CH

AP

TE

R17:

LOG

ICA

LF

OU

ND

ATIO

NS

An

Introductionto

MultiagentS

ystems

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

1O

verview

•T

heaim

isto

givean

overviewofthe

ways

thattheorists

conceptualiseagents,and

tosum

marise

some

ofthekey

developments

inagenttheory.

•B

eginby

answering

thequestion:

why

theory?

•D

iscussthe

variousdifferentattitudes

thatmay

beused

tocharacterise

agents.

•Introduce

some

problems

associatedw

ithform

alisingattitudes.

•Introduce

modallogic

asa

toolforreasoning

aboutattitudes,focussing

onknow

ledge/belief.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

1

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•D

iscussM

oore’stheory

ofability.

•Introduce

theC

ohen-Levesquetheory

ofintentionas

acase

studyin

agenttheory.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

2

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

2W

hyT

heory?

•F

ormalm

ethodshave

(arguably)had

littleim

pactofgeneralpractice

ofsoftware

development:

why

shouldthey

berelevantin

agentbasedsystem

s?

•T

heansw

eris

thatwe

needto

beable

togive

asem

anticsto

thearchitectures,languages,and

toolsthatw

euse

—literally,a

meaning.

•W

ithoutsucha

semantics,itis

neverclear

exactlyw

hatishappening,or

why

itworks.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

3

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•E

ndusers

(e.g.,programm

ers)need

neverread

orunderstand

thesesem

antics,butprogresscannotbe

made

inlanguage

developmentuntilthese

semantics

exist.

•In

agent-basedsystem

s,we

havea

bagofconcepts

andtools,w

hichare

intuitivelyeasy

tounderstand

(bym

eansofm

etaphorand

analogy),andhave

obviouspotential.

•B

utwe

needtheory

toreach

anykind

ofprofoundunderstanding

ofthesetools.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

4

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

3A

gents=

IntentionalSystem

s

•W

heredo

theoristsstartfrom

?

•T

henotion

ofanagentas

anintentionalsystem

...

•S

oagenttheorists

startwith

the(strong)

viewof

agentsas

intentionalsystems:

onew

hosesim

plestconsistentdescription

requiresthe

intentionalstance.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

5

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

4T

heoriesofA

ttitudes

•W

ew

anttobe

ableto

designand

buildcom

putersystem

sin

terms

of‘mentalistic’notions.

•B

eforew

ecan

dothis,w

eneed

toidentify

atractable

subsetoftheseattitudes,and

am

odelofhowthey

interacttogenerate

systembehaviour.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

6

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•S

ome

possibilities:

information

attitudes{

beliefknow

ledge

pro-attitudes

desireintentionobligationcom

mitm

entchoice...

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

7

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

5F

ormalising

Attitudes

•S

ohow

dow

eform

aliseattitudes?

•C

onsider...

Janinebelieves

Cronos

isfather

ofZeus.

•N

aivetranslation

intofirst-order

logic:

Bel(Janine,Father(Z

eus,Cronos))

•B

ut...

–the

secondargum

enttothe

Belpredicate

isa

formula

offirst-orderlogic,nota

term;

needto

beable

toapply

‘Bel’to

formulae;

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

8

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

–allow

sus

tosubstitute

terms

with

thesam

edenotation:

consider(Z

eus=

Jupiter)intentionalnotions

arereferentially

opaque.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

9

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•S

o,thereare

two

sortsofproblem

sto

beaddressed

indevelping

alogicalform

alismfor

intentionalnotions:

–a

syntacticone

(intentionalnotionsrefer

tosentences);and

–a

semantic

one(no

substitutionofequivalents).

•T

husany

formalism

canbe

characterizedin

terms

oftw

oattributes:

itslanguage

offormulation,and

semantic

model:

•Tw

ofundam

entalapproachesto

thesyntactic

problem:

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

10

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

–use

am

odallanguage,which

containsm

odaloperators ,w

hichare

appliedto

formulae;

–use

am

eta-language:a

first-orderlanguage

containingterm

sthatdenote

formulae

ofsome

otherobject-language.

•W

ew

illfocuson

modallanguages,and

inparticular,

normalm

odallogics,with

possiblew

orldssem

antics.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

11

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

6N

ormalM

odalLogicfor

Know

ledge

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

12

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•S

yntaxis

classicalpropositionallogic,plusan

operatorK

for‘know

sthat’.

Vocabulary:

Φ={p,q,r,...}

primitive

propositions∧,∨,¬,...

classicalconnectivesK

modalconnective

Syntax:

〈wff〉

::=any

mem

berof

Φ|¬〈w

ff〉|〈w

ff〉∨〈w

ff〉|

K〈w

ff〉

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

13

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•E

xample

formulae:

K(p∧

q)K

(p∧

Kq)

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

14

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•S

emantics

aretrickier.

The

ideais

thatanagent’s

beliefscan

becharacterized

asa

setof possiblew

orlds ,inthe

following

way.

•C

onsideran

agentplayinga

cardgam

esuch

aspoker,w

hopossessed

theace

ofspades.H

owcould

shededuce

whatcards

were

heldby

heropponents?

•F

irstcalculateallthe

variousw

aysthatthe

cardsin

thepack

couldpossibly

havebeen

distributedam

ongthe

variousplayers.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

15

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•T

hesystem

aticallyelim

inateallthose

configurationsw

hichare

notpossible,givenw

hatsheknow

s.(F

orexam

ple,anyconfiguration

inw

hichshe

didnot

possessthe

aceofspades

couldbe

rejected.)

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

16

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•E

achconfiguration

remaining

afterthis

isa

world;a

stateofaffairs

consideredpossible,given

whatshe

knows.

•S

omething

truein

allouragent’s

possibilitiesis

believedby

theagent.

For

example,in

allouragent’s

epistemic

alternatives,she

hasthe

aceofspades.

•Tw

oadvantages:

–rem

ainsneutralon

thecognitive

structureofagents;

–the

associatedm

athematicaltheory

isvery

nice!

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

17

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•To

formalise

allthis,letW

bea

setofworlds,and

letR⊆

W×

Wbe

abinary

relationon

W,characterising

whatw

orldsthe

agentconsiderspossible.

•F

orexam

ple,if(w,w

′)∈

R,then

iftheagentw

asactually

inw

orldw

,thenas

faras

itwas

concerned,itm

ightbein

world

w′.

•S

emantics

offormulae

aregiven

relativeto

worlds:

inparticular:Kφ

istrue

inw

orldw

iffφ

istrue

inallw

orldsw′such

that(w,w

′)∈

R.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

18

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•Tw

obasic

propertiesofthis

definition:

–the

following

axiomschem

ais

valid:K

(φ⇒

ψ)⇒

(Kφ⇒

Kψ

)

–ifφ

isvalid,then

Kφ

isvalid.

•T

husagent’s

knowledge

isclosed

underlogical

consequence :this

islogicalom

niscience.T

hisis

notadesirable

property!

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

19

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•T

hem

ostinterestingproperties

ofthislogic

turnoutto

bethose

relatingto

theproperties

we

canim

poseon

accessibilityrelation

R.

By

imposing

variousconstraints,w

eend

upgetting

outvariousaxiom

s;thereare

lotsofthese,butthe

mostim

portantare:TKφ⇒

φ

DKφ⇒

¬K¬φ

4Kφ⇒

KKφ

5¬

Kφ⇒

K¬

Kφ.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

20

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

Interpretingthe

Axiom

s

•A

xiomT

isthe

knowledge

axiom:

itsaysthatw

hatisknow

nis

true.

•A

xiomD

isthe

consistencyaxiom

:ifyou

knowφ

,youcan’talso

know¬φ

.

•A

xiom4

ispositive

introspection:ifyou

knowφ

,youknow

youknow

φ.

•A

xiom5

isnegative

introspection:you

areaw

areof

whatyou

don’tknow.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

21

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

System

sofK

nowledge

&B

elief

•W

ecan

(toa

certainextent)

pickand

choosew

hichaxiom

sw

ew

anttorepresentour

agents.

•A

llofthese(K

TD

45)constitute

thelogicalsystem

S5.

Often

chosenas

alogic

of idealisedknow

ledge.

•S

5w

ithoutTis

weak-S

5,orK

D45.

Often

chosenas

alogic

of idealisedbelief.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

22

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

7K

nowledge

&A

ction

•M

ost-studiedaspectofpracticalreasoning

agents:

interactionbetw

eenknow

ledgeand

action.

•M

oore’s1977

analysisis

best-known

inthis

area.

•F

ormaltools:

–a

modallogic

with

Kripke

semantics

+dynam

iclogic-style

representationfor

action;–

butshowed

howK

ripkesem

anticscould

beaxiom

atizedin

afirst-order

meta-language;

–m

odalformulae

thentranslated

tom

eta-languageusing

axiomatization;

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

23

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

–m

odaltheoremproving

reducesto

meta-language

theoremproving.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

24

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•M

ooreconsidered

2aspects

ofinteractionbetw

eenknow

ledgeand

action:

1.A

sa

resultofperforming

anaction,an

agentcangain

knowledge.

Agents

canperform

“test”actions,in

orderto

findthings

out.2.

Inorder

toperform

some

actions,anagentneeds

knowledge:

theseare

knowledge

pre-conditions.F

orexam

ple,inorder

toopen

asafe,itis

necessaryto

knowthe

combination.

•C

ulminated

indefn

ofability:w

hatitmeans

tobe

ableto

dobring

something

about.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

25

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•A

xiomatising

standardlogicalconnectives:

∀w.True(w

,d¬φe)⇔

¬True(w

,dφe)

∀w.True(w

,dφ

∧ψe)⇔

True(w,dφ

e)∧

True(w,dψ

e)

∀w.True(w

,dφ

∨ψe)⇔

True(w,dφ

e)∨

True(w,dψ

e)

∀w.True(w

,dφ

⇒ψe)⇔

True(w,dφ

e)⇒

True(w,dψ

e)

∀w.True(w

,dφ

⇔ψe)⇔

(True(w,dφ

e)⇔

True(w,dψ

e))

Here,

Trueis

am

eta-languagepredicate:

–1stargum

entisa

termdenoting

aw

orld;–

2ndargum

entaterm

denotingm

odallanguageform

ula.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

26

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

Fregequotes,

de,used

toquote

modallanguage

formula.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

27

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•A

xiomatizing

theknow

ledgeconnective:

basicpossible

world

semantics:

∀w·True(w

,d(K

nowφ) e)

⇔∀

w′·K

(w,w

′)⇒

True(w′,dφ

e)

Here,

Kis

am

eta-languagepredicate

usedto

representtheknow

ledgeaccessibility

relation.

•O

theraxiom

sadded

torepresentproperties

ofknow

ledge.R

eflexive:∀

w.K

(w,w

)

Transitive:∀

w,w

′,w′′·K

(w,w

′)∧

K(w

′,w′′)⇒

K(w,w

′′)

Euclidean:

∀w,w

′,w′′·K

(w,w

′)∧

K(w

′′,w′)⇒

K(w,w

′′)

Ensures

thatK

isequivalence

relation.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

28

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•N

oww

eneed

some

apparatusfor

representingactions.

•A

dda

meta-language

predicateR

(a,w,w

′)to

mean

thatw′is

aw

orldthatcould

resultfromperform

ingaction

ain

world

w.

•T

henintroduce

am

odaloperator(R

esaφ)

tom

eanthat after

actiona

isperform

ed,φ

willbe

true.

∀w.True(w

,d(R

esaφ) e)

⇔

∃w′·R

(a,w,w

′)∧∀

w′′·R

(a,w,w

′′)⇒

True(w′′,dφ

e)

–firstconjunctsays

theaction

ispossible;

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

29

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

–second

saysthata

neccesaryconsequence

ofperform

ingaction

isφ

.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

30

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•N

oww

ecan

defineability,via

modal

Can

operator.

∀w·True(w

,d(C

anφ) e)

⇔

∃a.True(w

,d(K

now

(Res

aφ)) e)

So

agentcanachieve

φifthere

existssom

eaction

a,such

thatagentknows

thattheresultofperform

inga

isφ

.

•N

otethe

way

ais

quantifiedw

.r.t.theK

now

modality.

Implies

agentknows

theidentity

oftheaction.

Has

a“definite

description”ofit.

(Terminology:

ais

quantifiedde

re.)

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

31

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•W

ecan

weaken

thedefinition,to

capturethe

casew

herean

agentperforms

anaction

tofind

outhowto

achievegoal.

∀w·True(w

,d(C

anφ) e)

⇔

∃a.True(w

,d(K

now

(Res

aφ)) e)

∨

∃a.True(w

,d(K

now

(Res

a(C

anφ))) e)

Acircular

definition?N

o,interpretasa

fixedpoint.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

32

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•C

ritiqueofM

oore’sform

aism:

1.Translating

modallanguage

intoa

first-orderone

andthen

theoremproving

infirst-order

languageis

inefficient.“H

ard-wired”

modaltheorem

proversw

illbem

oreefficient.

2.F

ormulae

resultingfrom

thetranslation

processare

complicated

andunintuitive.

Originalstructure

(andhence

sense)is

lost.3.

Moore’s

formalism

basedon

possiblew

orlds:falls

preyto

logicalomniscience.

Definition

ofabilityis

somew

hatvacuous.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

33

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•B

utprobablyfirstserious

attemptto

usetools

ofm

athematicallogic

(incl.modal&

dynamic

logic)to

bearon

rationalagency.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

34

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

8Intention

•W

ehave

oneaspectofan

agent,butknowledge/belief

alonedoes

notcompletely

characterisean

agents.

•W

eneed

asetofconnectives,for

talkingaboutan

agent’spro-attitudes

asw

ell.

•A

gentneedsto

achievea

rationalbalancebetw

eenits

attitudes:

–should

notbeover-com

mitted;

–should

notbeunder-com

mitted.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

35

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•H

ere,we

reviewone

attemptto

producea

coherentaccountofhow

thecom

ponentsofan

agent’scognitive

statehold

together:the

theoryofintention

developedby

Cohen

&Levesque.

•H

erew

em

eanintention

asin...

Itism

yintention

toprepare

my

slides.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

36

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

8.1W

hatisintention?

•Tw

osorts:

–presentdirected

∗attitude

toan

action∗

functioncausally

inproducing

behaviour.–

futuredirected

∗attitude

toa

proposition∗

serveto

coordinatefuture

activity.

•W

eare

hereconcerned

with

futuredirected

intentions.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

37

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

Follow

ingB

ratman

(1987)C

ohen-Levesqueidentify

sevenproperties

thatmustbe

satisfiedby

intention:

1.Intentionspose

problems

foragents,w

honeed

todeterm

inew

aysofachieving

them.

IfIhavean

intentiontoφ

,youw

ouldexpectm

eto

devoteresources

todeciding

howto

bringabout

φ.

2.Intentionsprovide

a‘filter’for

adoptingother

intentions,which

mustnotconflict.

IfIhavean

intentiontoφ

,youw

ouldexpectm

eto

adoptanintention

ψsuch

thatφ

andψ

arem

utuallyexclusive.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

38

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

3.Agents

trackthe

successoftheir

intentions,andare

inclinedto

tryagain

iftheirattem

ptsfail.

Ifanagent’s

firstattemptto

achieveφ

fails,thenall

otherthings

beingequal,itw

illtryan

alternativeplan

toachieve

φ.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

39

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

Inaddition...

•A

gentsbelieve

theirintentions

arepossible.

Thatis,they

believethere

isatleastsom

ew

aythat

theintentions

couldbe

broughtabout.(C

TL*

notation:E♦φ

).

•A

gentsdo

notbelievethey

willnotbring

abouttheirintentions.Itw

ouldnotbe

rationalofme

toadoptan

intentionto

φifIbelieved

φw

asnotpossible.

(CT

L*notation:

A¬φ

.)

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40

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•U

ndercertain

circumstances,agents

believethey

will

bringabouttheir

intentions.Itw

ouldnotnorm

allybe

rationalofme

tobelieve

thatIw

ouldbring

my

intentionsabout;intentions

canfail.

Moreover,itdoes

notmake

sensethatifIbelieve

φis

inevitable(C

TL*:

A♦φ

)thatIw

ouldadoptitas

anintention.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

41

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•A

gentsneed

notintendallthe

expectedside

effectsof

theirintentions.

IfIbelieveφ⇒

ψand

Iintendthat

φ,Ido

notnecessarily

intendψ

also.(Intentions

arenotclosed

underim

plication.)T

hislastproblem

isknow

nas

thedentistproblem

.I

may

believethatgoing

tothe

dentistinvolvespain,

andIm

ayalso

intendto

goto

thedentist—

butthisdoes

notimply

thatIintendto

sufferpain!

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

42

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•C

ohen-Levesqueuse

am

ulti-modallogic

with

thefollow

ingm

ajorconstructs:

(Belx

φ)

xbelieves

φ

(Goalx

φ)

xhas

goalofφ

(Hap

pen

sα

)action

αhappens

next(D

oneα

)action

αhas

justhappened•

Sem

anticsare

possiblew

orlds.

•E

achw

orldis

infinitelylong

linearsequence

ofstates.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

43

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•E

achagentallocated:

–beliefaccessibility

relation—

Bfor

everyagent/tim

epair,gives

asetofbelief

accessiblew

orlds;E

uclidean,serial,transitive—

givesbelieflogic

KD

45.–

goalaccessibilityrelation

—G

forevery

agent/time

pair,givesa

setofgoalaccessible

worlds.

Serial—

givesgoallogic

KD

.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

44

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•A

constraint:G⊆

B.

–G

ivesthe

following

inter-modalvalidity:

|=(B

eliφ)⇒

(Goali

φ)

–A

realismproperty

—agents

accepttheinevitable.

•A

notherconstraint:

|=(G

oali

φ)⇒

♦¬(G

oali

φ)

C&

Lclaim

thisassum

ptioncaptures

following

properties:

–agents

donotpersistw

ithgoals

forever;–

agentsdo

notindefinitelydefer

working

ongoals.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

45

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•A

ddin

some

operatorsfor

describingthe

structureof

eventsequencesα

;α′α

followed

byα′

α?

‘testaction’α

•A

lsoadd

some

operatorsoftem

porallogic,“”

(always),and

“♦”

(sometim

e)can

bedefined

asabbreviations,along

with

a“strict”

sometim

eoperator,

Later:

♦α

=̂∃

x·(H

appen

sx;α

?)α

=̂¬♦¬α

(Later

p)=̂

¬p∧

♦p

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

46

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•F

inally,atem

poralprecedenceoperator,

(Before

pq).

•F

irstmajor

derivedconstructis

apersistentgoal.

(P−

Goalx

p)=̂

(Goalx

(Later

p))∧

(Belx

¬p)

∧

Before

((Belx

p)∨

(Belx

¬p))

¬(G

oalx

(Later

p))

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

47

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•S

o,anagenthas

apersistentgoalof

pif:

1.Ithas

agoalthat

peventually

becomes

true,andbelieves

thatp

isnotcurrently

true.2.

Before

itdropsthe

goal,oneofthe

following

conditionsm

usthold:

–the

agentbelievesthe

goalhasbeen

satisfied;–

theagentbelieves

thegoalw

illneverbe

satisfied.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

48

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•N

ext,intention:

(Inten

dxα

)=̂

(P−

Goalx

[Done

x(B

elx(H

appen

sα

))?;α]

)

•S

o,anagenthas

anintention

todo

αif:

ithasa

persistentgoaltohave

believeditw

asaboutto

doα

,and

thendone

α.

•C

&L

discusshow

thisdefinition

satisfiesdesiderata

forintention.

•M

ainpoint:

avoidsever

comm

itment.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

49

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•A

daptationofdefinition

allows

forrelativised

intentions .E

xample:

Ihavean

intentionto

prepareslides

forthe

tutorial,relative

tothe

beliefthatIwillbe

paidfor

tutorial.IfI

evercom

eto

believethatIw

illnotbepaid,the

intentionevaporates...

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50

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•C

ritiqueofC

&L

theoryofintention

(Singh,1992):

–does

notcaptureand

adequatenotion

of“com

petence”;–

doesnotadequately

representintentionsto

docom

positeactions;

–requires

thatagentsknow

whatthey

areaboutto

do—

fullyelaborated

intentions;–

disallows

multiple

intentions.

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51

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

9S

emantics

forS

peechA

cts

•C

&L

usedtheir

theoryofintention

todevelop

atheory

ofseveralspeechacts.

•K

eyobservation:

illocutionaryacts

arecom

plexevent

types(cf.actions).

•C

&L

usetheir

dynamic

logic-styleform

alismfor

representingthese

actions.

•W

ew

illlookatrequest.

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52

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•F

irst,definealternating

belief.

(AltB

elnx

yp)

=̂(B

elx(B

ely(B

elx···(B

elx︸

︷︷

︸

ntim

es

p)···)

︸︷︷︸

ntim

es

•A

ndthe

relatedconceptofm

utualbelief.

(M−

Belx

yp)

=̂∀

n·(A

ltBeln

xy

p)

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

53

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•A

nattem

ptisdefined

asa

complex

actionexpression.

(Hence

theuse

ofcurlybrackets,to

distinguishfrom

predicateor

modaloperator.)

{Attem

pt

xe

pq}

=̂

(Belx

¬p)

∧(G

oalx

(Hap

pen

sx

e;p?))∧

(Inten

dx

e;q?)

?;e

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

54

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•In

English:

“An

attemptis

acom

plexaction

thatagentsperform

when

theydo

something

(e)desiring

tobring

aboutsome

effect(p)butw

ithintentto

produceatleastsom

eresult(q)”.

Here:

–p

representsultim

ategoalthatagentis

aiming

forby

doinge;

–proposition

qrepresents

whatittakes

toatleast

make

an“honesteffort”

toachieve

p.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

55

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•D

efinitionofhelpfulness

needed:

(Help

fulx

y)=̂

∀e·

[(B

elx(G

oaly

♦(Done

xe)))

∧¬

(Goalx

¬(D

one

xe))

]

⇒(G

oalx

♦(Done

xe))

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56

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•In

English:

“[C]onsider

anagent[x]to

behelpfulto

anotheragent[y]if,for

anyaction

[e]headopts

theother

agent’sgoalthathe

eventuallydo

thataction,w

heneversuch

agoalw

ouldnotconflictw

ithhis

own”.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

57

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•D

efinitionofrequests:

{Req

uest

spkraddr

eα}

=̂{Attem

pt

spkreφ

(M−

Beladdr

spkr(G

oalspkr

φ))

}

where

φis

♦(Done

addrα

)∧

(Inten

daddr

α[

(Goalspkr

♦(Done

addrα

))∧

(Help

fuladdr

spkr)

]

)

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

58

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•In

English:

Arequestis

anattem

ptonthe

partofspkr,by

doinge,to

bringabouta

statew

here,ideally,1)addr

intendsα

,(relativeto

thespkr

stillhavingthatgoal,and

addrstillbeing

helpfullyinclined

tospkr),and

2)addr

actuallyeventually

doesα

,oratleastbrings

aboutastate

where

addrbelieves

itism

utuallybelieved

thatitwants

theideal

situation.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

59

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•B

ythis

definition,thereis

noprim

itiverequestact:

“[A]speaker

isview

edas

havingperform

eda

requestifheexecutes

anysequence

ofactionsthatproduces

theneeded

effects”.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

60

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

10A

Theory

ofCooperation

•W

enow

move

onto

atheory

ofcooperation(or

more

precisely,cooperativeproblem

solving).

•T

histheory

draws

onw

orksuch

asC

&L’s

modelof

intention,andtheir

semantics

forspeech

acts.

•Ituses

connectivessuch

as‘intend’as

thebuilding

blocks.

•T

hetheory

intendsto

explainhow

anagentcan

startw

ithan

desire,andbe

moved

togetother

agentsinvolved

with

achievingthis

desire.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

61

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

11A

(nother)F

ormalFram

ework

•W

eform

aliseour

theoryby

expressingitin

aquantified

multi-m

odallogic.

–beliefs;

–goals;

–dynam

iclogic

styleaction

constructors;–

pathquantifiers

(branchingtim

e);–

groups(sets

ofagents)as

terms

inthe

language—

settheoreticm

echanismfor

reasoningabout

groups;–

actions(transitions

inbranching

time

structure)associated

with

agents.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

62

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•F

ormalsem

anticsin

thepaper!

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63

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

12T

heF

our-Stage

Model

1.Recognition.

CP

Sbegins

when

some

agentrecognisesthe

potentialforcooperative

action.M

ayhappen

becausean

agenthasa

goalthatitisunable

toachieve

inisolation,or

becausethe

agentprefers

assistance.

2.Teamform

ation.T

heagentthatrecognised

thepotentialfor

cooperativeaction

atstage(1)

solicitsassistance.

Ifteamform

ationsuccessful,then

itwillend

with

agroup

havinga

jointcomm

itmentto

collectiveaction.

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64

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

3.Plan

formation.

The

agentsattem

pttonegotiate

ajointplan

thattheybelieve

willachieve

thedesired

goal.

4.Teamaction.

The

newly

agreedplan

ofjointactionis

executedby

theagents,w

hichm

aintaina

close-knitrelationshipthroughout.

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65

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

12.1R

ecognition

•C

PS

typicallybegins

when

some

agentina

hasa

goal,andrecognises

thepotentialfor

cooperativeaction

with

respecttothatgoal.

•R

ecognitionm

ayoccur

forseveralreasons:

–T

heagentis

unableto

achieveits

goalinisolation,

dueto

alack

ofresources,butbelievesthat

cooperativeaction

canachieve

it.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

66

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

–A

nagentm

ayhave

theresources

toachieve

thegoal,butdoes

notwantto

usethem

.Itm

aybelieve

thatinw

orkingalone

onthis

particularproblem

,itwillclobber

oneofits

othergoals,or

itmay

believethata

cooperativesolution

willin

some

way

bebetter.

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67

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•F

ormally...

(Poten

tial−for

−Coop

iφ)=̂

(Goali

φ)∧

∃g·(B

eli(J−

Can

gφ))∧

¬(C

aniφ)∨

(Beli

∀α·(A

gtα

i)∧(A

chieves

αφ)⇒

(Goali

(Doesn

tα

)))

•N

ote:

–Can

isessentially

Moore’s;

–J−

Can

isa

generalizationofM

oore’s–

(Ach

ievesαφ)

isdynam

iclogic

[α]φ

;–

Doesn

tm

eansitdoesn’thappen

next.

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68

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

12.2Team

Form

ation

•H

avingidentified

thepotentialfor

cooperativeaction

with

respecttoone

ofitsgoals,a

rationalagentwill

solicitassistancefrom

some

groupofagents

thatitbelieves

canachieve

thegoal.

•Ifthe

agentissuccessful,then

itwillhave

broughtabouta

mentalstate

wherein

thegroup

hasa

jointcom

mitm

enttocollective

action.

•N

otethatagentcannotguarantee

thatitwillbe

successfulinform

inga

team;itcan

onlyattem

ptit.

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69

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•F

ormally...

(PreT

eamgφ

i)=̂

(M−

Belg

(J−

Can

gφ))∧

(J−

Com

mit

g(T

eamgφ

i)(G

oali

φ)...)

•N

otethat:

–Team

isdefined

inlater;

–J−

Com

mit

issim

ilarto

J−

P−

Goal.

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70

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•T

hem

ainassum

ptionconcerning

teamform

ationcan

nowbe

stated.

|=∀

i·(B

eli(P

oten

tial−for

−Coop

iφ))⇒

A♦∃

g·∃α·(H

appen

s{Attem

pt

iα

pq})

wherep

=̂(P

reTeam

gφ

i)q

=̂(M

−Belg

(Goali

φ)∧

(Beli

(J−

Can

gφ))).

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

71

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

12.3P

lanF

ormation

•Ifteam

formation

issuccessful,then

therew

illbea

groupofagents

with

ajointcom

mitm

enttocollective

action.

•B

utcollectiveaction

cannotbeginuntilthe

groupagree

onw

hattheyw

illactuallydo.

•H

encethe

nextstagein

theC

PS

process:plan

formation,w

hichinvolves

negotiation.

•U

nfortunately,negotiationis

extremely

complex

—w

esim

plyoffer

some

observationsaboutthe

weakest

conditionsunder

which

negotiationcan

besaid

tohave

occurred.

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72

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•N

otethatnegotiation

may

fail:the

collectivem

aysim

plybe

unableto

reachagreem

ent.

•In

thiscase,the

minim

umcondition

requiredfor

usto

beable

tosay

thatnegotiationoccurred

atallisthat at

leastoneagentproposed

acourse

ofactionthatit

believedw

ouldtake

thecollective

closerto

thegoal.

•Ifnegotiation

succeeds,we

expectateam

actionstage

tofollow

.

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

73

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•W

em

ightalsoassum

ethatagents

willattem

pttobring

abouttheirpreferences .

For

example,ifan

agenthasan

objectionto

some

plan,thenitw

illattemptto

preventthisplan

beingcarried

out.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

74

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

•T

hem

ainassum

ptionis

then:

|=(P

reTeam

gφ

i)⇒

A♦∃α·(H

appen

s{J−

Attem

pt

gα

pq})

where

p=̂

(M−

Know

g(T

eamgφ

i))q

=̂∃

j·∃α·(j∈

g)∧

(M−

Belg

(Belj

(Agtsα

g)∧

(Ach

ievesαφ))).

http://www.csc.liv.ac.uk/˜mjw/pubs/imas/

75

Chapter

17A

nIntroduction

toM

ultiagentS

ystems

2e

12.4Team

Action

•Team

actionsim

plyinvolves

theteam

jointlyintending

toachieve

thegoal.

•T

heform

alisationof

Team

issim

ple.

(Team

gφ

i)=̂∃α·(A

chieves

αφ)∧

(J−

Inten

dgα

(Goali

φ))

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76