A hybrid model of automatic indexing based on paraconsistent logic

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• A hybrid model of automatic indexing based on
  paraconsistent logic
• Carlos Alberto Correa (University of São Paulo)
• Nair Yumiko Kobashi (University of São Paulo)

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Preliminary considerations...

• The aim of the paper is to argue the theoretical
  potential in order to use a non-classical logic
  in hybrid models of automatic indexing.
• This study is justified by
• the use of other non-classical logic in this
  context as, for example, fuzzy logic
• the use of theories that enable to cope with
  uncertainty, imprecision an vagueness as, for
  example, Dempster-Shafer theory.

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• Summary
• Indexing and automatic indexing
• An introduction to paraconsistent logic
• Automatic indexing and Paraconsistent logic
• Conclusions

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• Summary
• Indexing and automatic indexing
• An introduction to paraconsistent logic
• Automatic indexing and paraconsistent logic
• Conclusions

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• A chart to synthesize the importance and the
  influences in automatic indexing...

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Information organization
Space Vector model
Information Visualization
Statistic
Information analysis
Linguistic
Indexing/ Automatic indexing
Hybrid models
Fuzzy logic
Similarity measures
Knowledge domain visualization
Information retrieval
Dempster Shafer theory
Other influences
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• Indexing and automatic indexing
• An introduction to paraconsistent logic
• Automatic indexing and Paraconsistent logic
• Conclusions

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Paraconsistent Logic

• Classical logic is based on three principles...
• Identity every object is identical to itself
• Non-contradiction a proposition can not be true
  and false at the same time
• Excluded middle a proposition is true or false
  an there is not another possibility

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Paraconsistent Logic

• Paraconsistent logic suppresses the principle of
  non-contradiction.
• So, it...
• tolerates the existence of contradictory
  propositions
• develops methods similar to those of classical
  logic, as a basis for developing theories and
  calculations where the phenomenon of
  contradiction occurs
• enables the development of methods to provide the
  treatment of uncertainty, imprecision and
  vagueness.

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Paraconsistent Logic

• Annotated paraconsistent logic is a variation of
  original paraconsitent logic. It...
• attributes two variables to a proposition,
  ranging in the interval 0,1 the degrees of
  belief and unbelief

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Paraconsistent Logic

• The approach of annotated paraconsistent logic...
• makes possible to establish four logical states
  (true, false, inconsistent and indeterminate )
  instead of the two of classical logic (true and
  false)
• establishes the logical states based on the
  values of a pair of variables (µ1, µ2), the
  degrees of belief and unbelief.

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Paraconsistent Logic

• Example of the relations between the degrees of
  belief and unbelief - (µ1, µ2), and the four
  logical states.
• (1,0) means total belief and absence of unbelief
  true
• (0,1) means absence of belief and total unbelief
  false
• (1,1) means total belief and total unbelief
  inconsistent
• (0,0) means absence of belief and total unbelief
  indeterminate.
• Others values in the interval of 0,1 can be
  assingned, allowing the stablishment of
  intermediate states to the four previously
  defined.

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1. Indexing and automatic indexing
2. An introduction o paraconsistent logic
3. Automatic indexing and Paraconsistent logic
4. Conclusions

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Paraconsistent logic and automatic indexing

• Fuzzy logic and Dempster-Shafer theory, in the
  context of automatic indexing, establish a
  function to determine the degree of aggregation
  of one or more terms and the document where it
  occurs. These functions are named as membership
  function (fuzzy logic) and belief function
  (Dempster-Shafer theory).
• What about the dissociation of a term ?

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Paraconsistent logic and automatic indexing

• Making some questions...
• What about the dissociation of a term ?
• What about the unbelief of a term ?
• Here is the potential usage of paraconsistent
  logic...

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Paraconsistent logic and automatic indexing

• In annotated paraconsitent logic is possible a
  variable for the degree of belief (or
  aggregation) and a variable for the degree of
  unbelief (or dissociation) for one proposition.
• Lets consider, for example, the proposition pt
  the term t is a good term for index the document
  D.
• Is possible to assign values for µ1 and µ2,
  determined by some calculation or heuristic and
  then establish precisely how the proposition is
  close to one of the four logical states.
• This systematic enables to establish the
  usefulness of term t taking into account two
  variables instead of one.

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Final considerations...

• It is believed that the use of two variables
  the degrees of belief and unbelief will enable
  the development of a indexing systematic that
  enhance the effetiveness of retrieval and
  visualization of information.
• The tests of the model will be done using an
  information visualization system developed at
  University of São Paulo.