Achieving Mediated Agreements Using Agreement Spaces

IntroductionContext Spaces

Agreement ConceptsAgreement-Related Interaction Protocols

Using Agreement Spaces for MediatorsExample

Conclusions

Achieving Mediated Agreements

Using Agreement Space Modeling

C. Carrascosa and M. Rebollo

Univ. Politécnica de Valencia (Spain)

Workshop on Agreement TechnologiesNovember 2009, Sevilla

Carrascosa & Rebollo Achieving Mediated Agreements. . .




Conclusions

Outline

1 Introduction

2 Context Spaces

3 Agreement Concepts

4 Agreement-Related Interaction Protocols

5 Using Agreement Spaces for Mediators

6 Example

7 ConclusionsCarrascosa & Rebollo Achieving Mediated Agreements. . .




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





Conclusions

Context Spaces

Context-aware computing: context defined as a set ofattributes and their domains

Context algebra to represent states and reason about them

Operations: scalar difference (similarity) and intersection (newspaces)

States are multi-dimensional objects

Regions of acceptable values defined

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





Conclusions

Agreement DefinitionAgreement ProcessAgreement Space

Agreement Definitions

Definition (Agreement)

An agreement Ag is defined as Ag = (E ,Cx), where:

E = {E1,E2, . . .En} is a set of participant entities

Cx = {(cxo, cx Io)|cxo ∈

⋃i Oi , cx I

o ⊆ Do}





Conclusions


Agreement Definitions

Definition (Agreement Discourse Universe (ADU))

It is the set of concepts known by at least two entities participatingin the agreement and it is defined as ADU(Ag) =

⋃i Oi − D





Conclusions


Agreement Process

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

2 Agreement execution





Conclusions


Agreement Space

Definition (Agreement Discourse Space (ADS))

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





Conclusions


Agreement Space

Definition (Agreement Space))

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





Conclusions


Agreement Space

Definition (Agreement Local Space)

for entity Ei in the agreement Ag is defined as the projection overthe dimensions of interest of entity Ei in such Agreement Space.





Conclusions

ADU Interaction ProtocolMediated Agreement Interaction Protocol

Agreement-Related Interaction Protocols

WS-Agreement: standard to model conversations forone-to-one negotiation processes

service agreement: service provider selection using FIPAiterated contract net

Protocols to conversate with Counselor

ADU Iteraction Protocol: vocabulary definition

Mediated-Agreement Interaction Protocol: space definition





Conclusions


ADU Interaction Protocol

Initiator Counsellor Participant i

call for counsellor

refuse

agree

not-understood

failure-no-match

call for agreement

refuse

agree

not-understood

failure-proxy

inform

m

n

j <= n

k <= n - j

l = n - j - k

request

refuse

agree

not-understood

p

r <= p

s <= p - r

t = p - r - s

p

t

t

t

deadline





Conclusions


Mediated Agreement Interaction Protocol

Initiator Counsellor Participant i

call for agreement

refuse

agree

not-understood

call for context

refuse

agree

not-understood

agreement terms

subprotocol

proxied-communicative-act

reply-message

p

r <= p

s <= p - r

t = p - r - s

p

Counsellor Participant i

inform-context p

call-for-terms p

inform-term

[redundant]reject

[¬consistent]reject

[consistent]accept

p

inform-done

failure

call-for-terms

(a) (b)





Conclusions


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





Conclusions

Agreement Spaces as a CSPCounselor Algorithm

Agreement Spaces as a CSP

Participant entities must arrange a valid interval for eachdimension

Participant restrictions can be considered as CSP constraintsin the n-dimensional space

Mediator checks incrementally the consistence among all theconstraints

The Agreement Space is the result of the constraintsintersection

HSA 6= algorithm is used to check the coherence and to buildthe space





Conclusions

Agreement Spaces as a CSPCounselor Algorithm

Agreement Spaces as a CSP

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





Conclusions

Example. Definition

Let it be a set of agents interested in taking piano classes. Thegroup is formed by one teacher and two students. They agree tonegotiate over three dimensions: the number of classes (n), itsduration (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





Conclusions

Example. Execution

Agent Mess Param Agent Mess Param1 C inform n, d ,p 16 C accept n ≤ 202 C call-for-terms 17 C call-for-terms3 T inform n ≥ 10 18 S2 inform d ≥ 454 C accept n ≥ 10 19 C reject d ≥ 455 C call-for-terms 20 C call-for-terms6 S1 inform p ≤ 30 21 T inform d ≤ 1207 C accept p ≤ 30 22 C accept d ≤ 1208 C call-for-terms 23 C call-for-terms9 S2 inform n ≥ 15 24 T inform p ≥ 2010 C accept n ≥ 15 25 C accept p ≥ 2011 C call-for-terms 26 C call-for-terms12 T inform d ≥ 60 27 S2 inform d ≤ 9013 C accept d ≥ 60 28 C accept d ≤ 9014 C call-for-terms 29 C inform-done15 S1 inform n ≤ 20





Conclusions

Conclusions

Context spaces seems a valid approach to model agreements

The agreement space is a hyperpolyedron in a n-dimensionalspace

The problem of defining the space associated with anagreement can be seen as a CSP

Mediators are used to check the consistence of the spaceincrementally

The communication protocols and algorithms used by themediator have been presented

As future work, the dynamics of the agreement are going to bestudied.


Achieving Mediated Agreements Using Agreement Spaces

Technology

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