Reasoning in Circumscriptive Description Logics

1
Reasoning in Circumscriptive Description Logics

• Stephan Grimm
• FZI Research Center for Information
  Technologies

2
Outline

• NMR with Circumscriptive Description Logic
• Semantics of Circumscriptive DL
• Tableaux for Circumscriptive DL
• Outlook

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NMR in Circumscriptive Description Logic

• Circumscribed DL knowledge bases
• explicit minimisation of concept extensions

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Semantics of Circumscriptive DL

• Preference relation ltCP on Interpretations I
  (?I,? I)
• models of circCP(KB) are ltCP-minimal models of
  KB,i.e. the preferred models of KB w.r.t. CP.

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Reasoning with Circumscribed KBs

• Reasoning tasks in circumscriptive DL
• defined with respect to models of circCP(KB)
• Concept Satisfiability
• A concept C is satisfiable w.r.t.
  circCP(KB)if some model of circCP(KB)
  satisfies CI ? ?
• Subsumption
• C ? D holds w.r.t. circCP(KB) if CI ? DI
  holdsfor all models I of circCP(KB)
• Entailment
• circCP(KB) ? C(a) holds if a ? CI holdsfor
  all models I of circCP(KB)

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DL Tableaux and Preference Clashes
KB EUCity ? ?cur.Euro ? AbEUCity ,
EUCity(Berlin)

• tableaux algorithm constructs a model for KB
• tableaux branches represent (potential) models of
  KB
• clashes represent contradictions in KB
• eliminate non-preferred models by introducing
  additional preference clashes
• preference clashes indicate non-minimality

KB ? ?cur.Euro(Berlin) ?
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Preference Clash Detection

• collect positive assertions to minimised concepts
• freeze extensions of minimised concepts KB
  KB ? AbEUCity ? Berlin
• ensure minimalitycondition in KB
• KB ? (? AbEUCity ? Berlin) (?)
  new individual ?
• test KB for consistency KB is consistent
  ? B has a preference clash

8
Conclusion

• Summary
• Circumscriptive DL accounts for NMR
• Reasoning procedure extending classical DL
  tableaux by preference clashes
• Outlook
• Tableaux for circumscriptive ALCIOcurrently
  submitted work
• Extension to OWL as future step