Slides used in the Workshop of Agreement Technologies (WAT'09). Sevilla (Spain)

1. 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. . .

2. Introduction
Context Spaces
Agreement Concepts
Agreement-Related Interaction Protocols
Using Agreement Spaces for Mediators
Example
Conclusions
Outline
1 Introduction
2 Context Spaces
3 Agreement Concepts
4 Agreement-Related Interaction Protocols
5 Using Agreement Spaces for Mediators
6 Example
Carrascosa & Rebollo Achieving Mediated Agreements. . .

3. Introduction
Context Spaces
Agreement Concepts
Agreement-Related Interaction Protocols
Using Agreement Spaces for Mediators
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
Carrascosa & Rebollo Achieving Mediated Agreements. . .

4. Introduction
Context Spaces
Agreement Concepts
Agreement-Related Interaction Protocols
Using Agreement Spaces for Mediators
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.
Carrascosa & Rebollo Achieving Mediated Agreements. . .

5. 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
Carrascosa & Rebollo Achieving Mediated Agreements. . .

6. 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 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
Carrascosa & Rebollo Achieving Mediated Agreements. . .

7. Introduction
Context Spaces
Agreement Concepts Agreement Definition
Agreement-Related Interaction Protocols Agreement Process
Using Agreement Spaces for Mediators Agreement Space
Example
Conclusions
Agreement Process
1 Reach an agreement:
1 ADU definition (common vocabulary)
2 agreement terms defined (valid instances)
2 Agreement execution
Carrascosa & Rebollo Achieving Mediated Agreements. . .

8. Introduction
Context Spaces
Agreement Concepts Agreement Definition
Agreement-Related Interaction Protocols Agreement Process
Using Agreement Spaces for Mediators Agreement Space
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)
Carrascosa & Rebollo Achieving Mediated Agreements. . .

9. Introduction
Context Spaces
Agreement Concepts Agreement Definition
Agreement-Related Interaction Protocols Agreement Process
Using Agreement Spaces for Mediators Agreement Space
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)).
Carrascosa & Rebollo Achieving Mediated Agreements. . .

10. Introduction
Context Spaces
Agreement Concepts Agreement Definition
Agreement-Related Interaction Protocols Agreement Process
Using Agreement Spaces for Mediators Agreement Space
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.
Carrascosa & Rebollo Achieving Mediated Agreements. . .

11. Introduction
Context Spaces
Agreement Concepts
ADU Interaction Protocol
Agreement-Related Interaction Protocols
Mediated Agreement Interaction Protocol
Using Agreement Spaces for Mediators
Example
Conclusions
Agreement-Related Interaction Protocols
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
Carrascosa & Rebollo Achieving Mediated Agreements. . .

12. Introduction
Context Spaces
Agreement Concepts
ADU Interaction Protocol
Agreement-Related Interaction Protocols
Mediated Agreement Interaction Protocol
Using Agreement Spaces for Mediators
Example
Conclusions
ADU Interaction Protocol
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
Carrascosa & Rebollo Achieving Mediated Agreements. . .

13. Introduction
Context Spaces
Agreement Concepts
ADU Interaction Protocol
Agreement-Related Interaction Protocols
Mediated Agreement Interaction Protocol
Using Agreement Spaces for Mediators
Example
Conclusions
Mediated Agreement Interaction Protocol
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
Carrascosa & Rebollo Achieving Mediated Agreements. . .

14. Introduction
Context Spaces
Agreement Concepts
ADU Interaction Protocol
Agreement-Related Interaction Protocols
Mediated Agreement Interaction Protocol
Using Agreement Spaces for Mediators
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.
Carrascosa & Rebollo Achieving Mediated Agreements. . .

15. Introduction
Context Spaces
Agreement Concepts
Agreement Spaces as a CSP
Agreement-Related Interaction Protocols
Counselor Algorithm
Using Agreement Spaces for Mediators
Example
Conclusions
Agreement Spaces as a CSP
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
Carrascosa & Rebollo Achieving Mediated Agreements. . .

16. Introduction
Context Spaces
Agreement Concepts
Agreement Spaces as a CSP
Agreement-Related Interaction Protocols
Counselor Algorithm
Using Agreement Spaces for Mediators
Example
Conclusions
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
Carrascosa & Rebollo Achieving Mediated Agreements. . .

17. Introduction
Context Spaces
Agreement Concepts
Agreement-Related Interaction Protocols
Using Agreement Spaces for Mediators
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
Carrascosa & Rebollo Achieving Mediated Agreements. . .

18. Introduction
Context Spaces
Agreement Concepts
Agreement-Related Interaction Protocols
Using Agreement Spaces for Mediators
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
5 C call-for-terms 20 C call-for-terms
6 S1 inform p ≤ 30 21 T inform d ≤ 120
7 C accept p ≤ 30 22 C accept d ≤ 120
8 C call-for-terms 23 C call-for-terms
9 S2 inform n ≥ 15 24 T inform p ≥ 20
10 C accept n ≥ 15 25 C accept p ≥ 20
11 C call-for-terms 26 C call-for-terms
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
Carrascosa & Rebollo Achieving Mediated Agreements. . .

19. Introduction
Context Spaces
Agreement Concepts
Agreement-Related Interaction Protocols
Using Agreement Spaces for Mediators
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.
Carrascosa & Rebollo Achieving Mediated Agreements. . .