Negotiating over Ontological Correspondences with Asymmetric and Incomplete Knowledge

Negotiating over Ontological
Correspondences
with Asymmetric and Incomplete
Knowledge
Terry Payne & Valentina Tamma
University of Liverpool
T.R.Payne@liverpool.ac.uk
V.Tamma@liverpool.ac.uk

Negotiating over Ontological Correspondences
with Asymmetric and Incomplete Knowledge
Terry Payne
Open Systems, Ontologies
and Alignment
• Agents 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

Terry Payne
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.
• 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.
3

Terry Payne
Aims and Contribution
• Correspondence Inclusion Dialogue (CID)
• Allows two agents to exchange knowledge about correspondences to agree
upon a mutually acceptable ﬁnal alignment AL.
• This alignment aligns only those entities in each agents’ working ontologies,
without disclosing the ontologies, or all of the known correspondences.
• Assumptions
1. Each agent knows about different correspondences from different sources
2. This knowledge is partial, and possibly ambiguous; i.e. more than one
correspondence exists for a given entity
3. Agents associate a utility (Degree of Belief) κc to each unique correspondence
4. Correspondences with a joint utility below the admissibility threshold ϵ should
be rejected
4

Terry Payne
• Correspondences are modelled as Beliefs
• The degree of belief κc reﬂects the agent speciﬁc belief of the utility
of c aligning its corresponding entities in the two working ontologies
• The beliefs of both agents for a correspondence can be combined
into a joint belief
Modelling and Aggregating
Beliefs
5
= hc, ci, where correspondence c = he, e0
, =i and e 2 W, e0
2 W0
joint(c) =
8
><
>:
avg(x
c , ˆx
c ) if beliefs from both agents x and ˆx are disclosed
1
2 (ˆx
c ) if the beliefs of c is only known to x
avg(x
c , x
upper) when ˆx ’s belief of c is not yet known

Terry Payne
Knowledge Model
6
Working Ontology
(a fragment of the
agent’s ontology)
contains the entities
to be aligned
Alignment Store
contains the
correspondences
known to the agent
Joint Belief Store
tracks all beliefs
(commitments)
disclosed by both
agents
As beliefs are
shared, the agent
builds up a joint
degree of belief of
the utility of the
correspondence
Joint Belief Store JB
bob
= hha, x, =i, 0.6i
alice
= hha, x, =i, 0.8i
alice
= hhb, x, =i, 0.5i
bob
= hhb, x, =i, 0.8i
···
Alignment Store
Ontology O
joint(ha, x, =i) = 0.7
joint(hb, x, =i) = 0.65
alice
= hhb, z, =i, 0.9i
alice
= hha, x, =i, 0.8i
alice
= hhb, w, =i, 0.6i
alice
= hhb, x, =i, 0.5i
Alice
···
W =
{a, b, a v b}
Public KnowledgePrivate Knowledge

Terry Payne
Ambiguity and Attacks
7
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
• Agents therefore need a mechanism for selecting
the ‘best’ set of correspondences

Terry Payne
Correspondence Inclusion
Dialogue (CID)
• Inquiry Dialogue, use to determine mutually
acceptable correspondences to facilitate some task
• Agents take turns to select and propose a belief they know of, that
has not yet been asserted, based on its utility 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 the paper
8

Terry Payne
Commitment Strategy
• Correspondences are selected (asserted) for
disclosure:
1. Agents assert the best undisclosed correspondence (i.e. with the
highest κc) in any round
2. Disclosed correspondences should be grounded in the working
ontology
3. A correspondence should not be disclosed if the joint degree of belief
is guaranteed to be less than the admissibility threshold.
9

Terry Payne
Objecting Strategy
10
…
2 Alice -> Bob:ASSERT <0.9, {http://l#b = http://h#z}>
3 Bob -> Alice:OBJECT <0.8, {http://l#b = http://h#x}> to <0.0, {http://l#b = http://h#z}>
4 Alice -> Bob:OBJECT <0.8, {http://l#a = http://h#x}> to <0.5, {http://l#b = http://h#x}>
5 Bob -> Alice:ACCEPT <0.6, {http://l#a = http://h#x}>
6 Bob -> Alice:OBJECT <0.4, {http://l#b = http://h#w}> to <0.0, {http://l#b = http://h#z}>
7 Alice -> Bob:ACCEPT <0.6, {http://l#b = http://h#w}>
…
a
b
c
z
w
x
y
• Alternate correspondences are counter-proposed
(through an objection):
1. If an agent has an undisclosed correspondence that shares an entity
and:
2. It’s estimated κc is greater than the joint degree of belief for the
current correspondence
• Each objection results in the agent’s actual degree
of belief being disclosed.

Terry Payne
Example Dialogue
Public Knowledge Private Knowledge
Ontology O
W = {w, x, y, z,
x v w}
Alignment Store
bob
= hhb, x, =i, 0.8i
bob
= hha, x, =i, 0.6i
bob
= hhb, w, =i, 0.4i
Alignment Store
alice
= hhb, z, =i, 0.9i
alice
= hha, x, =i, 0.8i
alice
= hhb, x, =i, 0.5i
alice
= hhb, w, =i, 0.6i
W = {a, b, c,
a v b}
Ontology O Joint Belief Store JB
Alice asserts the correspondence with the highest κc

Terry Payne
Example Dialogue
Ontology O
W = {w, x, y, z,
x v w}
Alignment Store
bob
= hhb, x, =i, 0.8i
bob
= hha, x, =i, 0.6i
bob
= hhb, w, =i, 0.4i
alice
= hhb, z, =i, 0.9i
Alignment Store
alice
= hhb, z, =i, 0.9i
alice
= hha, x, =i, 0.8i
alice
= hhb, x, =i, 0.5i
alice
= hhb, w, =i, 0.6i
W = {a, b, c,
a v b}
hAlice, assert, hhb, z, =i, 0.9i, nili
alice
= hhb, z, =i, 0.9i
Alice asserts the correspondence with the highest κc

Terry Payne
Example Dialogue
Ontology O
W = {w, x, y, z,
x v w}
Alignment Store
bob
= hhb, x, =i, 0.8i
bob
= hha, x, =i, 0.6i
bob
= hhb, w, =i, 0.4i
alice
= hhb, z, =i, 0.9i
Alignment Store
alice
= hhb, z, =i, 0.9i
alice
= hha, x, =i, 0.8i
alice
= hhb, x, =i, 0.5i
alice
= hhb, w, =i, 0.6i
W = {a, b, c,
a v b}
alice
= hhb, z, =i, 0.9i
Bob realises that joint(⟨b,z,=⟩) = 0.45, and ﬁnds an
alternative c with jointest(⟨b,x,=⟩) = 0.85

Terry Payne
Example Dialogue
Ontology O
W = {w, x, y, z,
x v w}
Alignment Store
bob
= hhb, x, =i, 0.8i
bob
= hha, x, =i, 0.6i
bob
= hhb, w, =i, 0.4i
alice
= hhb, z, =i, 0.9i
Alignment Store
alice
= hhb, z, =i, 0.9i
alice
= hha, x, =i, 0.8i
alice
= hhb, x, =i, 0.5i
alice
= hhb, w, =i, 0.6i
W = {a, b, c,
a v b}
alice
= hhb, z, =i, 0.9i
joint(hb, z, =i) = 0.45
hBob, object, hhb, x, =i, 0.8i, hhb, z, =i, 0.0ii
bob
= hhb, z, =i, 0.0i
bob
= hhb, x, =i, 0.8i
bob
= hhb, z, =i, 0.0i
bob
= hhb, x, =i, 0.8i
Using the Upper Bound
Alice’s previous assertion was a belief
with a utility of 0.9. Therefore the
utility of ⟨b,x,=⟩ ≤ 0.9.
As Bob’s ⟨b,x,=⟩ is 0.8, he calculates
jointest(⟨b,x,=⟩) = avg(0.9, 0.8)

Terry Payne
Example Dialogue
Ontology O
W = {w, x, y, z,
x v w}
Alignment Store
bob
= hhb, x, =i, 0.8i
bob
= hha, x, =i, 0.6i
bob
= hhb, w, =i, 0.4i
alice
= hhb, z, =i, 0.9i
Alignment Store
alice
= hhb, z, =i, 0.9i
alice
= hha, x, =i, 0.8i
alice
= hhb, x, =i, 0.5i
alice
= hhb, w, =i, 0.6i
W = {a, b, c,
a v b}
alice
= hhb, z, =i, 0.9i
joint(hb, z, =i) = 0.45
bob
= hhb, z, =i, 0.0i
bob
= hhb, x, =i, 0.8i
bob
= hhb, z, =i, 0.0i
bob
= hhb, x, =i, 0.8i
joint(hb, z, =i) = 0.45

Terry Payne
Example Dialogue
Ontology O
W = {w, x, y, z,
x v w}
Alignment Store
bob
= hhb, x, =i, 0.8i
bob
= hha, x, =i, 0.6i
bob
= hhb, w, =i, 0.4i
alice
= hhb, z, =i, 0.9i
Alignment Store
alice
= hhb, z, =i, 0.9i
alice
= hha, x, =i, 0.8i
alice
= hhb, x, =i, 0.5i
alice
= hhb, w, =i, 0.6i
W = {a, b, c,
a v b}
alice
= hhb, z, =i, 0.9i
joint(hb, z, =i) = 0.45
bob
= hhb, z, =i, 0.0i
bob
= hhb, x, =i, 0.8i
bob
= hhb, z, =i, 0.0i
Alice calculates joint(⟨b,x,=⟩) is 0.65. As jointest(⟨a,x,=⟩) is
0.9, which is greater than joint(⟨b,x,=⟩), she objects.
bob
= hhb, x, =i, 0.8i
joint(hb, z, =i) = 0.45
hAlice, object, hha, x, =i, 0.8i, hhb, x, =i, 0.5ii
joint(hb, x, =i) = 0.65

Terry Payne
Example Dialogue
Ontology O
W = {w, x, y, z,
x v w}
Alignment Store
bob
= hhb, x, =i, 0.8i
bob
= hha, x, =i, 0.6i
bob
= hhb, w, =i, 0.4i
alice
= hhb, z, =i, 0.9i
Alignment Store
alice
= hhb, z, =i, 0.9i
alice
= hha, x, =i, 0.8i
alice
= hhb, x, =i, 0.5i
alice
= hhb, w, =i, 0.6i
W = {a, b, c,
a v b}
alice
= hhb, z, =i, 0.9i
joint(hb, z, =i) = 0.45
bob
= hhb, z, =i, 0.0i
bob
= hhb, x, =i, 0.8i
bob
= hhb, z, =i, 0.0i
Bob calculates joint(⟨a,x,=⟩) is 0.7. As he has no further
objections, he accepts this.
bob
= hhb, x, =i, 0.8i
joint(hb, z, =i) = 0.45
joint(hb, x, =i) = 0.65
alice
= hhb, x, =i, 0.5i
alice
= hha, x, =i, 0.8i
hBob, accepts, hha, x, =i, 0.6ii
alice
= hha, x, =i, 0.8i
joint(hb, x, =i) = 0.65
alice
= hhb, x, =i, 0.5i
joint(ha, x, =i) = 0.7

Terry Payne
Example Dialogue
Ontology O
W = {w, x, y, z,
x v w}
Alignment Store
bob
= hhb, x, =i, 0.8i
bob
= hha, x, =i, 0.6i
bob
= hhb, w, =i, 0.4i
alice
= hhb, z, =i, 0.9i
Alignment Store
alice
= hhb, z, =i, 0.9i
alice
= hha, x, =i, 0.8i
alice
= hhb, x, =i, 0.5i
alice
= hhb, w, =i, 0.6i
W = {a, b, c,
a v b}
alice
= hhb, z, =i, 0.9i
joint(hb, z, =i) = 0.45
bob
= hhb, z, =i, 0.0i
bob
= hhb, x, =i, 0.8i
bob
= hhb, z, =i, 0.0i
The agents continue until they have no more
correspondences to consider.
bob
= hhb, x, =i, 0.8i
joint(hb, z, =i) = 0.45
joint(hb, x, =i) = 0.65
alice
= hhb, x, =i, 0.5i
alice
= hha, x, =i, 0.8i
hBob, accepts, hha, x, =i, 0.6ii
bob
= hha, x, =i, 0.6i
alice
= hha, x, =i, 0.8i
joint(hb, x, =i) = 0.65
alice
= hhb, x, =i, 0.5i
bob
= hha, x, =i, 0.6i
joint(ha, x, =i) = 0.7 joint(ha, x, =i) = 0.7
joint(hb, w, =i) = 0.5 joint(hb, w, =i) = 0.5
hBob, object, hhb, w, =i, 0.4i, hhb, z, =i, 0.0ii
hAlice, accepts, hhb, w, =i, 0.6ii
· · ·
bob
= hhb, w, =i, 0.4i
alice
= hhb, w, =i, 0.6i
bob
= hhb, w, =i, 0.4i
alice
= hhb, w, =i, 0.6i

Terry Payne
Modelling the objections as
an attack graph
• The objections can form a Dungian attack graph
• Attacks can be directed by the difference in the degree of belief
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
16
⟨a,x,=⟩
0.7
⟨b,x,=⟩
0.65
⟨b,w,=⟩
0.5
⟨b,z,=⟩
0.45

Terry Payne
Empirical Analysis:
Datasets
• Datasets taken from the Ontology Alignment
Evaluation Initiative (2012) Conference Track
• 7 Ontologies, each describing the conference domain
• Each included a reference ontology, used by OAEI to evaluate
alignment performance.
• 17 Alignment systems used to generate pairwise alignments
between the ontologies
• 21 pairwise alignments tested
• 357 alignments in total
17

Terry Payne
Experimental Method
• Evaluate alignment generated through two agents
negotiating
• Each agent starts with 8 of 17 randomly selected alignments
form the OAEI repository.
• Degree of Belief κc based on the probability of a
correspondence appearing in the alignments
• Admissibility thresholds ϵ were varied between 1/16 (no ﬁltering)
to 1 in 1/16ths
• Each experiment was run 500 times for statistical
signiﬁcance
18

Terry Payne
Hypothesis 1:
Are we ﬁt for purpose?
• Compare each alignment AL generated through
dialogue with OAEI reference ontology
• Performance evaluated using Precision, Recall and F-measure
• Baseline result based on selecting a single alignment at random
19

Terry Payne
Hypothesis 1:
Are we ﬁt for purpose?
20
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
2/16 4/16 6/16 8/16 10/16 12/16 14/16 16/16
DifferenceinF-measurefromRandomAlignmentAverage
Admissibility Threshold
Delta f-measure performance for all 21 Ontology Pairs
F-measure for each ontology pair
found to be statistically higher
than baseline for 3/16 ≤ ϵ < 14/16

Terry Payne
Hypothesis 2:
Can filtering out correspondences help?
• Calculate percentage of unique mappings disclosed/
messages exchanged during the negotiation.
• Results averaged across all ontology pairs
• Evaluate the significance of the upper-bound κupper in the strategy
• Determine the percent of correspondences in final alignment AL
21

Terry Payne
Hypothesis 2:
Can filtering out correspondences help?
22
0
20
40
60
80
100
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
PercentageofCombinedUniqueCorrespondences
Admissibility Threshold
Percentage of Correspondences Disclosed or in the Final Alignment
% in final alignment
% disclosed (using the upper boud)
% disclosed (no upper bound)
jointest(c) ≈ 0.5 when κupper is fixed
(i.e. not used) and ϵ ≤ 9/16
the number of ambiguous
correspondences falls as
ϵ increases
When ϵ > 9/16, low κc
correspondences are
filtered

Terry Payne
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
• By modelling the opponent’s assertions, an agent can more accurately
estimate the joint utility of the correspondence, resulting in an
exponential drop in correspondences disclosed and messages
exchanged as the threshold increases
23

Negotiating over Ontological Correspondences with Asymmetric and Incomplete Knowledge

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