The alignment of disparate ontology is of fundamental importance to support opportunistic communication within open agent systems, and as such has become an established and active research area. Traditional alignment mechanisms typically exploit the lexical and structural resemblance between the entities (concepts, properties and individuals) found within the ontologies, and as such often require agents to make their ontology available to an oracle (either one of the agents them- selves or a third party). However, these approaches are used irrespectively of whether they are suitable given the intended models underlying the ontologies and hence their overlap, and usually require the disclosure of the full ontological model. This prevents the agents from strategically disclosing only part of their ontological model on the grounds of privacy or confidentiality issues. In this paper we present a dialogue based mechanism that allows two agents with limited or no prior knowledge of the other’s ontological model to determine whether it is possible to achieve some form of alignment between the two ontologies. We show how two agents, each possessing incomplete sets of private, heterogeneous (and typically ambiguous) correspondences, can derive an unambiguous alignment from a set of ambiguous, but mutually acceptable correspondences generated using an inquiry dialogue. The termination properties of the dialogue are formally proved, and the presentation and instantiation of an abstract preference-based argumentation is given. We demonstrate how ambiguity can be eliminated through the use of undercuts and rebuttals, given preference relations over the arguments. This paper was presented at the Principles and Practice of Multi-Agent Systems (PRIMA 2015) Conference.

1. Using preferences in
Negotiations over Ontological
Correspondences
Terry Payne & Valentina Tamma
University of Liverpool
T.R.Payne@liverpool.ac.uk
V.Tamma@liverpool.ac.uk

2. Using preferences in Negotiations over Ontological Correspondences
Terry Payne
University of Liverpool
Open Systems, Ontologies
and Alignment
• Agents (applications, devices, services) can assume different
ontological models
• Modelled implicitly, or explicitly by defining entities (classes, roles etc), typically using some
logical theory, i.e. an Ontology
• Alignment Systems align similar ontologies
• If we assume that different alignments exist, how do agents choose
which to use?
2
Alignment
Correspondence

3. Using preferences in Negotiations over Ontological Correspondences
Terry Payne
University of Liverpool
Align Everything?
• What does the agent know?
• Pre-computed alignments exist, and can be shared
• Different agents may possess different alignment fragments from
different sources.
3

4. Using preferences in Negotiations over Ontological Correspondences
Terry Payne
University of Liverpool
Align Everything?
• Do we need everything to be aligned?
• An agent may aggregate several ontologies for a variety of domains
• A task may be relevant to only a single module within an ontology
• Fragments of the ontological space may be confidential, or
commercially sensitive.
4

5. Using preferences in Negotiations over Ontological Correspondences
Terry Payne
University of Liverpool
Correspondence Inclusion
Dialogue (CID)
• Formal Inquiry Dialogue that…
• Allows two agents to exchange knowledge about
correspondences to agree upon a mutually acceptable final
alignment AL.
• Aligns only those entities in each agents’ working ontologies,
without disclosing the ontologies, or all of the known
correspondences.
5

6. Using preferences in Negotiations over Ontological Correspondences
Terry Payne
University of Liverpool
Correspondence Inclusion
Dialogue (CID)
• Assumptions
1. Agents typically possess some knowledge about different
correspondences from different sources
2. This knowledge is partial, asymmetric, and possibly ambiguous; i.e.
more than one correspondence exists for a given entity
3. Agents each associate a weight (Degree of Belief) κc to each unique
correspondence
4. Joint weights are computed when a correspondence is disclosed
5. Correspondences with a joint weight below the admissibility threshold
ϵ should be rejected
6

7. Using preferences in Negotiations over Ontological Correspondences
Terry Payne
University of Liverpool
Dialogue Moves
• Dialogue consists of a sequence of moves
• Agents take turns to select and propose a belief they know of, that
has not yet been asserted, based on its weight κc
• A shared, or asserted correspondence is:
• accepted based on their combined κc (i.e. joint(c))
• rejected if joint(c) < ϵ, the admissibility threshold
• objected to if an agent believes a better correspondence exists for
one of the entities in the correspondence
• The dialogue is presented formally in Payne & Tamma, AAMAS14
7
Payne T.R., and Tamma, V. (2014) Negotiating over Ontological Correspondences with Asymmetric and Incomplete
Knowledge. In: 13th International Conference on Autonomous Agents and MultiAgent Systems. (AAMAS’14), Paris.

8. Using preferences in Negotiations over Ontological Correspondences
Terry Payne
University of Liverpool
Dialogue Moves
8
Payne T.R., and Tamma, V. (2014) Negotiating over Ontological Correspondences with Asymmetric and Incomplete
Knowledge. In: 13th International Conference on Autonomous Agents and MultiAgent Systems. (AAMAS’14), Paris.
join
matched-close
join
matched-close
object
object
accept
reject
accept
endassert
endassert
reject
endassert
endassert
assert
assert
join
join
object
object
Alice
&
Bob
3ABBob
2B
Alice
2A
Alice
1A
Bob
1B
Alice
5A
Alice
4A
Bob
6B
Alice
6A
Bob
4B
object
object
Bob
5B

9. Using preferences in Negotiations over Ontological Correspondences
Terry Payne
University of Liverpool
Ambiguity and Objections
9
publication
article
author
submittedPaper
reviewedPaper
paper
editor
• Alignments typically consist of one-to-one mappings
• Combining correspondences from different alignment fragments can
result in one-to-many correspondences; i.e. ambiguity
• Which of these should be selected?
• Should selection be deferred until all candidates are found?
• Could it be resolved though objections within the dialogue?

10. Using preferences in Negotiations over Ontological Correspondences
Terry Payne
University of Liverpool
Finding an injective alignment?
10
article
publication
draft
paper
0.5
0.6
0.7
• Option 1:
• Reduce problem to that of finding a
Matching in a bipartite graph with weighted
edges
• The problem becomes one of finding the right
objective function
• Use Stable Marriage algorithm to prefer stable
(highly weighted) edges
• Use Hungarian algorithm to maximise the total
weight of edges
• However:
• All candidate correspondences need to be found.
• Solution based purely on joint weights
Stable Solution:
⟨article,paper,≣⟩
Maximal Solution:
⟨article,draft,≣⟩
⟨publication,paper,≣⟩
Payne T.R., and Tamma, V. (2014) A Dialectical Approach to Selectively Reusing Ontological Correspondences. In: 19th
International Conference on Knowledge Engineering and Knowledge Management (EKAW2014).

11. Using preferences in Negotiations over Ontological Correspondences
Terry Payne
University of Liverpool
⟨article, reviewedPaper,≣⟩
0.45
⟨article, paper,≣⟩
0.65
11
• Option 2:
• Build a simple attack graph during the dialogue
• Alternate correspondences are counter-proposed (through an objection)
to form an attack graph
• Attacks can be directed by the difference in the weight of each correspondence
• Bi-directional attacks are resolved by random selection of one of the alternatives
• Can then use grounded semantics to determine the extension
Finding an injective alignment?
⟨article, submittedPaper,≣⟩
0.5
⟨publication, paper,≣⟩
0.7

12. Using preferences in Negotiations over Ontological Correspondences
Terry Payne
University of Liverpool
12
• Option 2:
• Build a simple attack graph during the dialogue
• Alternate correspondences are counter-proposed (through an objection)
to form an attack graph
• Attacks can be directed by the difference in the weight of each correspondence
• Bi-directional attacks are resolved by random selection of one of the alternatives
• Can then use grounded semantics to determine the extension
Finding an injective alignment?
⟨article, submittedPaper,≣⟩
0.5
⟨publication, paper,≣⟩
0.7 publication
article
author
submittedPaper
reviewedPaper
paper
editor

13. Using preferences in Negotiations over Ontological Correspondences
Terry Payne
University of Liverpool
13
• Option 3:
• Build a preference-based argumentation graph during the
dialogue
• Based on the work of Parsons, Wooldridge, & Amgoud (2003)
• Arguments are modelled as a tuple S = (H, c) where
• c = the claim or conclusion of the argument - i.e. the correspondence
• H = the support, such that the claim holds
• Attacks occur as:
• rebuts - if the claim of one argument negates another (e.g. c1 ≣ ¬c2)
• undercut - if the claim of one argument negates an element of the support S
Finding an injective alignment?

14. Using preferences in Negotiations over Ontological Correspondences
Terry Payne
University of Liverpool
• Agents represent the correspondences symbolically within
a (potentially inconsistent) stratified knowledge base 𝛴.
• A propositional symbol is used to represent the correspondences
• The knowledge base is stratified into disjoint sets corresponding to the
weights of the correspondences
• Correspondences accepted by both agents are added to the sets,
based on their weights
Stratifying Arguments
14
⌃0.7 = {i}
⌃0.65 = {j}
⌃0.5 = {k}
⌃0.45 = {m}
p c c
i hpublication, paper, ⌘i 0.70
j harticle, paper, ⌘i 0.65
k harticle, submittedPaper, ⌘i 0.5
l harticle, reviewedPaper, ⌘i 0.45

15. Using preferences in Negotiations over Ontological Correspondences
Terry Payne
University of Liverpool
• Objections within the dialogue are modelled within
the knowledge bases.
• If a correspondence c was raised as an objection to another
c’ (due to an ambiguity), then they must be disjoint:
Modelling Objections
15
p c c
i hpublication, paper, ⌘i 0.70
j harticle, paper, ⌘i 0.65
k harticle, submittedPaper, ⌘i 0.5
l harticle, reviewedPaper, ⌘i 0.45
⌃0.7 = {i, i $ ¬j}
⌃0.65 = {j, j $ ¬i, j $ ¬k, j $ ¬l}
⌃0.5 = {k, k $ ¬j, k $ ¬l}
⌃0.45 = {l, l $ ¬j, l $ ¬k}
hAlice, object, hpublication, paper, 0.7i, harticle, paper, 0.65ii
hBob, object, harticle, paper, 0.65i, harticle, submittedPaper, 0.5ii
hBob, object, harticle, paper, 0.65i, harticle, reviewedPaper, 0.45ii
hAlice, object, harticle, submittedPaper, 0.5i, harticle, reviewedPaper, 0.45ii
if ambiguous(c, c0
), then (c =) ¬c0
) ^ (c0
=) ¬c)

16. Using preferences in Negotiations over Ontological Correspondences
Terry Payne
University of Liverpool
Modelling Objections
16
p c c
i hpublication, paper, ⌘i 0.70
j harticle, paper, ⌘i 0.65
k harticle, submittedPaper, ⌘i 0.5
l harticle, reviewedPaper, ⌘i 0.45
1. a1 undercuts a2
2. As a consequence
2.1. a1 undercuts a3
2.2. a1 undercuts a5
a1 = ({i, i $ ¬j}, ¬j) a5 = ({j, j $ ¬l}, ¬l)
a2 = ({j, j $ ¬i}, ¬i) a6 = ({l, l $ ¬j}, ¬j)
a3 = ({j, j $ ¬k}, ¬k) a7 = ({k, k $ ¬l}, ¬l)
a4 = ({k, k $ ¬j}, ¬j) a8 = ({l, l $ ¬k}, ¬k)
3. As a7 is not attacked by a3:
3.1. a7 undercuts a8
3.2. a7 undercuts a6
Solution: publication
article
author
submittedPaper
reviewedPaper
paper
editor
a1, a4, a7 = {i, k, i $ ¬j, k $ ¬j, i $ ¬l}
AL = {hpublication, paper, =i,
harticle, submittedPaper, =i}.

17. Using preferences in Negotiations over Ontological Correspondences
Terry Payne
University of Liverpool
Conclusions
• Developed a formal Inquiry Dialogue that supports the sharing of
ontological correspondences between agents
• Only those correspondences relating to the agents working ontology are
aligned, thus avoiding unnecessary alignment
• Implemented a full version of the dialogue for evaluation
• The resulting alignment performs significantly better in most cases than the
average performance of other approaches, when tested with a reference
alignment (AAMAS ‘2014)
• Preference based argumentation can be used as a modelling
paradigm for objections
• Currently investigating how to encode other ontological constraints
propositionally within this framework
17

18. Using preferences in Negotiations over Ontological Correspondences
Terry Payne
University of Liverpool
Questions
18
For other papers on this and our other related work:
http://www.csc.liv.ac.uk/~trp/Knowledge-Based-Agents.html