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
Using preferences in Negotiations over Ontological CorrespondencesTerry 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.
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Using preferences in Negotiations over Ontological CorrespondencesTerry 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.
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Using preferences in Negotiations over Ontological CorrespondencesTerry 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.
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Using preferences in Negotiations over Ontological CorrespondencesTerry Payne University of Liverpool
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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Using preferences in Negotiations over Ontological CorrespondencesTerry 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
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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.
Using preferences in Negotiations over Ontological CorrespondencesTerry Payne University of Liverpool
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
Using preferences in Negotiations over Ontological CorrespondencesTerry Payne University of Liverpool
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?
Using preferences in Negotiations over Ontological CorrespondencesTerry Payne University of Liverpool
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).
Using preferences in Negotiations over Ontological CorrespondencesTerry Payne University of Liverpool
⟨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
Finding an injective alignment?
⟨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
Finding an injective alignment?
⟨article, submittedPaper,≣⟩ 0.5
⟨publication, paper,≣⟩ 0.7 publication
article author
submittedPaper reviewedPaper paper editor
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
Finding an injective alignment?
Using preferences in Negotiations over Ontological CorrespondencesTerry 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
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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
Using preferences in Negotiations over Ontological CorrespondencesTerry 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
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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, 0.65iihBob, 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)
Using preferences in Negotiations over Ontological CorrespondencesTerry Payne University of Liverpool
Modelling Objections
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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}.
Using preferences in Negotiations over Ontological CorrespondencesTerry 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
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Using preferences in Negotiations over Ontological CorrespondencesTerry Payne University of Liverpool
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