Using Preferences in Negotiations over Ontological Correspondences

Using preferences in Negotiations over Ontological

Correspondences

Terry Payne & Valentina TammaUniversity of Liverpool

[email protected]@liverpool.ac.uk

Using preferences in Negotiations over Ontological CorrespondencesTerry 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?

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Alignment

Correspondence


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.

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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.

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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.

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Correspondence Inclusion Dialogue (CID)

• Assumptions1. 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

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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

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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.


Dialogue Moves

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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

rejectaccept

endassert

endassert

reject

endassert

endassert

assert

assert

join

join

object

object

Alice&Bob

3ABBob2B

Alice2A

Alice1A

Bob1B

Alice5A

Alice4A

Bob6B

Alice6A

Bob4B

object

object

Bob5B


Ambiguity and Objections

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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?


Finding an injective alignment?

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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).


⟨article, reviewedPaper,≣⟩ 0.45

⟨article, paper,≣⟩ 0.65

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• 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


⟨article, submittedPaper,≣⟩ 0.5

⟨publication, paper,≣⟩ 0.7

Using preferences in Negotiations over Ontological CorrespondencesTerry 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


⟨article, submittedPaper,≣⟩ 0.5

⟨publication, paper,≣⟩ 0.7 publication

article author


Using preferences in Negotiations over Ontological CorrespondencesTerry 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



• 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

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⌃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


• 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

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p c c





⌃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, 0.65iihBob, object, harticle, paper, 0.65i, harticle, submittedPaper, 0.5iihBob, object, harticle, paper, 0.65i, harticle, reviewedPaper, 0.45iihAlice, object, harticle, submittedPaper, 0.5i, harticle, reviewedPaper, 0.45ii

if ambiguous(c, c0), then (c =) ¬c0) ^ (c0 =) ¬c)


Modelling Objections

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p c c





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


a1, a4, a7 = {i, k, i $ ¬j, k $ ¬j, i $ ¬l}AL = {hpublication, paper,=i,

harticle, submittedPaper,=i}.


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

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Questions

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For other papers on this and our other related work:

http://www.csc.liv.ac.uk/~trp/Knowledge-Based-Agents.html

http://www.csc.liv.ac.uk/~trp/Knowledge-Based-Agents.html

Using Preferences in Negotiations over Ontological Correspondences

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