (indicative, imperative, neutral) • 3) L might be interpreted as a language