Read the summary and the most important questions on Computational Logics for AI

• 3 Propositional logic part

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• 3.2 Semanatics

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• Variable assignment σ_S

  
  A function that maps each variable x in V to an element of D :
  σ_S(x) in D

• 7 Nonmonotonic reasoning default logic

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• Legal reasoning - incomplete information

  Somebody is assumed innoncent unless their guilt has been proven

• Legal reasoning - rules with exceptions

  Criminal foreigners are expelled ecept when the foreigner is a political refugee

• Approchaces to nonmonotonic reasoning

  Default logic, autoepistemic logic and circumscription

• 7.1 Default logic

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• brid(x): flies(x)----------------------flies(x)

  If x is a bird and if it is consistent to assume that x flies, than conclude that x flies

• Difficulties of using classical logic

  • All possible preconditions should be listed
  • usage of the rull (before applied all preconditions should be true)

• Prototypical reaoning (def)

  
  Most instances of a concept have some property
  
  "typically, children have parents"
  child(x) : has-parents(x)
  __________________________
  has-parents(x)

• No-risk reasoning (def)

  
  Situations where a conclusion is drawn even if it is not hte most probably becuae another decision could lead to disaster
  
  "In absence of evidence to the contrary assume taht the accused is innocent"
  accused(x) : innocent(x)
  -------------------------------------
  innocent(x)

• A set of formulas Φ is called deductively closed

  
  
  Φ = TH(Φ) = {F | Φ |= F }
  
  
  
  Een set formules Φ is deductief gesloten als elke formule die volgt uit Φ, ook in Φ zit. Dit betekent dat Φ dezelfde formules bevat als de verzameling die wordt afgeleid uit Φ.

• 7.2 Operational semantics of default logic

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• A set of formulas in an extension if

  There is some closed and succesful proces Π of T such that set of formulas is IN( Π)