Mediated Agreements Using Agreement Space Modeling

Introduction
Context Spaces
Agreement Concepts
Agreement-Related Interaction Protocols
Using Agreement Spaces for Mediators
Example
Conclusions

Achieving Mediated Agreements
Using Agreement Space Modeling

C. Carrascosa and M. Rebollo
Univ. Politécnica de Valencia (Spain)

Workshop on Agreement Technologies
November 2009, Sevilla

Carrascosa & Rebollo Achieving Mediated Agreements. . .

Introduction
Context Spaces
Agreement Concepts
Example
Conclusions

Outline

1 Introduction

2 Context Spaces

3 Agreement Concepts

4 Agreement-Related Interaction Protocols

5 Using Agreement Spaces for Mediators

6 Example

Introduction
Context Spaces
Agreement Concepts
Example
Conclusions

Introduction

Importance of the context
Approach focused on the agreement concept itself
Agreement deﬁned as a multi-dimensional Euclidean space
Geometrical properties of agreements → solved as a CSP
A counselor mediates the process to evaluate its feasibility


Introduction
Context Spaces
Agreement Concepts
Example
Conclusions

Context Spaces

Context-aware computing: context defined as a set of
attributes and their domains
Context algebra to represent states and reason about them
Operations: scalar difference (similarity) and intersection (new
spaces)
States are multi-dimensional objects
Regions of acceptable values defined

Each attribute is considered one dimension in a multi-dimensional
Euclidean space.


Introduction
Context Spaces
Agreement Concepts Agreement Definition
Agreement-Related Interaction Protocols Agreement Process
Using Agreement Spaces for Mediators Agreement Space
Example
Conclusions

Agreement Definitions

Definition (Agreement)
An agreement Ag is defined as Ag = (E , Cx ), where:
E = {E1 , E2 , . . . En } is a set of participant entities
I
Cx = {(cxo , cxo )|cxo ∈ I
Oi , cxo ⊆ Do }
i


Introduction
Context Spaces
Example
Conclusions

Agreement Definitions

Definition (Agreement Discourse Universe (ADU))
It is the set of concepts known by at least two entities participating
in the agreement and it is defined as ADU(Ag) = i Oi − D


Introduction
Context Spaces
Example
Conclusions

Agreement Process

1 Reach an agreement:
1 ADU deﬁnition (common vocabulary)
2 agreement terms deﬁned (valid instances)
2 Agreement execution


Introduction
Context Spaces
Example
Conclusions

Agreement Space

Deﬁnition (Agreement Discourse Space (ADS))
The Agreement Discourse Space of an agreement Ag ADS(Ag) is
deﬁned by considering as a dimension (in an Euclidean space) each
concept included in an Agreement Discourse Universe of an
agreement Ag. That is, the ADS(Ag) is an n-dimensional space,
where n is the cardinality of the ADU(Ag)

Introduction
Context Spaces
Example
Conclusions

Agreement Space

Definition (Agreement Space))
It is a projection of the Agreement Discourse Space onto the
dimensions defining the agreement. That is, this space will be
defined by the features the different entities Ei making the
agreement are going to negotiate (Cx ), each one of such features
defining a dimension in this space (∀i : di ∈ dim(Ei , Ag)).

Introduction
Context Spaces
Example
Conclusions

Agreement Space

Deﬁnition (Agreement Local Space)
for entity Ei in the agreement Ag is deﬁned as the projection over
the dimensions of interest of entity Ei in such Agreement Space.


Introduction
Context Spaces
Agreement Concepts
ADU Interaction Protocol
Mediated Agreement Interaction Protocol
Example
Conclusions


WS-Agreement: standard to model conversations for
one-to-one negotiation processes
service agreement: service provider selection using FIPA
iterated contract net

Protocols to conversate with Counselor
ADU Iteraction Protocol: vocabulary deﬁnition
Mediated-Agreement Interaction Protocol: space deﬁnition


Introduction
Context Spaces
Agreement Concepts
Example
Conclusions

Initiator Counsellor Participant i

call for counsellor m

j <= n not-understood

n
k <= n - j refuse

l=n-j-k agree

failure-no-match deadline

request

not-understood

refuse

agree

call for agreement p

r <= p not-understood
p
s <= p - r refuse

t=p-r-s agree

failure-proxy t

t inform t


Introduction
Context Spaces
Agreement Concepts
Example
Conclusions


Initiator Counsellor Participant i (a) Counsellor Participant i (b)

inform-context p
call for agreement

not-understood call-for-terms p
p

refuse
inform-term

agree
[¬consistent]
reject
call for context p

[redundant]
r <= p not-understood reject
p
s <= p - r refuse [consistent]
accept
t=p-r-s agree

call-for-terms

proxied-communicative-act
inform-done

agreement
terms failure
subprotocol

reply-message


Introduction
Context Spaces
Agreement Concepts
Example
Conclusions

The ﬁnal result is the deﬁnition of the Agreement Space, modeled
as a hyperpolyhedron formed by all accepted constraints
(agreement terms). During the execution of the agreement, all
interactions have to be inside this space as the participants have
agreed.


Introduction
Context Spaces
Agreement Concepts
Agreement Spaces as a CSP
Counselor Algorithm
Example
Conclusions


Participant entities must arrange a valid interval for each
dimension
Participant restrictions can be considered as CSP constraints
in the n-dimensional space
Mediator checks incrementally the consistence among all the
constraints
The Agreement Space is the result of the constraints
intersection
HSA = algorithm is used to check the coherence and to build
the space


Introduction
Context Spaces
Agreement Concepts
Counselor Algorithm
Example
Conclusions


Counselor Algorithm
Receive a new constraint Ci
if ¬ consistent( Ci , Polyh )
reject Ci
else if redundant( Ci , Polyh )
reject Ci
else
accept Ci
add_constraint( Ci , Polyh )
endif


Introduction
Context Spaces
Agreement Concepts
Example
Conclusions

Example. Deﬁnition

Let it be a set of agents interested in taking piano classes. The
group is formed by one teacher and two students. They agree to
negotiate over three dimensions: the number of classes (n), its
duration (d) and its price (p).
Teacher
at least 10 classes: n ≥ 10
duration between 60 and 120 min: d ≥ 60 and d ≤ 120
at least 20 euros/hour: p ≥ 20
Student 1
no more than 20 classes: n ≤ 20
less than 30 euros/hour: p ≤ 30
Student 2
minimum 15 classes: n ≥ 15
duration between 45 and 90 min: d ≥ 45 and d ≤ 90


Introduction
Context Spaces
Agreement Concepts
Example
Conclusions

Example. Execution

Agent Mess Param Agent Mess Param
1 C inform n, d ,p 16 C accept n ≤ 20
2 C call-for-terms 17 C call-for-terms
3 T inform n ≥ 10 18 S2 inform d ≥ 45
4 C accept n ≥ 10 19 C reject d ≥ 45
6 S1 inform p ≤ 30 21 T inform d ≤ 120
7 C accept p ≤ 30 22 C accept d ≤ 120
9 S2 inform n ≥ 15 24 T inform p ≥ 20
10 C accept n ≥ 15 25 C accept p ≥ 20
12 T inform d ≥ 60 27 S2 inform d ≤ 90
13 C accept d ≥ 60 28 C accept d ≤ 90
14 C call-for-terms 29 C inform-done
15 S1 inform n ≤ 20


Introduction
Context Spaces
Agreement Concepts
Example
Conclusions

Conclusions

Context spaces seems a valid approach to model agreements
The agreement space is a hyperpolyedron in a n-dimensional
space
The problem of deﬁning the space associated with an
agreement can be seen as a CSP
Mediators are used to check the consistence of the space
incrementally
The communication protocols and algorithms used by the
mediator have been presented
As future work, the dynamics of the agreement are going to be
studied.

Mediated Agreements Using Agreement Space Modeling

Recommended

Recommended

More Related Content

More from Miguel Rebollo

More from Miguel Rebollo (20)

Recently uploaded

Recently uploaded (20)

Mediated Agreements Using Agreement Space Modeling