Example of Multi-Use Ontology: Units and Measures

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Example of Multi-Use Ontology Units and Measures
Professor Richard Fikes
CS222 Winter 2001
Computer Science Department Stanford University
Knowledge Systems Laboratory, Stanford University
2/7/01
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Units and Measures

• Mathematical models of engineered systems
• Physical-Quantities
• E.g., 3 meters, 80 kilometers/hour
• Physical-Dimensions
• E.g., length, velocity, weight, time
• Units-Of-Measure
• E.g., meters, kilometers/hour
• Magnitudes
• E.g., scalars, vectors, tensors, and functions
  thereof

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Magnitude of a Quantity in a Unit

• Physical-Dimension
• Instance-Of Class
• Standard-Unit
• Slot-Cardinality 1
• Value-Type Unit-Of-Measure
• Unit-Of-Measure
• Instance-Of Class
• Unit-Dimension
• Slot-Cardinality 1
• Value-Type Physical-Dimension

• Physical-Quantity
• Instance-Of Class
• Quantity-Dimension
• Slot-Cardinality 1
• Value-Type Physical-Dimension
• Magnitude
• Instance-Of Class

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Unit

• (Deffunction Unit
• Unit is an associative commutative
  mapping of all pairs
• of units to units
• (and (gt (Instance-Of ?u1 Unit-Of-Measure)
• (Instance-Of ?u2
  Unit-Of-Measure)
• (Unit-Of-Measure (Unit ?u1
  ?u2)))
• ( (Unit ?u1 ?u2) (Unit ?u2
  ?u1))
• ( (Unit ?u1 (Unit ?u2 ?u3))
• (Unit (Unit ?u1 ?u2) ?u3))))

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Unit

• (Deffunction Unit
• Unit is a mapping of reals to units that
  has the algebraic
• properties of exponentiation
• (and (gt (Instance-Of ?u Unit-Of-Measure)
• (Instance-Of ?r Real-Number)
• (Unit-Of-Measure (Unit ?u
  ?r)))
• ( (Unit ?u 1) ?u)
• ( (Unit (Unit ?u ?r1) (Unit ?u
  ?r2))
• (Unit ?u ( ?r1 ?r2)))
• ( (Unit (Unit ?u1 ?u2) ?r)
• (Unit (Unit ?u1 ?r) (Unit
  ?u2 ?r)))))
• Example
• (Defobject Meter/Second (Unit Meter (Unit
  Second 1)))

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Magnitude of Physical Quantities

• (Deffunction Quantity-Magnitude
• The magnitude of a physical quantity in
  a given unit of measure
• (gt (and (Quantity-Magnitude ?q ?u ?m)
  (/ ?m ))
• (and (Instance-Of ?q
  Physical-Quantity)
• (Instance-Of ?u
  Unit-Of-Measure)
• (Instance-Of ?m Magnitude)
• ( (Quantity-Dimension ?q)
  (Unit-Dimension ?u)))
• (Deffunction The-Quantity
• The physical quantity with a given
  magnitude in a given unit of measure
• (ltgt (The-Quantity ?m ?u ?q)
  (Quantity-Magnitude ?q ?u ?m))
• E.g., (Debobject Real-Fast (The-Quantity
  10000 Meter/Second))
• (gt (Instance-Of ?q1 Physical-Quantity)
  (Instance-Of ?q2 Physical-Quantity)
• (ltgt ( ?q1 ?q2) (and
  (Quantity-Dimension ?q1 (Quantity-Dimension ?q2))
• 
  (gt (Instance-Of ?u Unit-Of-Measure)
• 
  (Unit-Dimension ?u (Quantity-Dimension ?q1))
• 
  (Quantity-Magnitude ?q1 ?u
  (Quantity-Magnitude ?q2 ?u))))))

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Example Definitions

• Length-Dimension
• Instance-of Physical-Dimension
• Standard-Unit Meter
• Length-Unit-Of-Measure
• Subclass-Of Unit-Of-Measure
• Unit-Dimension Length-Dimension
• Meter
• Instance-Of Length-Unit-Of-Measure
• Kilometer
• Instance-Of Length-Unit-Of-Measure
• 
  
• (gt (and (Instance-Of ?q1 Physical-Quantity)
• (Quantity-Dimension ?q1
  Length-Dimension))
• ( (Quantity-Magnitude ?q1 Kilometer)
• (/ (Quantity-Magnitude ?q1 Meter)
  1000)))