Data Integration using Argumentation

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Data Integration using Argumentation

• Shekhar Pradhan
• Marist College
• shekhar.pradhan_at_marist.edu

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Two Integration Perspectives

• Integrating data from different sources to answer
  a query which cannot be answered by a single
  source.
• E.g., Tsimmis, Hermes, Information Manifold, etc.
• Integrating data, possibly from different
  sources, to determine how much confidence should
  be placed in an answer to a query.
• E.g., Argumentation databases (ICLP, 03).
• We will call this credibility integration.

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Universe of Information
p1c1
p2c2
p5c5
p7c7
p3c3
p6c6
pc4

• Confidence value may depend on
• the certainty associated with the information by
  a source
• perceived reliability of the source on a given
  topic
• the probability of the information being true.

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Universe of Information with support and attack
relationships
p1c1
p2c2
p5c5
p7c7
p3c3
p6c6
pc4
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Credibility Integration
Credibility integration of information is the
process by which the confidence value associated
with information is adjusted taking into account
all the information that is relevant to this
information through the relationships of support
and attack.
Example How much confidence should be placed in
the claim that Cat Stevens is a terror threat to
the US taking into account all the evidence for
and against the claim and all the evidence for
and against the claims that are used to provide
evidence for or against, and so on.
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Decisions

• What should confidence values (c-values)
  represent?
• What sort of relation among information should
  count as a
• a supporting relation
• an attacking relation?
• What policies should be adopted for adjusting the
  confidence value of p taking into account
• the information supporting p?
• the information attacking p?
• How should supporting and attacking relations be
  represented?

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C-values as probabilities

• Advantage Probability calculus is
  well-understood.
• Problems
• A person may not have the relevant information to
  determine probabilities.
• May not have a way of determining conditional
  probabilities given some relevant information.
• Confidence of x in p should not imply a
  confidence of 1-x in not p.
• But probability calculus forces this.

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C-values

• Relative to a user or a community of users of the
  information.
• A c-value expresses the degree of confidence that
  a person has in the information being true.
• C-values in this sense can be distinguished from
  probability values (ask any gambler).
• But rational agents do not have a higher
  confidence than warranted by probability.

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Representing confidence values

• A lattice of values.
• No-Confidence High-Confidence
• The set of real numbers between 0.0 and 1.0 with
  the usual ordering.
• Must not assume that these numbers are anything
  more than an ordered set of labels.
• Question what constraints should be satisfied by
  c-values for them to represent (subjective)
  probabilities.
• How should such subjective probabilities be
  combined with objective probabilities (i.e.,
  reliability of an information source).

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Supporting Relations

• What sort of relations should count as supporting
  relations?
• Corroboration Two or more sources making the
  same claim independently.
• Evidence One or more claims providing evidence
  for another claim.
• these claims can be made by the same source or
  different sources.
• Evidence relations can be cast as arguments.

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Attacking relations

• A claim p can be considered as an attack on a
  claim q if it diminishes the confidence one has
  in q.
• These claims can be made by the same source or
  different source.
• There can be degrees of attacks.
• There can be attack thresholds.
• How confident does one have to be in p for it to
  be permitted as an attack on q.

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Representing supporting relations

• Supporting relations can be represented in terms
  of rules using the language of annotated logic
  programming (V.S. Subrahmanian).

• Corroboration pf1(v1, v2) ? pv1S1, pv2,S2.

• Evidence pf2(v1, v2) ? qv1X, rv2,Y.

• Inferences can be made in terms of these rules
  and appropriate facts.

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Representing Attack Relations

• A tuple consisting of the attacking statement,
  the attacked statement, the threshold of attack
  and the degree of attack.

• One way of understanding the degree of attack is
  the extent to which it should diminish confidence
  in the attacked statement, if the attack is
  successful.

• And one way of understanding that is that a
  successful attack of degree v puts a cap of v on
  the attacked statement.

• Should two independent attacks on the same
  statement considered jointly be regarded as of a
  stronger degree than each taken separately?
• If yes, then we need policies for merging
  degrees of attacks.

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Attacking Arguments

• An attacking statement can be supported by an
  argument, A.
• A can be viewed as an argument against the
  statement being attacked.
• But A can itself be attacked by another argument,
  and so on.
• Thus, there can be an interacting set of
  arguments, each of which can potentially change
  the c-value of some statement.
• We need a way of computing the effect of all
  these interacting arguments on the c-value of
  some statement.

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Example

• Claim p Cat Stevens is a terror threat to the
  USA.

• Argument for the claim based on the claims that
  he is a convert to Islam and he is a supporter of
  Hamas. Confers a c-value of 0.7 on p.

• Attack on p of degree 0.2 by q with threshold
  0.8, where q C.S. is a man of peace.

• Supporting argument (for q) based on the claim
  that he is a peace activist and a critic of
  terrorism. Confers a c-value of 0.9 on q.

• Attack on q of degree 0.4 by r with threshold
  0.7, where r C.S. supported the fatwa against
  Rushdie.

• Assume that the arguments for p, q, and r taken
  by themselves establish them with c-values 0.7,
  0.9, 0.7, resp. What c-value should p have,
  taking into account all the interacting
  arguments?

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Contested Annotated Logic Program

• Argumentation Databases (ICLP, 03) describes an
  operational semantics for theories (CALP)
  consisting of facts and rules annotated with
  c-values and attack relations (called
  contestations).

• Attack relations are compiled into rules.

• A complete lattice of interpretations for a
  compiled theory is described.

• A monotonic operator that computes all the
  immediate consequences of the compiled theory
  relative to an interpretation is specified.

• Any annotated sentence in the lfp of this
  operator is a consequence of theory and its
  c-value annotation represents the effect of all
  the interacting arguments.

• Based on this semantics we give a bottom-up
  procedure for computing the effect of interacting
  arguments.

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Architecture Argumentation Databases
Contains Corroboration and Evidence rules and
attack relations.
Argumentation Manager
Query
Answer to queries
Queries
Mediator
sub-query
sub-query
sub-query
Wrapper
Wrapper
Wrapper
DB 1
DB 2
DB 3
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Argumentation Manager

• Contains the annotated rules and the
  contestations (attack relations).
• Provided with the capacity for managing a mini
  database, which is initially empty.
• Equipped with backward (top-down) and forward
  (bottom-up) inferencing mechanisms.
• Contains knowledge about the schema in the
  mediator.
• Communicates with the mediator by sending queries
  and receiving answers to queries.

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The Query Answering Process

• The initial query is translated by the AM into
  logic programming notation.

• The rules and contestations relevant to
  answering the query are determined.

• The contestations are compiled into the rules.

• Using top-down inferencing, the original query
  is transformed into a set of queries that can be
  sent to the mediator.

• The tuples needed to answer the query from the
  underlying DBs are retrieved by sending these
  queries to the mediator.

• The initial c-values to be assigned to the
  tuples are determined.

• Using bottom-up inferencing mechanism on the
  annotated rules and using the annotated tuples as
  facts, the annotated answers to the initial query
  are determined.

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Conclusions

• Proposed a type of integration of information
  that consists in modifying the degree of
  confidence in some information taking into
  account all the information relevant to that
  information.
• Relevance has been understood in terms of
  relations of support and attack.
• Briefly described our work on contested annotated
  logic programs and argumentation databases.