1. Valentina Tamma
University of Liverpool
V.Tamma@liverpool.ac.uk
in collaboration with Ernesto Jimenez Ruiz, Terry Payne and
Alessandro Solimando
Avoiding Alignment-based
Conservativity Violations
through Dialogue
2. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
Open Systems and
Ontologies
• Agents (applications, devices, services) can
assume different ontological models
• Especially true in dynamic environments characterised by transient,
opportunistic transactions
• Collaborating agents need to be understood
• Not a problem if the agents all use the same ontology
• What happens when the ontologies differ?
• They need to be aligned!
2
3. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
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.
3
4. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
• Formal Inquiry Dialogue that…
• Allows two agents to exchange knowledge about correspondences
to agree upon a mutually acceptable final alignment A
• Aligns only those entities in each agents’ working fragments, without
disclosing the ontologies, or all of the known correspondences
Correspondence
Inclusion Dialogue (CID)
4
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.
5. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
• Extend the CID that…
• Allows two agents to exchange knowledge about correspondences
to agree upon a mutually acceptable final alignment A
• Aligns only those entities in each agents’ working ontologies, without
disclosing the ontologies, or all of the known correspondences
Correspondence
Inclusion Dialogue (CID)
5
6. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
• Extend the CID that…
• Allows two agents to exchange knowledge about correspondences
to agree upon a mutually acceptable final alignment A
• Aligns only those entities in each agents’ working ontologies, without
disclosing the ontologies, or all of the known correspondences
• Identify potential conservativity violations and extend the dialogue
to exchange repairs.
Correspondence
Inclusion Dialogue (CID)
5
7. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
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 static weight 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. The assertion of a new correspondence c is tested locally within the agent’s
ontology and A to check for conservativity violations
6
κc
8. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
7
Preliminaries
Ox
- ontology
Σx
- signature
Oˆx
- ontology
Σ
ˆx
- signature
• The dialogue incrementally creates an alignment with no conservativity
violation:
• set of correspondences establishing a logical relationship
between the entities in and those in
• Each correspondence c has a weight associated - - denoting the level of
confidence in the correctness of the correspondence
• Each agent maintains:
• a private correspondence store ∆ storing the correspondences and their
private weights
• a shared commitment store CS, with the trace of all the moves uttered by
each agent
r { , , }
Σx
Σ
ˆx
κc
9. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
• Dialogue made of a sequence of moves
• Agents take turns in asserting the admissibility of a
correspondence c and its associated weights
• Admissible responses to this assertions are:
• confirm the admissibility of c as is, without the need for any repair
• propose a possible repair to A to allow c to be added to A without
introducing any conservativity violations
• by weakening or removing an existing correspondence
• reject the assertion of c
The dialogue
8
10. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
• Dialogue made of a set of move types
M = {join, assert, acceptC, rejectC, repair, acceptR, rejectR, close}
The dialogue
9
ms = x, τ, c, κc, R , where:
• x is the agent making the move;
• τ M is the move type;
• c is the subject of the move;
• κc is either the personal or joint weight associated with c, 0 κc 1;
• R is a repair for correspondences within A or the correspondence c
11. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
• Agents assign a static weight to the correspondences they
know of.
• During the course of the dialogue:
• Agents are initially unaware of whether the other agent knows
the correspondence c being discussed and of the
corresponding weight assigned;
• By using the dialogue moves, the agents disclose the weight
they assign to the correspondence c if this is known;
• The dialogue forms consensus on the joint weight to assign to c,
based either on the individual weights or on the agents attitudes
Dealing with Weights
10
12. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
• Weights are aggregated considering their joint function:
Aggregating Weights
11
Avoiding Alignment-based Conservativity Violations through Dialogue 7
has not yet been disclosed to ˆx (c 2 x
; c /2 CS) and if ˆx
c has not been disclosed
by ˆx, then an upper bound x
u estimate is assumed (Case 3). The upper bound, x
u is
explained below.
Definition 2: The function joint : C 7! [0, 1] returns the joint weight for c 2 C:
joint(c) =
8
>>><
>>>:
avg(x
c , ˆx
c ) Case 1: c 2 x
ˆx
, c 2 CS
0 Case 2a: (sceptical) c /2 x
, c 2 CS
ˆx
c Case 2b: (credulous) c /2 x
, c 2 CS
avg(x
c , x
u) Case 3: c 2 x
, c /2 CS
Each agent takes turns to propose a correspondence, and the other participant con-
firms if the joint weight joint
c ✏. Proposals are made by identifying an undisclosed
correspondence with the highest weight x
c . As the dialogue proceeds, each subsequent
correspondence asserted will have an equivalent or lower weight than that previously
asserted by the same agent.
Whenever a correspondence is asserted, the agent should check that its estimated
joint weight est
c is not less than the admissibility threshold, ✏. Because the estimate is
13. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
• Weights are aggregated considering their joint function:
Aggregating Weights
11
Both agents know the
correspondence and have
disclosed their weights
Avoiding Alignment-based Conservativity Violations through Dialogue 7
has not yet been disclosed to ˆx (c 2 x
; c /2 CS) and if ˆx
c has not been disclosed
by ˆx, then an upper bound x
u estimate is assumed (Case 3). The upper bound, x
u is
explained below.
Definition 2: The function joint : C 7! [0, 1] returns the joint weight for c 2 C:
joint(c) =
8
>>><
>>>:
avg(x
c , ˆx
c ) Case 1: c 2 x
ˆx
, c 2 CS
0 Case 2a: (sceptical) c /2 x
, c 2 CS
ˆx
c Case 2b: (credulous) c /2 x
, c 2 CS
avg(x
c , x
u) Case 3: c 2 x
, c /2 CS
Each agent takes turns to propose a correspondence, and the other participant con-
firms if the joint weight joint
c ✏. Proposals are made by identifying an undisclosed
correspondence with the highest weight x
c . As the dialogue proceeds, each subsequent
correspondence asserted will have an equivalent or lower weight than that previously
asserted by the same agent.
Whenever a correspondence is asserted, the agent should check that its estimated
joint weight est
c is not less than the admissibility threshold, ✏. Because the estimate is
14. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
• Weights are aggregated considering their joint function:
Aggregating Weights
11
Both agents know the
correspondence and have
disclosed their weights
𝑥 has not yet disclosed
c and does not know
what is the other agent’s
weight for c
Avoiding Alignment-based Conservativity Violations through Dialogue 7
has not yet been disclosed to ˆx (c 2 x
; c /2 CS) and if ˆx
c has not been disclosed
by ˆx, then an upper bound x
u estimate is assumed (Case 3). The upper bound, x
u is
explained below.
Definition 2: The function joint : C 7! [0, 1] returns the joint weight for c 2 C:
joint(c) =
8
>>><
>>>:
avg(x
c , ˆx
c ) Case 1: c 2 x
ˆx
, c 2 CS
0 Case 2a: (sceptical) c /2 x
, c 2 CS
ˆx
c Case 2b: (credulous) c /2 x
, c 2 CS
avg(x
c , x
u) Case 3: c 2 x
, c /2 CS
Each agent takes turns to propose a correspondence, and the other participant con-
firms if the joint weight joint
c ✏. Proposals are made by identifying an undisclosed
correspondence with the highest weight x
c . As the dialogue proceeds, each subsequent
correspondence asserted will have an equivalent or lower weight than that previously
asserted by the same agent.
Whenever a correspondence is asserted, the agent should check that its estimated
joint weight est
c is not less than the admissibility threshold, ✏. Because the estimate is
15. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
• Weights are aggregated considering their joint function:
Aggregating Weights
11
Both agents know the
correspondence and have
disclosed their weights
𝑥 has not yet disclosed
c and does not know
what is the other agent’s
weight for c
𝑥 is sceptical, and has
no prior knowledge of c,
hence c is rejected
Avoiding Alignment-based Conservativity Violations through Dialogue 7
has not yet been disclosed to ˆx (c 2 x
; c /2 CS) and if ˆx
c has not been disclosed
by ˆx, then an upper bound x
u estimate is assumed (Case 3). The upper bound, x
u is
explained below.
Definition 2: The function joint : C 7! [0, 1] returns the joint weight for c 2 C:
joint(c) =
8
>>><
>>>:
avg(x
c , ˆx
c ) Case 1: c 2 x
ˆx
, c 2 CS
0 Case 2a: (sceptical) c /2 x
, c 2 CS
ˆx
c Case 2b: (credulous) c /2 x
, c 2 CS
avg(x
c , x
u) Case 3: c 2 x
, c /2 CS
Each agent takes turns to propose a correspondence, and the other participant con-
firms if the joint weight joint
c ✏. Proposals are made by identifying an undisclosed
correspondence with the highest weight x
c . As the dialogue proceeds, each subsequent
correspondence asserted will have an equivalent or lower weight than that previously
asserted by the same agent.
Whenever a correspondence is asserted, the agent should check that its estimated
joint weight est
c is not less than the admissibility threshold, ✏. Because the estimate is
16. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
• Weights are aggregated considering their joint function:
Aggregating Weights
11
Both agents know the
correspondence and have
disclosed their weights
𝑥 has not yet disclosed
c and does not know
what is the other agent’s
weight for c
𝑥 is sceptical, and has
no prior knowledge of c,
hence c is rejected
𝑥 accepts the belief of the
other agent on c since it is
credulous and has no prior
knowledge of c
Avoiding Alignment-based Conservativity Violations through Dialogue 7
has not yet been disclosed to ˆx (c 2 x
; c /2 CS) and if ˆx
c has not been disclosed
by ˆx, then an upper bound x
u estimate is assumed (Case 3). The upper bound, x
u is
explained below.
Definition 2: The function joint : C 7! [0, 1] returns the joint weight for c 2 C:
joint(c) =
8
>>><
>>>:
avg(x
c , ˆx
c ) Case 1: c 2 x
ˆx
, c 2 CS
0 Case 2a: (sceptical) c /2 x
, c 2 CS
ˆx
c Case 2b: (credulous) c /2 x
, c 2 CS
avg(x
c , x
u) Case 3: c 2 x
, c /2 CS
Each agent takes turns to propose a correspondence, and the other participant con-
firms if the joint weight joint
c ✏. Proposals are made by identifying an undisclosed
correspondence with the highest weight x
c . As the dialogue proceeds, each subsequent
correspondence asserted will have an equivalent or lower weight than that previously
asserted by the same agent.
Whenever a correspondence is asserted, the agent should check that its estimated
joint weight est
c is not less than the admissibility threshold, ✏. Because the estimate is
17. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
• Through the dialogue each agent extends their ontology by including
correspondences that facilitate communication with the other agent
• however the integrated ontology should not introduce any
change at least in the hierarchy of
• Incomplete knowledge about the other agent means the agents only
assess the changes introduced by
• Modify the repair mechanism by Solimando et al. to incrementally
check for violations as new correspondences are proposed
Repairs with
incomplete knowledge
12
Ox
A Oˆx
Ox
Ox
A
18. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
Repairs with
incomplete knowledge
13
A
• Repairs do not modify the ontologies but can only affect:
• a subset of the alignment being generated
• the correspondence
Alignemnt repair: Let A be the new set of correspondences A {c} where
c is a candidate correspondence and A is the current alignment w.r.t. Ox
for
which there is a conservativity violation. An alignment R A is a repair for
A w.r.t. Ox
iff there are no such violations in Ox
A R
19. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
Dialogue Moves
14
x asserts c for inclusion in A as it is the undisclosed correspondence with
the highest κc. If c causes a conservativity violation in A Ox
, then R contains
a repair plan either for either A or c.
Follows an assert. If κjoint
c ε and the repair was successful, then c is
accepted and the joint weight is shared.
Follows an assert. If κjoint
c < ε or a violation was subsequently found that
removes c from A then c is rejected.
Follows an acceptC when R applied on A has violations. repair communi-
cates to ˆx that c is acceptable if R is accepted and κjoint
c ε. The repair will not
be applied until ˆx accepts it.
x accepts the repair R for c and updates A. ˆx updates A
If x rejects R by weakening or removeing a mapping deemed necessary,
then it can reject the repair, which will also result in c being rejected
Moves Description
assert
acceptC
rejectC
repair
acceptR
rejectR
20. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
Allowed sequences
15
assert
rejectC
acceptC
repair
acceptR
Alice
5A
Bob
8B
Alice
3A
Bob
4B
Alice
7A
Bob
6B
rejectR
assert
rejectC
acceptC
repair
acceptR
rejectR
join
matched-close
join
Bob
2B
Alice
1A
matched-close
close
close
21. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
Example Dialogue
16
Public Knowledge
Private Knowledge
Alice asserts his next correspondence with the highest κc
b v a
c v a
Ontology
x ⌘ y
z v y
w
Ontology
ha, w, ⌘i Alice
c = 0.25
ha, x, ⌘i Alice
c = 0.9
hb, x, ⌘i Alice
c = 0.55
hb, y, ⌘i Alice
c = 0.4
hb, z, ⌘i Alice
c = 0.6
Correspondence Store Correspondence Store
ha, w, ⌘i Bob
c = 0.3
ha, x, ⌘i Bob
c = 0.85
hb, x, ⌘i Bob
c = 0.5
hb, y, ⌘i Bob
c = 0.55
hb, z, ⌘i Bob
c = 0.575
Commitment Store CS
Alice
ha,x,⌘i = 0.9 joint
ha,x,⌘i = 0.85
Bob
hb,y,⌘i = 0.7 joint
hb,y,⌘i = 0.55
Public Knowledge
Private Knowledge
Commitment Store CS
Alice
ha,x,⌘i = 0.9 joint
ha,x,⌘i = 0.85
Bob
hb,y,⌘i = 0.7 joint
hb,y,⌘i = 0.55
a
b c
x y
z
w
≣
⊑⊑
⊑
a
x
w
b
c
y
z
≣
≣hAlice, assert, hb, z, ⌘i, 0.6, ?i
22. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
Example Dialogue
17
Public Knowledge
Private Knowledge
Bob discovers a conservatively violation!!!
b v a
c v a
Ontology
x ⌘ y
z v y
w
Ontology
ha, w, ⌘i Alice
c = 0.25
ha, x, ⌘i Alice
c = 0.9
hb, x, ⌘i Alice
c = 0.55
hb, y, ⌘i Alice
c = 0.4
hb, z, ⌘i Alice
c = 0.6
Correspondence Store Correspondence Store
ha, w, ⌘i Bob
c = 0.3
ha, x, ⌘i Bob
c = 0.85
hb, x, ⌘i Bob
c = 0.5
hb, y, ⌘i Bob
c = 0.55
hb, z, ⌘i Bob
c = 0.575
Commitment Store CS
Alice
ha,x,⌘i = 0.9 joint
ha,x,⌘i = 0.85
Bob
hb,y,⌘i = 0.7 joint
hb,y,⌘i = 0.55
Public Knowledge
Private Knowledge
Commitment Store CS
Alice
ha,x,⌘i = 0.9 joint
ha,x,⌘i = 0.85
Bob
hb,y,⌘i = 0.7 joint
hb,y,⌘i = 0.55
a
b c
a
x
w
b
c
y
z
x y
z
w
≣≣
⊑⊑
⊑
≣
hAlice, assert, hb, z, ⌘i, 0.6, ?i
As Bob has the axiom z v y, the
inclusion of b ⌘ y and b ⌘ z would
infer: y v z (similarly for x v z)
a
x
w
b
c
y
z
≣
≣
23. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
Example Dialogue
18
Public Knowledge
Private Knowledge
Bob suggests a repair by weakening the alignment
between b and y
b v a
c v a
Ontology
x ⌘ y
z v y
w
Ontology
ha, w, ⌘i Alice
c = 0.25
ha, x, ⌘i Alice
c = 0.9
hb, x, ⌘i Alice
c = 0.55
hb, y, ⌘i Alice
c = 0.4
hb, z, ⌘i Alice
c = 0.6
Correspondence Store Correspondence Store
ha, w, ⌘i Bob
c = 0.3
ha, x, ⌘i Bob
c = 0.85
hb, x, ⌘i Bob
c = 0.5
hb, y, ⌘i Bob
c = 0.55
hb, z, ⌘i Bob
c = 0.575
Commitment Store CS
Alice
ha,x,⌘i = 0.9 joint
ha,x,⌘i = 0.85
Bob
hb,y,⌘i = 0.7 joint
hb,y,⌘i = 0.55
Public Knowledge
Private Knowledge
Commitment Store CS
Alice
ha,x,⌘i = 0.9 joint
ha,x,⌘i = 0.85
Bob
hb,y,⌘i = 0.7 joint
hb,y,⌘i = 0.55
a
b c
a
x
w
b
c
y
z
x y
z
w
≣≣
⊑⊑
⊑
≣
hBob, repair, hb, z, ⌘i, 0.575, {hb, y, wi}i
a
x
w
b
c
y
z
≣
≣
Either b ⌘ y or b ⌘ z should be weakened!
As joint
hb,y,⌘i < joint
hb,z,⌘i, Bob suggests a repair
that weakens b ⌘ y by removing b w y,
leaving the correspondence b v y
24. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
Example Dialogue
19
Public Knowledge
Private Knowledge
Alice accepts the repair, and the knowledge bases are
updated
b v a
c v a
Ontology
x ⌘ y
z v y
w
Ontology
ha, w, ⌘i Alice
c = 0.25
ha, x, ⌘i Alice
c = 0.9
hb, x, ⌘i Alice
c = 0.55
hb, y, ⌘i Alice
c = 0.4
hb, z, ⌘i Alice
c = 0.6
Correspondence Store Correspondence Store
ha, w, ⌘i Bob
c = 0.3
ha, x, ⌘i Bob
c = 0.85
hb, x, ⌘i Bob
c = 0.5
hb, y, ⌘i Bob
c = 0.55
hb, z, ⌘i Bob
c = 0.575
Commitment Store CS
Public Knowledge
Private Knowledge
Commitment Store CS
a
b c
a
x
w
b
c
y
z
x y
z
w
≣≣
⊑⊑
⊑hAlice, acceptR, hb, z, ⌘i, 0.575, nil, nili
Alice
ha,x,⌘i = 0.9 joint
ha,x,⌘i = 0.85
Bob
hb,y,⌘i = 0.7 joint
hb,y,⌘i = 0.55
Alice
hb,y,⌘i = 0.6 joint
hb,y,⌘i = 0.575
Alice
ha,x,⌘i = 0.9 joint
ha,x,⌘i = 0.85
Bob
hb,y,⌘i = 0.7 joint
hb,y,⌘i = 0.55
Alice
hb,y,⌘i = 0.6 joint
hb,y,⌘i = 0.575
≣
⊑
25. Avoiding Alignment-based Conservativity Violations through Dialogue
Valentina Tamma
University of Liverpool
Conclusions
• We extended the CID to include the incremental check and
repair for conservativity violations
• introduced a modified notion of repair to account for the agents’ incomplete
knowledge about the other agent’s ontology
• Our dialogue enables two agents to selectively disclose private
correspondences given their perceived correctness.
• Ambiguous correspondences are only permitted when they do
not introduce conservativity violations for each agent’s ontology
in isolation
• Next step full evaluation of the approach and extension to other
types of violations
20
