Notes 8: Predicate logic and inference

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Notes 8Predicate logic and inference

• ICS 171 Fall 2006

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Propositional logic is not expressive

• Needs to refer to objects in the world,
• Needs to express general rules
• On(x,y) à clear(y)
• All man are mortal
• Everyone who passed age 21 can drink
• One student in this class got perfect score
• Etc.
• First order logic, also called Predicate calculus
  allows more expressiveness

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Semantics Models

• An interpretation satisfies a wff (sentence) if
  the wff has the value true under the
  interpretation.
• An interpretation that satisfies a wff is a model
  of that wff
• Any wff that has the value true under all
  interpretations is valid
• Any wff that does not have a model is
  inconsistent or unsatisfiable
• If a wff w has a value true under all the models
  of a set of sentences delta then delta logically
  entails w

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Example of models

• The formulas
• On(A,F1) ? Clear(B)
• Clear(B) and Clear(C) ? On(A,F1)
• Clear(B) or Clear(A)
• Clear(B)
• Clear(C)
• Possible interpretations which are models
• On ltB,Agt,ltA,floorgt,ltC,Floorgt
• Clear ltCgt,ltBgt

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Modeling a domain Conceptualization

• The kinship domain
• object are people
• Properties include gender and they are related by
  relations such as parenthood, brotherhood,marriage
  
• predicates Male, Female (unary)
  Parent,Sibling,Daughter,Son...
• FunctionMother Father

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