Restrictions in Protg

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Restrictions in Protégé
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Overview

• Types of restrictions
• The Protégé Reasoner
• Necessary and sufficient conditions
• Open World Reasoning

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Restrictions

• Describe a class of individuals
• Quantifier
• Existential (pizzas that have vegetable toppings)
• Universal (pizzas that only have vegetable
  toppings)
• Cardinality
• Pizzas have exactly one base
• hasValue
• Pizzas that have Italy as their country of origin
  (similar to existential)

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Existential and universal restrictions

• ? hasTopping MozzarellaTopping (hasTopping some
  MozzarellaToping)
• ? hasTopping MozzarellaTopping (hasTopping only
  MozzarelaTopping)

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Restrictions
Anomymous superclasses
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Some exercises

• Create a subclass of Pizza called NamedPizza, and
  a subclass of NamedPizza called MargheritaPizza
• Create two existential (some) restrictions on
  MargheritaPizza to specify that it has at least
  one MozzarellaTopping and one TomatoTopping
• Create AmericanaPizza by cloning and modifying
  the description of MargheritaPizza (adding an
  existential restriction for pepperoni topping)
• Create an AmericanHotPizza which is the same as
  AmericanaPizza but with additional
  JalapenoPepperTopping
• Create a SohoPizza which is similar to
  MargheritaPizza but with additional OilveTopping
  and ParmesanTopping

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The Protégé Reasoner

• Available in ontologies of OWL-DL (description
  logic)
• Validates hierarchy (creates the inferred
  hierarchy)
• Performs consistency checking

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Primitive and defined classes
CheeseTopping
CheesePizza
hasTopping
hasTopping
Pizza
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Universal restrictions

• ? hasTopping VegetableTopping (hasTopping only
  VegetableTopping)
• Only those individual whose hasTopping
  relationships are to members of the class
  VegetableTopping
• Or do not have any hasTopping relationships
  whatsoever!
• Create a VegetarianPizza (cheese or vegetable
  toppings) as a defined subclass of Pizza
• Classify (with Pellet 1.5) and see what happens

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Open World Reasoning

• Margherita and Soho have not been classified as
  VegetarianPizza
• Reasoning in OWL-DL is based on the Open World
  Assumption
• Non-existence cannot be assumed, it has to be
  stated explicitly
• Pizzas could have additional toppings
• Definitions need closure axiom (to say class has
  only the referred restrictions)

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Closure axiom
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More on closure axioms

• Create NonVegetarianPizza as subclass of Pizza,
  disjoint and complement of (not) VegetarianPizza
• Classify and check that American Hot and
  Americana are non vegetarian
• Create UnclosedPizza as subclass of NamedPizza
  with MozzarellaTopping and no closure axiom
• After classifying UnclosedPizza is neither
  vegetarian nor non vegetarian

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Cardinality restrictions

• Specify numeric attributes for restrictions
• min (at least)
• max (at most)
• exactly (exactly that amount)
• With different individuals
• Create a DoubleVeggyPizza that has at least two
  vegetarian toppings
• hasTopping min 2 VegetableTopping

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Summary

• Restrictions define classes of individuals
• Existential
• Universal
• Cardinality
• Classes can be primitive or defined
• The Reasoner classifies the class hierarchy
• In Open World Reasoning non-existence cannot be
  assumed