Ostensive Automatic Schema Mapping for Taxonomybased PeertoPeer Systems

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Ostensive Automatic Schema Mapping for
Taxonomy-based Peer-to-Peer Systems

• Yannis Tzitzikas and Carlo Meghini
• Instituto di Scienza e Tecnologie dell
  Informazione ISTI
• Consiglio Nazionale delle Ricerche CNR, Pisa,
  Italy

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Outline of the presentation

• Context and Problem
• One solution Ostensive Mapping
• Basic idea
• Formal Framework
• The Method/Protocol
• Application for Taxonomy-based Sources
• Ostensive Articulation and P2P Systems
• Concluding Remarks Further Research

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Context P2P systems that support semantic
retrieval services
Tzitzikas et al.ER2003, Tzitzikas et al.
CoopIS2003
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Integrated Global Access Requires Semantic
Articulation
Who is going to define these mappings ?

• Semantic articulation is laborious
• In the P2P paradigm it is even harder as
• No central control or authority
• Large number of participants
• The membership of the nodes is dynamic and
  unpredictable
• The fully heterogeneous conceptual models makes
  uniform global access extremely challenging.

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Approaches for Constructing Mappings State of
the Art

• Model Driven approaches
• Based on the similarity of names or structure
• Exploit dictionaries and user input

• Data Driven approaches
• Require two dbs with common objects
• They can be automated

• Current State
• Applicable if the objects are texts
• They are used to integrate two entire conceptual
  models
• They cannot produce mapping between queries.
• The game requires at least 3 players

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Two autonomous agents
We come in peace
Vettä, kiitos
No communication is possible
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The Method
The ostensive method
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Formal Framework
We view each source as a function
? P(Obj), Obj the set of stored objects
Let QN be the set of names (QN ?Q).
However this is not always possible as S is not
always an onto function (A ?? P(Obj))
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Approximate Naming Functions
Let (Q,??) be the ordering over queries (q ?q
if S(q) ? S(q')). qq if q ?q and q ?q ?
is a partial order over Q (the set of
equivalence classes induced by over Q).
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The Method
Consider two sources
and
Assume that
Objective find the relationships that are
extensionally valid in C.
What kind of mappings we want ?
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The Method (II)
The naming functions is all that we want
Suppose that Si wants to articulate a query qi
of Qi.
qi should be articulated as follows
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The Protocol for articulating a term or query qi
a12
gt Only two messages have to be exchanged
The sources can run this protocol for one,
several or all of its terms (or queries)
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Application to Taxonomy-based Sources

• We view a taxonomy-based source S as a quadruple
  S (T, ??, I, Q) where
• T is a finite set of names called terms, e.g.
  tomatoes, apples,
• ? is a reflexive and transitive binary relation
  over T called subsumption,
• e.g. apples ? foods
• I is a function IT? P(Obj) called interpretation
  where Obj is a finite set of objects, e.g.
  I(tomatoes) 1,2,
• Q is the set of queries defined by the grammar
  q t q ??q q?q ?q(q) where t is a term
  in T.

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Query Answering in Taxonomy-based Sources
The answer S(q) of a query q if defined as
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Naming Functions for Taxonomy-based Sources
QN All queries that do not contain negation
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Examples of Upper and Lower names
foods
apples
tomatos
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1
2
3
4
green
red
fruits
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Example
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Ostensive Mapping and P2P
What can we do if the domain of two peers is
disjoint ?
gt Reference Collections

• Each peer before joining the network has to index
  a small set of objects X
• It can then run the articulation protocol on
  this reference collection X.

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Ostensive Mapping Concluding Remarks

• It can be used in order to articulate both simple
  terms and queries
• It can be used in order to articulate only the
  desired terms/queries of a CM
• It can be implemented efficiently by a
  communication protocol
• The common domain of the peers is discovered
  during the run of the protocol
• Is independent of the nature of the objects(i.e.
  the objects may be images, audio, videos)

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Further Research

• Naming functions for other kinds of sources
• relational databases
• semi-structured databases
• Description Logics-based information sources
• Information Retrieval Systems
• Optimal algorithms for full articulation