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Paraconsistent
Reasoning in Ontopedia

   http://psi.ontopedia.net/Dmitry_Bogachev
   http://psi.ontopedia.net/Ontopedia
Large-scale systems of assertions

• Any large-scale system of assertions modeling
  real world is inconsistent
• Inconsis...
Possible alternative: Paraconsistent logic



• Paraconsistent logic allows to make reasonable
  inferences inside of inco...
Ontopedia

•   PSI Server (http://psi.ontopedia.net)
Ontopedia

•   Inconsistency tolerant system of assertions populated by
    users (external systems, inference modules)
Ontopedia: Proposals

•   Each assertion can have multiple proposals from different
    sources with different truth value...
Ontopedia: Multivalued truth assignment

•   Each assertion has truth
    value:

    •   monotonic false

    •   default...
Ontopedia: Contradiction Level

•   Each assertion has contradiction level:

    •   no contradictions

    •   default co...
Ontopedia: Decision Procedure

•   Decision procedure tries to calculate truth value of an
    assertion based on existing...
Why




•   Paraconsistent reasoning allows to collect assertions from
    various sources and “safely” infer new informat...
Interested?

•   Take a look at Paraconsistent Logic

•   Learn about Carl Hewitt’s work (Actors, Planner,
    Organizatio...
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Open Space Session at TMRA 2009

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Paraconsistent Reasoning in Ontopedia

  1. 1. Paraconsistent Reasoning in Ontopedia http://psi.ontopedia.net/Dmitry_Bogachev http://psi.ontopedia.net/Ontopedia
  2. 2. Large-scale systems of assertions • Any large-scale system of assertions modeling real world is inconsistent • Inconsistency is the norm • With traditional logic: • if we have a contradiction, we can infer any assertion • Not very useful for modeling systems with large-scale number of assertions
  3. 3. Possible alternative: Paraconsistent logic • Paraconsistent logic allows to make reasonable inferences inside of inconsistent assertion systems • Many Paraconsistent logics are interesting puzzles • Some can be useful (I think so) • Direct Logic (Carl Hewitt)
  4. 4. Ontopedia • PSI Server (http://psi.ontopedia.net)
  5. 5. Ontopedia • Inconsistency tolerant system of assertions populated by users (external systems, inference modules)
  6. 6. Ontopedia: Proposals • Each assertion can have multiple proposals from different sources with different truth values • Proposals can be provided by: • people • external systems (scanning topic maps, RDF, REST API) • with (known mapping to) Ontopedia’s PSIs • inference modules (in future)
  7. 7. Ontopedia: Multivalued truth assignment • Each assertion has truth value: • monotonic false • default false • unknown • default true • monotonic true
  8. 8. Ontopedia: Contradiction Level • Each assertion has contradiction level: • no contradictions • default contradiction • monotonic contradiction • We can calculate contradiction level for topics, any fragment, and full knowledge base • In general, Ontopedia tries to keep contradiction level “under control” and minimize it when it is possible
  9. 9. Ontopedia: Decision Procedure • Decision procedure tries to calculate truth value of an assertion based on existing proposals • Decision procedure also calculates contradiction level • Result of decision procedure is “visible assertion” • New proposals can change truth value and/or contradiction level (non monotonic system) • Contradictions do not participate in future inferences • Engine can suppress some pervious inferences
  10. 10. Why • Paraconsistent reasoning allows to collect assertions from various sources and “safely” infer new information
  11. 11. Interested? • Take a look at Paraconsistent Logic • Learn about Carl Hewitt’s work (Actors, Planner, Organizational Computing, ORGs, Direct Logic) • db3000@mac.com

Open Space Session at TMRA 2009

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