Hypotheses

Refinement

under

Topological

Communication

Constraints

Gauvain

Bourgne,

Gael

Hette,

Nicolas

Maudet,

and

Suzanne

Pinson

LAMSADE,

Univ.

Paris-Dauphine,

France

{bourgne,hette,maudet,pinson}@lamsade.dauphine.fr

ABSTRACT

We

investigate

the

properties

of

a

multiagent

system

where

each

(distributed)

agent

locally

perceives

its

environment.

Upon

perception

of

an

unexpected

event,

each

agent

locally

computes

its

favoured

hypothesis

and

tries

to

propagate

it

to

other

agents,

by

exchanging

hypotheses

and

supporting

arguments

(observations).

However,

we

further

assume

that

communication

opportunities

are

severely

constrained

and

change

dynamically.

In

this

paper,

we

mostly

investigate

the

convergence

of

such

systems

towards

global

consistency.

We

first

show

that

(for

a

wide

class

of

protocols

that

we

shall

define),

the

communication

constraints

induced

by

the

topology

will

not

prevent

the

convergence

of

the

system,

at

the

condition

that

the

system

dynamics

guarantees

that

no

agent

will

ever

be

isolated

forever,

and

that

agents

have

unlimited

time

for

computation

and

arguments

exchange.

As

this

assumption

cannot

be

made

in

most

situations

though,

we

then

set

up

an

experimental

framework

aiming

at

comparing

the

relative

efficiency

and

effectiveness

of

different

interaction

protocols

for

hypotheses

exchange.

We

study

a

critical

situation

involving

a

number

of

agents

aiming

at

escaping

from

a

burning

building.

The

results

reported

here

provide

some

insights

regarding

the

design

of

optimal

protocol

for

hypotheses

refinement

in

this

context.

Categories

and

Subject

Descriptors

[Artificial

Intelligence]:

Distributed

Artificial

Intelligence-Multiagent

systems

General

Terms

Theory,

Experimentation

INTRODUCTION

We

consider

a

multiagent

system

where

each

(distributed)

agent

locally

perceives

its

environment,

and

we

assume

that

some

unexpected

event

occurs

in

that

system.

If

each

agent

computes

only

locally

its

favoured

hypothesis,

it

is

only

natural

to

assume

that

agents

will

seek

to

coordinate

and

refine

their

hypotheses

by

confronting

their

observations

with

other

agents.

If,

in

addition,

the

communication

opportunities

are

severely

constrained

(for

instance,

agents

can

only

communicate

when

they

are

close

enough

to

some

other

agent),

and

dynamically

changing

(for

instance,

agents

may

change

their

locations),

it

becomes

crucial

to

carefully

design

protocols

that

will

allow

agents

to

converge

to

some

desired

state

of

global

consistency.

In

this

paper

we

exhibit

some

sufficient

conditions

on

the

system

dynamics

and

on

the

protocol/strategy

structures

that

allow

to

guarantee

that

property,

and

we

experimentally

study

some

contexts

where

(some

of)

these

assumptions

are

relaxed.

While

problems

of

diagnosis

are

among

the

venerable

classics

in

the

AI

tradition,

their

multiagent

counterparts

have

much

more

recently

attracted

some

attention.

Roos

and

colleagues

in

particular

study

a

situation

where

a

number

of

distributed

entities

try

to

come

up

with

a

satisfying

global

diagnosis

of

the

whole

system.

They

show

in

particular

that

the

number

of

messages

required

to

establish

this

global

diagnosis

is

bound

to

be

prohibitive,

unless

the

communication

is

enhanced

with

some

suitable

protocol.

However,

they

do

not

put

any

restrictions

on

agents"

communication

options,

and

do

not

assume

either

that

the

system

is

dynamic.

The

benefits

of

enhancing

communication

with

supporting

information

to

make

convergence

to

a

desired

global

state

of

a

system

more

efficient

has

often

been

put

forward

in

the

literature.

This

is

for

instance

one

of

the

main

idea

underlying

the

argumentation-based

negotiation

approach

where

the

desired

state

is

a

compromise

between

agents

with

conflicting

preferences.

Many

of

these

works

however

make

the

assumption

that

this

approach

is

beneficial

to

start

with,

and

study

the

technical

facets

of

the

problem

(or

instead

emphasize

other

advantages

of

using

argumentation).

Notable

exceptions

are

the

works

of

which

studied

in

contexts

different

from

ours

the

efficiency

of

argumentation.

The

rest

of

the

paper

is

as

follows.

Section

specifies

the

basic

elements

of

our

model,

and

Section

goes

on

to

presenting

the

different

protocols

and

strategies

used

by

the

agents

to

exchange

hypotheses

and

observations.

We

put

special

attention

at

clearly

emphasizing

the

conditions

on

the

system

dynamics

and

protocols/strategies

that

will

be

exploited

in

the

rest

of

the

paper.

Section

details

one

of

(RPS)

c

IFAAMAS

the

main

results

of

the

paper,

namely

the

fact

that

under

the

aforementioned

conditions,

the

constraints

that

we

put

on

the

topology

will

not

prevent

the

convergence

of

the

system

towards

global

consistency,

at

the

condition

that

no

agent

ever

gets

completely

lost

forever

in

the

system,

and

that

unlimited

time

is

allowed

for

computation

and

argument

exchange.

While

the

conditions

on

protocols

and

strategies

are

fairly

mild,

it

is

also

clear

that

these

system

requirements

look

much

more

problematic,

even

frankly

unrealistic

in

critical

situations

where

distributed

approaches

are

precisely

advocated.

To

get

a

clearer

picture

of

the

situation

induced

when

time

is

a

critical

factor,

we

have

set

up

an

experimental

framework

that

we

introduce

and

discuss

in

Section

The

critical

situation

involves

a

number

of

agents

aiming

at

escaping

from

a

burning

building.

The

results

reported

here

show

that

the

effectiveness

of

argument

exchange

crucially

depends

upon

the

nature

of

the

building,

and

provide

some

insights

regarding

the

design

of

optimal

protocol

for

hypotheses

refinement

in

this

context.

BASIC

NOTIONS

We

start

by

defining

the

basic

elements

of

our

system.

Environment

Let

O

be

the

(potentially

infinite)

set

of

possible

observations.

We

assume

the

sensors

of

our

agents

to

be

perfect,

hence

the

observations

to

be

certain.

Let

H

be

the

set

of

hypotheses,

uncertain

and

revisable.

Let

Cons(h,

O)

be

the

consistency

relation,

a

binary

relation

between

a

hypothesis

h

H

and

a

set

of

observations

O

O.

In

most

cases,

Cons

will

refer

to

classical

consistency

relation,

however,

we

may

overload

its

meaning

and

add

some

additional

properties

to

that

relation

(in

which

case

we

will

mention

it).

The

environment

may

include

some

dynamics,

and

change

over

the

course

of

time.

We

define

below

sequences

of

time

points

to

deal

with

it:

Definition

(Sequence

of

time

points).

A

sequence

of

time

points

tn

from

t

is

an

ordered

set

of

time

points

tn

such

that

t

and

∀i

n

ti.

Agent

We

take

a

system

populated

by

n

agents

an.

Each

agent

is

defined

as

a

tuple

F,

Oi,

hi

where:

F,

the

set

of

facts,

common

knowledge

to

all

agents.

Oi

the

set

of

observations

made

by

the

agent

so

far.

We

assume

a

perfect

memory,

hence

this

set

grows

monotonically.

hi

H,

the

favourite

hypothesis

of

the

agent.

A

key

notion

governing

the

formation

of

hypotheses

is

that

of

consistency,

defined

below:

Definition

(Consistency).

We

say

that:

An

agent

is

consistent

(Cons(ai))

iff

Cons(hi,

Oi)

(that

is,

its

hypothesis

is

consistent

with

its

observation

set).

An

agent

ai

consistent

with

a

partner

agent

aj

iff

Cons(ai)

and

Cons(hi,

Oj)

(that

is,

this

agent

is

consistent

and

its

hypothesis

can

explain

the

observation

set

of

the

other

agent).

Two

agents

ai

and

aj

are

mutually

consistent

(MCons(ai,

aj))

iff

Cons(ai,

aj)

and

Cons(aj,

ai).

A

system

is

consistent

iff

∀(i,

it

is

the

case

that

MCons(ai,

aj).

To

ensure

its

consistency,

each

agent

is

equipped

with

an

abstract

reasoning

machinery

that

we

shall

call

the

explanation

function

Eh.

This

(deterministic)

function

takes

a

set

of

observation

and

returns

a

single

prefered

hypothesis

H).

We

assume

h

Eh(O)

to

be

consistent

with

O

by

definition

of

Eh,

so

using

this

function

on

its

observation

set

to

determine

its

favourite

hypothesis

is

a

sure

way

for

the

agent

to

achieve

consistency.

Note

however

that

an

hypothesis

does

not

need

to

be

generated

by

Eh

to

be

consistent

with

an

observation

set.

As

a

concrete

example

of

such

a

function,

and

one

of

the

main

inspiration

of

this

work,

one

can

cite

the

Theorist

reasoning

system

-as

long

as

it

is

coupled

with

a

filter

selecting

a

single

prefered

theory

among

the

ones

initially

selected

by

Theorist.

Note

also

that

hi

may

only

be

modified

as

a

consequence

of

the

application

Eh.

We

refer

to

this

as

the

autonomy

of

the

agent:

no

other

agent

can

directly

impose

a

given

hypothesis

to

an

agent.

As

a

consequence,

only

a

new

observation

(being

it

a

new

perception,

or

an

observation

communicated

by

a

fellow

agent)

can

result

in

a

modification

of

its

prefered

hypothesis

hi

(but

not

necessarily

of

course).

We

finally

define

a

property

of

the

system

that

we

shall

use

in

the

rest

of

the

paper:

Definition

(Bounded

Perceptions).

A

system

involves

a

bounded

perception

for

agents

iff

s.t.

∀t|

∪N

Oi|

(That

is,

the

number

of

observations

to

be

made

by

the

agents

in

the

system

is

not

infinite.)

Agent

Cycle

Now

we

need

to

see

how

these

agents

will

evolve

and

interact

in

their

environment.

In

our

context,

agents

evolve

in

a

dynamic

environment,

and

we

classicaly

assume

the

following

system

cycle:

Environment

dynamics:

the

environment

evolves

according

to

the

defined

rules

of

the

system

dynamics.

Perception

step

agents

get

perceptions

from

the

environment.

These

perceptions

are

typically

partial

(e.g.

the

agent

can

only

see

a

portion

of

a

map).

Reasoning

step:

agents

compare

perception

with

predictions,

seek

explanations

for

(potential)

difference(s),

refine

their

hypothesis,

draw

new

conclusions.

Communication

step:

agents

can

communicate

hypotheses

and

observations

with

other

agents

through

a

defined

protocol.

Any

agent

can

only

be

involved

in

one

communication

with

another

agent

by

step.

Action

step:

agents

do

some

practical

reasoning

using

the

models

obtained

from

the

previous

steps

and

select

an

action.

They

can

then

modify

the

environment

by

executing

it.

The

communication

of

the

agents

will

be

further

constrained

by

topological

consideration.

At

a

given

time,

an

agent

will

only

be

able

to

communicate

with

a

number

of

neighbours.

Its

connexions

with

these

others

agents

may

The

Sixth

Intl.

Joint

Conf.

on

Autonomous

Agents

and

Multi-Agent

Systems

(AAMAS

evolve

with

its

situation

in

the

environment.

Typically,

an

agent

can

only

communicate

with

agents

that

it

can

sense,

but

one

could

imagine

evolving

topological

constraints

on

communication

based

on

a

network

of

communications

between

agents

where

the

links

are

not

always

active.

Communication

In

our

system,

agents

will

be

able

to

communicate

with

each

other.

However,

due

to

the

aforementionned

topological

constraints,

they

will

not

be

able

to

communicate

with

any

agents

at

anytime.

Who

an

agent

can

communicate

with

will

be

defined

dynamically

(for

instance,

this

can

be

a

consequence

of

the

agents

being

close

enough

to

get

in

touch).

We

will

abstractly

denote

by

C(ai,

aj,

t)

the

communication

property,

in

other

words,

the

fact

that

agents

ai

and

aj

can

communicate

at

time

t

(note

that

this

relation

is

assumed

to

be

symetric,

but

of

course

not

transitive).

We

are

now

in

a

position

to

define

two

essential

properties

of

our

system.

Definition

(Temporal

Path).

There

exists

a

temporal

communication

path

at

horizon

tf

(noted

Ltf

(aI

aJ

between

ai

and

aj

iff

there

exists

a

sequence

of

time

points

tn

from

tf

and

a

sequence

of

agents

kn

s.t.

(i)

C(aI

(ii)

C(akn

aJ

(iii)

∀i

n],

C(aki

ti)

Intuitively,

what

this

property

says

is

that

it

is

possible

to

find

a

temporal

path

in

the

future

that

would

allow

to

link

agent

ai

and

aj

via

a

sequence

of

intermediary

agents.

Note

that

the

time

points

are

not

necessarily

successive,

and

that

the

sequence

of

agents

may

involve

the

same

agents

several

times.

Definition

(Temporal

Connexity).

A

system

is

temporaly

connex

iff

∀t

∀(i,

Lt(ai,

aj)

In

short,

a

temporaly

connex

system

guarantees

that

any

agent

will

be

able

to

communicate

with

any

other

agents,

no

matter

how

long

it

might

take

to

do

so,

at

any

time.

To

put

it

another

way,

it

is

never

the

case

that

an

agent

will

be

isolated

for

ever

from

another

agent

of

the

system.

We

will

next

discuss

the

detail

of

how

communication

concretely

takes

place

in

our

system.

Remember

that

in

this

paper,

we

only

consider

the

case

of

bilateral

exchanges

(an

agent

can

only

speak

to

a

single

other

agent),

and

that

we

also

assume

that

any

agent

can

only

engage

in

a

single

exchange

in

a

given

round.

PROTOCOLS

AND

STRATEGIES

In

this

section,

we

discuss

the

requirements

of

the

interaction

protocols

that

govern

the

exchange

of

messages

between

agents,

and

provide

some

example

instantiation

of

such

protocols.

To

clarify

the

presentation,

we

distinguish

two

levels:

the

local

level,

which

is

concerned

with

the

regulation

of

bilateral

exchanges;

and

the

global

level,which

essentially

regulates

the

way

agents

can

actually

engage

into

a

conversation.

At

each

level,

we

separate

what

is

specified

by

the

protocol,

and

what

is

left

to

agents"

strategies.

Local

Protocol

and

Strategies

We

start

by

inspecting

local

protocols

and

strategies

that

will

regulate

the

communication

between

the

agents

of

the

system.

As

we

limit

ourselves

to

bilateral

communication,

these

protocols

will

simply

involve

two

agents.

Such

protocol

will

have

to

meet

one

basic

requirement

to

be

satisfying.

consistency

(CONS)-

a

local

protocol

has

to

guarantee

the

mutual

consistency

of

agents

upon

termination

(which

implies

termination

of

course).

Figure

A

Hypotheses

Exchange

Protocol

One

example

such

protocol

is

the

protocol

described

in

that

is

pictured

in

Fig.

To

further

illustrate

how

such

protocol

can

be

used

by

agents,

we

give

some

details

on

a

possible

strategy:

upon

receiving

a

hypothesis

or

from

agent

is

in

state

and

has

the

following

possible

replies:

counterexample

(if

the

agent

knows

an

example

contradicting

the

hypothesis,

or

not

explained

by

this

hypothesis),

challenge

(if

the

agents

lacks

evidence

to

accept

this

hypothesis),

counterpropose

(if

the

agent

agrees

with

the

hypothesis

but

prefers

another

one),

or

accept

(if

it

is

indeed

as

good

as

its

favourite

hypothesis).

This

strategy

guarantees,

among

other

properties,

the

eventual

mutual

logical

consistency

of

the

involved

agents

Global

Protocol

The

global

protocol

regulates

the

way

bilateral

exchanges

will

be

initiated

between

agents.

At

each

turn,

agents

will

concurrently

send

one

weighted

request

to

communicate

to

other

agents.

This

weight

is

a

value

measuring

the

agent"s

willingness

to

converse

with

the

targeted

agent

(in

practice,

this

can

be

based

on

different

heuristics,

but

we

shall

make

some

assumptions

on

agents"

strategies,

see

below).

Sending

such

a

request

is

a

kind

of

conditional

commitment

for

the

agent.

An

agent

sending

a

weighted

request

commits

to

engage

in

conversation

with

the

target

if

he

does

not

receive

and

accept

himself

another

request.

Once

all

request

have

been

received,

each

agent

replies

with

either

an

acccept

or

a

reject.

By

answering

with

an

accept,

an

agent

makes

a

full

commitment

to

engage

in

conversation

with

the

sender.

Therefore,

it

can

only

send

one

accept

in

a

given

round,

as

an

agent

can

only

participate

in

one

conversation

per

time

step.

When

all

response

have

been

received,

each

agent

receiving

an

accept

can

either

initiate

a

conversation

using

the

local

protocol

or

send

a

cancel

if

it

has

accepted

another

request.

At

the

end

of

all

the

bilateral

exchanges,

the

agents

engaged

in

conversation

are

discarded

from

the

protocol.

Then

each

of

the

remaining

agents

resends

a

request

and

the

process

iterates

until

no

more

requests

are

sent.

Global

Strategy

We

now

define

four

requirements

for

the

strategies

used

by

agents,

depending

on

their

role

in

the

protocol:

two

are

concerned

with

the

requestee

role

(how

to

decide

who

the

The

Sixth

Intl.

Joint

Conf.

on

Autonomous

Agents

and

Multi-Agent

Systems

(AAMAS

agent

wishes

to

communicate

with?),

the

other

two

with

the

responder

role

(how

to

decide

which

communication

request

to

accept

or

not?).

Willingness

to

solve

inconsistancies

(SOLVE)-agents

want

to

communicate

with

any

other

agents

unless

they

know

they

are

mutually

consistent.

Focus

on

solving

inconsistencies

(FOCUS)-agents

do

not

request

communication

with

an

agent

with

whom

they

know

they

are

mutually

consistent.

Willingness

to

communicate

(COMM)-agents

cannot

refuse

a

weighted

communication

request,

unless

they

have

just

received

or

send

a

request

with

a

greater

weight.

Commitment

to

communication

request

(REQU)agents

cannot

accept

a

weighted

communication

request

if

they

have

themselves

sent

a

communication

request

with

a

greater

weight.

Therefore,

they

will

not

cancel

their

request

unless

they

have

received

a

communicational

request

with

greater

weight.

Now

the

protocol

structure,

together

with

the

properties

COMM+REQU,

ensure

that

a

request

can

only

be

rejected

if

its

target

agent

engages

in

communication

with

another

agent.

Suppose

indeed

that

agent

ai

wants

to

communicate

with

aj

by

sending

a

request

with

weight

w.

COMM

guarantees

that

an

agent

receiving

a

weighted

request

will

either

accept

this

communication,

accept

a

communication

with

a

greater

weight

or

wait

for

the

answer

to

a

request

with

a

greater

weight.

This

ensures

that

the

request

with

maximal

weight

will

be

accepted

and

not

cancelled

(as

REQU

ensures

that

an

agent

sending

a

request

can

only

cancel

it

if

he

accepts

another

request

with

greater

weight).

Therefore

at

least

two

agents

will

engage

in

conversation

per

round

of

the

global

protocol.

As

the

protocol

ensures

that

ai

can

resend

its

request

while

aj

is

not

engaged

in

a

conversation,

there

will

be

a

turn

in

which

aj

must

engage

in

a

conversation,

either

with

ai

or

another

agent.

These

requirements

concern

request

sending

and

acceptation,

but

agents

also

need

some

strategy

of

weight

attribution.

We

describe

below

an

altruist

strategy,

used

in

our

experiments.

Being

cooperative,

an

agent

may

want

to

know

more

of

the

communication

wishes

of

other

agents

in

order

to

improve

the

overall

allocation

of

exchanges

to

agents.

A

context

request

step

is

then

added

to

the

global

protocol.

Before

sending

their

chosen

weighted

request,

agents

attribute

a

weight

to

all

agents

they

are

prepared

to

communicate

with,

according

to

some

internal

factors.

In

the

simplest

case,

this

weight

will

be

for

all

agent

with

whom

the

agent

is

not

sure

of

being

mutually

consistent

(ensuring

SOLVE),

other

agent

being

not

considered

for

communication

(ensuring

FOCUS).

The

agent

then

sends

a

context

request

to

all

agents

with

whom

communication

is

considered.

This

request

also

provides

information

about

the

sender

(list

of

considered

communications

along

with

their

weight).

After

reception

of

all

the

context

requests,

agents

will

either

reply

with

a

deny,

iff

they

are

already

engaged

in

a

conversation

(in

which

case,

the

requesting

agent

will

not

consider

communication

with

them

anymore

in

this

turn),

or

an

inform

giving

the

requester

information

about

the

requests

it

has

sent

and

received.

When

all

replies

have

been

received,

each

agent

can

calculate

the

weight

of

all

requests

concerning

it.

It

does

so

by

substracting

from

the

weight

of

its

request

the

weight

of

all

requests

concerning

either

it

or

its

target

(that

is,

the

final

weight

of

the

request

from

ai

to

aj

is

Wi,j

wi,j

+wj,i

P

k∈R(i)−{j}

wi,k

P

k∈S(i)−{j}

wk,i

P

k∈R(j)−{i}

wj,k

P

k∈S(j)−{i}

wk,j)

where

wi,j

is

the

weight

of

the

request

of

ai

to

aj,

R(i)

is

the

set

of

indice

of

agents

having

received

a

request

from

ai

and

S(i)

is

the

set

of

indice

of

agents

having

send

a

request

to

ai).

It

then

finally

sends

a

weighted

request

to

the

agents

who

maximise

this

weight

(or

wait

for

a

request)

as

described

in

the

global

protocol.

(CONDITIONAL)

CONVERGENCE

TO

GLOBAL

CONSISTENCY

In

this

section

we

will

show

that

the

requirements

regarding

protocols

and

strategies

just

discussed

will

be

sufficient

to

ensure

that

the

system

will

eventually

converge

towards

global

consistency,

under

some

conditions.

We

first

show

that,

if

two

agents

are

not

mutually

consistent

at

some

time,

then

there

will

be

necessarily

a

time

in

the

future

such

that

an

agent

will

learn

a

new

observation,

being

it

because

it

is

new

for

the

system,

or

by

learning

it

from

another

agent.

Lemma

Let

S

be

a

system

populated

by

n

agents

an,

temporaly

connex,

and

involving

bounded

perceptions

for

these

agents.

Let

be

the

sum

of

cardinalities

of

the

intersection

of

pairwise

observation

sets.

P

|Oi

Oj|)

Let

be

the

cardinality

of

the

union

of

all

agents"

observations

sets.

∪N

Oi|).

If

¬MCons(ai,

aj)

at

time

there

is

necessarily

a

time

t

s.t.

either

or

will

increase.

Proof.

Suppose

that

there

exist

a

time

and

indices

(i,

j)

s.t.

¬MCons(ai,

aj).

We

will

use

P

εComm(ak,

al,

where

εComm(ak,

al,

if

ak

and

al

have

communicated

at

least

once

since

and

otherwise.

Temporal

connexity

guarantees

that

there

exist

and

km

s.t.

C(ai,

C(akm

aj,

and

∀p

m],

C(akp

tp).

Clearly,

if

MCons(ai,

MCons(akm

aj)

and

∀p,

MCons(akp

we

have

MCons(ai,

aj)

which

contradicts

our

hypothesis

(MCons

being

transitive,

MCons(ai,

implies

that

MCons(ai,

and

so

on

till

MCons(ai,

akm

MCons(akm

aj)

which

implies

MCons(ai,

aj)

At

least

two

agents

are

then

necessarily

inconsistent

(¬MCons(ai,

or

¬MCons(akm

aj),

or

t.q.

Let

ak

and

al

be

these

two

neighbours

at

a

time

t

The

SOLVE

property

ensures

that

either

ak

or

al

will

send

a

communication

request

to

the

other

agent

at

time

t

As

shown

before,

this

in

turn

ensures

that

at

least

one

of

these

agents

will

be

involved

in

a

communication.

Then

there

are

two

possibilities:

(case

i)

ak

and

al

communicate

at

time

t

In

this

case,

we

know

that

¬MCons(ak,

al).

This

and

the

CONS

property

ensures

that

at

least

one

of

the

agents

must

change

its

Strictly

speaking,

the

transitivity

of

MCons

only

ensure

that

ak

and

al

are

inconsistent

at

a

time

t

that

can

be

different

from

the

time

t

at

which

they

can

communicate.

But

if

they

become

consistent

between

t

and

t

(or

inconsistent

between

t

and

t

it

means

that

at

least

one

of

them

have

changed

its

hypothesis

between

t

and

t

that

is,

after

We

can

then

apply

the

reasoning

of

case

iib.

The

Sixth

Intl.

Joint

Conf.

on

Autonomous

Agents

and

Multi-Agent

Systems

(AAMAS

hypothesis,

which

in

turn,

since

agents

are

autonomous,

implies

at

least

one

exchange

of

observation.

But

then

|Ok

∩Ol|

is

bound

to

increase:

(case

ii)

ak

communicates

with

ap

at

time

t

We

then

have

again

two

possibilities:

(case

iia)

ak

and

ap

did

not

communicate

since

But

then

εComm(ak,

ap,

had

value

and

takes

value

Hence

increases.

(case

iib)

ak

and

ap

did

communicate

at

some

time

The

CONS

property

of

the

protocol

ensures

that

MCons(ak,

ap)

at

that

time.

Now

the

fact

that

they

communicate

and

FOCUS

implies

that

at

least

one

of

them

did

change

its

hypothesis

in

the

meantime.

The

fact

that

agents

are

autonomous

implies

in

turn

that

a

new

observation

(perceived

or

received

from

another

agent)

necessarily

provoked

this

change.

The

latter

case

would

ensure

the

existence

of

a

time

t

and

an

agent

aq

s.t.

either

|Op

∩Oq|

or

|Ok

∩Oq|

increases

of

at

that

time

(implying

The

former

case

means

that

the

agent

gets

a

new

perception

o

at

time

t

If

that

observation

was

unknown

in

the

system

before,

then

If

some

agent

aq

already

knew

this

observation

before,

then

either

Op

Oq

or

Ok

Oq

increases

of

at

time

t

(which

implies

that

Hence,

¬MCons(ai,

aj)

at

time

guarantees

that,

either:

−∃t

t.q.

or

−∃t

t.q.

or

−∃t

t.q.

increases

of

at

time

t

By

iterating

the

reasoning

with

t

(but

keeping

as

the

time

reference

for

we

can

eliminate

the

third

case

is

integer

and

bounded

by

which

means

that

after

a

maximum

of

iterations,

we

necessarily

will

be

in

one

of

two

other

cases.)

As

a

result,

we

have

proven

that

if

¬MCons(ai,

aj)

at

time

there

is

necessarily

a

time

t

s.t.

either

or

will

increase.

Theorem

(Global

consistency).

Let

S

be

a

system

populated

by

n

agents

an,

temporaly

connex,

and

involving

bounded

perceptions

for

these

agents.

Let

Cons(ai,

aj)

be

a

transitive

consistency

property.

Then

any

protocol

and

strategies

satisfying

properties

CONS,

SOLVE,

FOCUS,

COMM

and

REQU

guarantees

that

the

system

will

converge

towards

global

consistency.

Proof.

For

the

sake

of

contradiction,

let

us

assume

∃I,

J

N]

s.t.

∀t,

t,

t.q.

¬Cons(aI

aJ

Using

the

lemma,

this

implies

that

∃t

s.t.

either

or

But

we

can

apply

the

same

reasoning

taking

t

t

which

would

give

us

t

s.t.

¬Cons(aI

aJ

which

gives

us

t

s.t.

either

or

By

successive

iterations

we

can

then

construct

a

sequence

tn,

which

can

be

divided

in

two

sub-sequences

...tn

and

tn

s.t.

and

One

of

these

sub-sequences

has

to

be

infinite.

However,

and

are

strictly

growing,

integer,

and

bounded,

which

implies

that

both

are

finite.

Contradiction.

What

the

previous

result

essentially

shows

is

that,

in

a

system

where

no

agent

will

be

isolated

from

the

rest

of

the

agents

for

ever,

only

very

mild

assumptions

on

the

protocols

and

strategies

used

by

agents

suffice

to

guarantee

convergence

towards

system

consistency

in

a

finite

amount

of

time

(although

it

might

take

very

long).

Unfortunately,

in

many

critical

situations,

it

will

not

be

possible

to

assume

this

temporal

connexity.

As

distributed

approaches

as

the

one

advocated

in

this

paper

are

precisely

often

presented

as

a

good

way

to

tackle

problems

of

reliability

or

problems

of

dependence

to

a

center

that

are

of

utmost

importance

in

these

critical

applications,

it

is

certainly

interesting

to

further

explore

how

such

a

system

would

behave

when

we

relax

this

assumption.

EXPERIMENTAL

STUDY

This

experiment

involves

agents

trying

to

escape

from

a

burning

building.

The

environment

is

described

as

a

spatial

grid

with

a

set

of

walls

and

(thankfully)

some

exits.

Time

and

space

are

considered

discrete.

Time

is

divided

in

rounds.

Agents

are

localised

by

their

position

on

the

spatial

grid.

These

agents

can

move

and

communicate

with

other

agents.

In

a

round,

an

agent

can

move

of

one

cell

in

any

of

the

four

cardinal

directions,

provided

it

is

not

blocked

by

a

wall.

In

this

application,

agents

communicate

with

any

other

agent

(but,

recall,

a

single

one)

given

that

this

agent

is

in

view,

and

that

they

have

not

yet

exchanged

their

current

favoured

hypothesis.

Suddenly,

a

fire

erupts

in

these

premises.

From

this

moment,

the

fire

propagates.

Each

round,

for

each

cases

where

there

is

fire,

the

fire

propagates

in

the

four

directions.

However,

the

fire

cannot

propagate

through

a

wall.

If

the

fire

propagates

in

a

case

where

an

agent

is

positioned,

that

agent

burns

and

is

considered

dead.

It

can

of

course

no

longer

move

nor

communicate.

If

an

agent

gets

to

an

exit,

it

is

considered

saved,

and

can

no

longer

be

burned.

Agents

know

the

environment

and

the

rules

governing

the

dynamics

of

this

environment,

that

is,

they

know

the

map

as

well

as

the

rules

of

fire

propagation

previously

described.

They

also

locally

perceive

this

environment,

but

cannot

see

further

than

cases

away,

in

any

direction.

Walls

also

block

the

line

of

view,

preventing

agents

from

seeing

behind

them.

Within

their

sight,

they

can

see

other

agents

and

whether

or

not

the

cases

they

see

are

on

fire.

All

these

perceptions

are

memorised.

We

now

show

how

this

instantiates

the

abstract

framework

presented

the

paper.

O

{Fire(x,

y,

t),

NoFire(x,

y,

t),

Agent(ai,

x,

y,

t)}

Observations

can

then

be

positive

(o

P(O)

iff

∃h

H

s.t.

h

o)

or

negative

(o

N(O)

iff

∃h

H

s.t.

h

¬o).

yl,

tl)}

Hypotheses

are

conjunctions

of

FireOrigins.

Cons(h,

O)

consistency

relation

satisfies:

coherence

∀o

N(O),

h

¬o.

completeness

∀o

P(O),

h

o.

minimality

For

all

h

H,

if

h

is

coherent

and

complete

for

O,

then

h

is

prefered

to

h

according

to

the

preference

relation

(h

≤p

h

Selects

first

the

minimal

number

of

origins,

then

the

most

recent

(least

preemptive

strategy

then

uses

some

arbitrary

fixed

ranking

to

discriminate

ex-aequo.

The

resulting

relation

is

a

total

order,

hence

minimality

implies

that

there

will

be

a

single

h

s.t.Cons(O,

h)

for

a

given

O.

This

in

turn

means

that

MCons(ai,

aj)

iff

Cons(ai),

Cons(aj),

and

hi

hj.

This

relation

is

then

transitive

and

symmetric.

The

Sixth

Intl.

Joint

Conf.

on

Autonomous

Agents

and

Multi-Agent

Systems

(AAMAS

Eh

takes

O

as

argument

and

returns

min≤p

of

the

coherent

and

complete

hypothesis

for

O

Experimental

Evaluation

We

will

classically

(see

e.g.

assess

the

effectiveness

and

efficiency

of

different

interaction

protocols.

Effectiveness

of

a

protocol

The

proportion

of

agents

surviving

the

fire

over

the

initial

number

of

agents

involved

in

the

experiment

will

determine

the

effectiveness

of

a

given

protocol.

If

this

value

is

high,

the

protocol

has

been

effective

to

propagate

the

information

and/or

for

the

agents

to

refine

their

hypotheses

and

determine

the

best

way

to

the

exit.

Efficiency

of

a

protocol

Typically,

the

use

of

supporting

information

will

involve

a

communication

overhead.

We

will

assume

here

that

the

efficiency

of

a

given

protocol

is

characterised

by

the

data

flow

induced

by

this

protocol.

In

this

paper

we

will

only

discuss

this

aspect

wrt.

local

protocols.

The

main

measure

that

we

shall

then

use

here

is

the

mean

total

size

of

messages

that

are

exchanged

by

agents

per

exchange

(hence

taking

into

account

both

the

number

of

messages

and

the

actual

size

of

the

messages,

because

it

could

be

that

messages

happen

to

be

very

big,

containing

e.g.

a

large

number

of

observations,

which

could

counter-balance

a

low

number

of

messages).

Experimental

Settings

The

chosen

experimental

settings

are

the

following:

Environmental

topology-

Performances

of

information

propagation

are

highly

constrained

by

the

environment

topology.

The

perception

skills

of

the

agents

depend

on

the

openness

of

the

environment.

With

a

large

number

of

walls

the

perceptions

of

agents

are

limited,

and

also

the

number

of

possible

inter-agent

communications,

whereas

an

open

environment

will

provide

optimal

possibilities

of

perception

and

information

propagation.

Thus,

we

propose

a

topological

index

(see

below)

as

a

common

basis

to

charaterize

the

environments

(maps)

used

during

experimentations.

The

topological

index

(TI)

is

the

ratio

of

the

number

of

cells

that

can

be

perceived

by

agents

summed

up

from

all

possible

positions,

divided

by

the

number

of

cells

that

would

be

perceived

from

the

same

positions

but

without

any

walls.

(The

closer

to

the

more

open

the

environment).

We

shall

also

use

two

additional,

more

classical

measures:

the

characteristic

path

(CPL)

and

the

clustering

(CC).

Number

of

agents-

The

propagation

of

information

also

depends

on

the

initial

number

of

agents

involved

during

an

experimentation.

For

instance,

the

more

agents,

the

more

potential

communications

there

is.

This

means

that

there

will

be

more

potential

for

propagation,

but

also

that

the

bilateral

exchange

restriction

will

be

more

crucial.

The

CPL

is

the

median

of

the

means

of

the

shortest

path

lengths

connecting

each

node

to

all

other

nodes.

characterising

the

isolation

degree

of

a

region

of

an

environment

in

terms

of

acessibility

(number

of

roads

still

usable

to

reach

this

region).

Map

T.I.

C.P.L.

C.C.

Table

Topological

Characteristics

of

the

Maps

Initial

positions

of

the

agents-

Initial

positions

of

the

agents

have

a

significant

influence

on

the

overall

behavior

of

an

instance

of

our

system:

being

close

from

an

exit

will

(in

general)

ease

the

escape.

Experimental

environments

We

choose

to

realize

experiments

on

three

very

different

topological

indexes

for

open

environments,

for

mixed

environments,

and

for

labyrinth-like

environments).

Figure

Two

maps

(left:

right

We

designed

three

different

maps

for

each

index

(Fig.

shows

two

of

them),

containing

the

same

maximum

number

of

agents

agents

max.)

with

a

maximum

density

of

one

agent

per

cell,

the

same

number

of

exits

and

a

similar

fire

origin

(e.g.

starting

time

and

position).

The

three

differents

maps

of

a

given

index

are

designed

as

follows.

The

first

map

is

a

model

of

an

existing

building

floor.

The

second

map

has

the

same

enclosure,

exits

and

fire

origin

as

the

first

one,

but

the

number

and

location

of

walls

are

different

(wall

locations

are

designed

by

an

heuristic

which

randomly

creates

walls

on

the

spatial

grid

such

that

no

fully

closed

rooms

are

created

and

that

no

exit

is

closed).

The

third

map

is

characterised

by

geometrical

enclosure

in

wich

walls

location

is

also

designed

with

the

aforementioned

heuristic.

Table

summarizes

the

different

topological

measures

characterizing

these

different

maps.

It

is

worth

pointing

out

that

the

values

confirm

the

relevance

of

TI

(maps

with

a

high

TI

have

a

low

CPL

and

a

high

CC.

However

the

CPL

and

CC

allows

to

further

refine

the

difference

between

the

maps,

e.g.

between

and

Experimental

Results

For

each

triple

of

maps

defined

as

above

we

conduct

the

same

experiments.

In

each

experiment,

the

society

differs

in

terms

of

its

initial

proportion

of

involved

agents,

from

to

This

initial

proportion

represents

the

percentage

of

involved

agents

with

regards

to

the

possible

maximum

number

of

agents.

For

each

map

and

each

initial

proportion,

The

Sixth

Intl.

Joint

Conf.

on

Autonomous

Agents

and

Multi-Agent

Systems

(AAMAS

we

select

randomly

different

initial

agents"

locations.

For

each

of

those

different

locations

we

execute

the

system

one

time

for

each

different

interaction

protocol.

Effectiveness

of

Communication

and

Argumentation

The

first

experiment

that

we

set

up

aims

at

testing

how

effective

is

hypotheses

exchange

(HE),

and

in

particular

how

the

topological

aspects

will

affect

this

effectiveness.

In

order

to

do

so,

we

have

computed

the

ratio

of

improvement

offered

by

that

protocol

over

a

situation

where

agents

could

simply

not

communicate

(no

comm).

To

get

further

insights

as

to

what

extent

the

hypotheses

exchange

was

really

crucial,

we

also

tested

a

much

less

elaborated

protocol

consisting

of

mere

observation

exchanges

(OE).

More

precisely,

this

protocol

requires

that

each

agent

stores

any

unexpected

observation

that

it

perceives,

and

agents

simply

exchange

their

respective

lists

of

observations

when

they

discuss.

In

this

case,

the

local

protocol

is

different

(note

in

particular

that

it

does

not

guarantee

mutual

consistency),

but

the

global

protocol

remains

the

same

(at

the

only

exception

that

agents"

motivation

to

communicate

is

to

synchronise

their

list

of

observations,

not

their

hypothesis).

If

this

protocol

is

at

best

as

effective

as

HE,

it

has

the

advantage

of

being

more

efficient

(this

is

obvious

wrt

the

number

of

messages

which

will

be

limited

to

less

straightforward

as

far

as

the

size

of

messages

is

concerned,

but

the

rough

observation

that

the

exchange

of

observations

can

be

viewed

as

a

flat

version

of

the

challenge

is

helpful

to

see

this).

The

results

of

these

experiments

are

reported

in

Fig.

Figure

Comparative

effectiveness

ratio

gain

of

protocols

when

the

proportion

of

agents

augments

The

first

observation

that

needs

to

be

made

is

that

communication

improves

the

effectiveness

of

the

process,

and

this

ratio

increases

as

the

number

of

agents

grows

in

the

system.

The

second

lesson

that

we

learn

here

is

that

closeness

relatively

makes

communication

more

effective

over

non

communication.

Maps

exhibiting

a

T.I.

of

are

constantly

above

the

two

others,

and

are

still

slightly

but

significantly

better

than

However,

these

curves

also

suggest,

perhaps

surprisingly,

that

HE

outperforms

OE

in

precisely

those

situations

where

the

ratio

gain

is

less

important

(the

only

noticeable

difference

occurs

for

rather

open

maps

where

T.I.

is

This

may

be

explained

as

follows:

when

a

map

is

open,

agents

have

many

potential

explanation

candidates,

and

argumentation

becomes

useful

to

discriminate

between

those.

When

a

map

is

labyrinth-like,

there

are

fewer

possible

explanations

to

an

unexpected

event.

Importance

of

the

Global

Protocol

The

second

set

of

experiments

seeks

to

evaluate

the

importance

of

the

design

of

the

global

protocol.

We

tested

our

protocol

against

a

local

broadcast

(LB)

protocol.

Local

broadcast

means

that

all

the

neighbours

agents

perceived

by

an

agent

will

be

involved

in

a

communication

with

that

agent

in

a

given

round

-we

alleviate

the

constraint

of

a

single

communication

by

agent.

This

gives

us

a

rough

upper

bound

upon

the

possible

ratio

gain

in

the

system

(for

a

given

local

protocol).

Again,

we

evaluated

the

ratio

gain

induced

by

that

LB

over

our

classical

HE,

for

the

three

different

classes

of

maps.

The

results

are

reported

in

Fig.

Figure

Ratio

gain

of

local

broadcast

over

hypotheses

exchange

Note

to

begin

with

that

the

ratio

gain

is

when

the

proportion

of

agents

is

which

is

easily

explained

by

the

fact

that

it

corresponds

to

situations

involving

only

two

agents.

We

first

observe

that

all

classes

of

maps

witness

a

ratio

gain

increasing

when

the

proportion

of

agents

augments:

the

gain

reaches

to

depending

on

the

class

of

maps

considered.

If

one

compares

this

with

the

improvement

reported

in

the

previous

experiment,

it

appears

to

be

of

the

same

magnitude.

This

illustrates

that

the

design

of

the

global

protocol

cannot

be

ignored,

especially

when

the

proportion

of

agents

is

high.

However,

we

also

note

that

the

effectiveness

ratio

gain

curves

have

very

different

shapes

in

both

cases:

the

gain

induced

by

the

accuracy

of

the

local

protocol

increases

very

quickly

with

the

proportion

of

agents,

while

the

curve

is

really

smooth

for

the

global

one.

Now

let

us

observe

more

carefully

the

results

reported

here:

the

curve

corresponding

to

a

TI

of

is

above

that

corresponding

to

This

is

so

because

the

more

open

a

map,

the

more

opportunities

to

communicate

with

more

than

one

agent

(and

hence

benefits

from

broadcast).

However,

we

also

observe

that

curve

for

is

below

that

for

This

is

explained

as

follows:

in

the

case

of

the

potential

gain

to

be

made

in

terms

of

surviving

agents

is

much

lower,

because

our

protocols

already

give

rather

efficient

outcomes

anyway

(quickly

reaching

see

Fig.

A

simple

rule

of

thumb

could

be

that

when

the

number

of

agents

is

small,

special

attention

should

be

put

on

the

local

The

Sixth

Intl.

Joint

Conf.

on

Autonomous

Agents

and

Multi-Agent

Systems

(AAMAS

protocol,

whereas

when

that

number

is

large,

one

should

carefully

design

the

global

one

(unless

the

map

is

so

open

that

the

protocol

is

already

almost

optimally

efficient).

Efficiency

of

the

Protocols

The

final

experiment

reported

here

is

concerned

with

the

analysis

of

the

efficiency

of

the

protocols.

We

analysis

here

the

mean

size

of

the

totality

of

the

messages

that

are

exchanged

by

agents

(mean

size

of

exchanges,

for

short)

using

the

following

protocols:

HE,

OE,

and

two

variant

protocols.

The

first

one

is

an

intermediary

restricted

hypotheses

exchange

protocol

(RHE).

RHE

is

as

follows:

it

does

not

involve

any

challenge

nor

counter-propose,

which

means

that

agents

cannot

switch

their

role

during

the

protocol

(this

differs

from

RE

in

that

respect).

In

short,

RHE

allows

an

agent

to

exhaust

its

partner"s

criticism,

and

eventually

this

partner

will

come

to

adopt

the

agent"s

hypothesis.

Note

that

this

means

that

the

autonomy

of

the

agent

is

not

preserved

here

(as

an

agent

will

essentially

accept

any

hypothesis

it

cannot

undermine),

with

the

hope

that

the

gain

in

efficiency

will

be

significant

enough

to

compensate

a

loss

in

effectiveness.

The

second

variant

protocol

is

a

complete

observation

exchange

protocol

(COE).

COE

uses

the

same

principles

as

OE,

but

includes

in

addition

all

critical

negative

examples

(nofire)

in

the

exchange

(thus

giving

all

examples

used

as

arguments

by

the

hypotheses

exchanges

protocol),

hence

improving

effectiveness.

Results

for

map

are

shown

on

Fig.

Figure

Mean

size

of

exchanges

First

we

can

observe

the

fact

that

the

ordering

of

the

protocols,

from

the

least

efficient

to

the

most

efficient,

is

COE,

HE,

RHE

and

then

OE.

HE

being

more

efficient

than

COE

proves

that

the

argumentation

process

gains

efficiency

by

selecting

when

it

is

needed

to

provide

negative

example,

which

have

less

impact

that

positive

ones

in

our

specific

testbed.

However,

by

communicating

hypotheses

before

eventually

giving

observation

to

support

it

(HE)

instead

of

directly

giving

the

most

crucial

observations

(OE),

the

argumentation

process

doubles

the

size

of

data

exchanges.

It

is

the

cost

for

ensuring

consistency

at

the

end

of

the

exchange

(a

property

that

OE

does

not

support).

Also

significant

is

the

fact

the

the

mean

size

of

exchanges

is

slightly

higher

when

the

number

of

agents

is

small.

This

is

explained

by

the

fact

that

in

these

cases

only

a

very

few

agents

have

relevant

informations

in

their

possession,

and

that

they

will

need

to

communicate

a

lot

in

order

to

come

up

with

a

common

view

of

the

situation.

When

the

number

of

agents

increases,

this

knowledge

is

distributed

over

more

agents

which

need

shorter

discussions

to

get

to

mutual

consistency.

As

a

consequence,

the

relative

gain

in

efficiency

of

using

RHE

appears

to

be

better

when

the

number

of

agents

is

small:

when

it

is

high,

they

will

hardly

argue

anyway.

Finally,

it

is

worth

noticing

that

the

standard

deviation

for

these

experiments

is

rather

high,

which

means

that

the

conversation

do

not

converge

to

any

stereotypic

pattern.

CONCLUSION

This

paper

has

investigated

the

properties

of

a

multiagent

system

where

each

(distributed)

agent

locally

perceives

its

environment,

and

tries

to

reach

consistency

with

other

agents

despite

severe

communication

restrictions.

In

particular

we

have

exhibited

conditions

allowing

convergence,

and

experimentally

investigated

a

typical

situation

where

those

conditions

cannot

hold.

There

are

many

possible

extensions

to

this

work,

the

first

being

to

further

investigate

the

properties

of

different

global

protocols

belonging

to

the

class

we

identified,

and

their

influence

on

the

outcome.

There

are

in

particular

many

heuristics,

highly

dependent

on

the

context

of

the

study,

that

could

intuitively

yield

interesting

results

(in

our

study,

selecting

the

recipient

on

the

basis

of

what

can

be

inferred

from

his

observed

actions

could

be

such

a

heuristic).

One

obvious

candidate

for

longer

term

issues

concern

the

relaxation

of

the

assumption

of

perfect

sensing.

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(AAMAS

O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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O O O O O O O O O O O O O O O O O O O O O O O

agent communication language and protocol

multiagent system
favoured hypothesis
global consistency
consistency
observation set
bounded perception
temporal path
bilateral exchange
context request step