Ontology

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Ontology
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Overview

• Knowledge bases, ontologies, and axioms
• Collections and structural relationships
• Basics of ontology design

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Examples of Ontologies

• Domains in databases
• Classes in OO programming
• Types in AI and Logic

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Some working definitions

• Ontology a theory of the kinds of things there
  are and can be (WHAT CAN EXIST)
• Manifests in a representation by the vocabulary
  of predicates and certain relationships between
  them (often called structural relations)
• Knowledge Base ontology axioms (WHAT DOES
  EXIST)
• Axioms essential to constraining meaning towards
  intended models
• Domain Theory KB control knowledge (HOW TO
  USE THAT KNOWLEDGE)
• Control knowledge makes the KB usable for various
  tasks

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Allegory of the Cave

• Ontology spans the cave and everything able to be
  experienced outside
• Knowledge Base includes only items that have been
  experienced
• Domain Theory does not allow for direct knowledge
  transfer. Hence communication is limited

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Human Ontologies

• What we created/use
• What we live

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Microworlds

• Limited domain
• Closed set
• B2B Integration

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Some specifics
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Continuants and Occurrents

• Continuant
• Stable properties/differentiates
• Occurrents
• In a state of flux
• Attributes may be analogous to prior versions,
  but they are not the same

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Individuals vs. Collections

• Individuals are things that arent sets or
  collections
• TheEiffelTower, NeilArmstrong, Dog32
• Collections are natural kinds or classes whose
  elements share important natural properties, i.e.
  some common attributes or relational
  commonalities.
• Tower, Astronaut, Dog
• Sets (as in the mathematical sense) have elements
  that might not have anything in common.

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Some distinct types of individuals

• Discrete objects
• Cut them up and you get something different
• Cars, people
• Substances
• Cut them up and you get more of the same
• Water, sand
• Mobs
• Like substance, but worth reifying particular
  elements
• Mountains in a range, feathers on a bird
• Events
• Something happening over time with substructure
• Processes
• Something happening over time that is internally
  uniform

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Collections

• Collections approximate categories
• Dog is the collection of all dogs
• The following are equivalent
• (Dog Dog32)
• (member Dog32 Dog)
• (isa Dog32 Dog)
• Comparison with psychological notion of category
• Typically no compact definition
• Organized via taxonomic relationships
• But no similarity effects, recognition criteria,
  exemplar-driven effects

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Inheritance from collections

• Collection membership supports inference
• (forall ?x
• (gt(elephant ?x)
• (exists ?t
• (and (elephant-trunk ?t)
• (physical-part ?x ?t)))))
• Inheritance generally treated as monotonic
• (forall ?x(gt(elephant ?x)(grey ?x))
• (and (elephant Clyde)(pink Clyde))

Whats This?
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Structural relations express common
representation patterns

• Genls
• Disjointness and partitions
• Type constraints on arguments

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Genls

• (genls ltsubgt ltsupergt) means
• (forall ?x(gt(ltsubgt ?x)(ltsupergt ?y)))
• (subset ltsubgt ltsupergt)
• genls is transitive
• Attribution/collection membership distributes
  across genls
• (gt (and (elephant Clyde)
• (genls elephant mammal)
• (genls mammal animal))
• (animal Clyde))

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Disjointness

• Taxonomic relationships support inference via
  exclusion
• Ex (elephant Clyde)
• (disjointWith animal plant)
• ? (not (plant Clyde))

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Type constraints on arguments

• Restrictions on types of arguments in a predicate
  are extremely common
• Ex
• (forall (?x ?y ?z)
• (gt (fluid-connection ?x ?y ?z)
• (and (fluid-path ?x) (container ?y)
  (container ?z))))
• Can express compactly by statements about reified
  collections that make intent clearer
• Ex
• (arg1-isa fluid-connection fluid-path)
• (arg2-isa fluid-connection container)
• (arg3-isa fluid-connection container)

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Building an Ontology
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Top-Down vs. Bottom-Up

• Philosophers tend toward Top-Down
• Programmers tend toward Bottom-Up (sort of)

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Ontology and KB Design

• Motivations for the design and use of an
  ontology
• Sharing information about the structure of
  information.
• Reuse of domain knowledge
• Making domain assumptions explicit and changeable
• Separation domain knowledge from operational
  knowledge
• Analysis of domain knowledge

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Designing a knowledge base

• Before you start
• What is the domain you are trying to model?
• How will the knowledge base be used? And by whom?
  
• Is there an existing underlying ontology, or do
  we start from scratch?

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Designing a knowledge base

• Concepts and structure
• What are the important concepts of your domain?
• How are they related?
• Are they individuals, collections? What are the
  sub- and super-classes for collections?

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Designing a knowledge base

• Axioms
• What is important about a particular concept?
• What makes it what it is (and not something
  else)?
• What consequences arise from it?

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The Cyc Upper Ontology
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Example Part-whole relationships
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Example Intangible Things and Individuals
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Common Mistakes

• Dont confuse individuals with collections
• Car is a collection, Car54 is an individual
  Depending on the level of detail used in your
  knowledge base, Car might have subclasses
• Car -gt PassengerCar -gt Sedan
• Avoid cycles in collection hierarchies
• Subclasses are transitive
• Sedan is a subclass of Car
• Dont make Car a subclass of Sedan!

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Common Mistakes

• Dont assign too much meaning to concept names
• TouristAttractionsInChicagoThatDoNotChargeAdmissio
  nOnTuesdays is a bad concept name
• Chair as an isolated concept, without being a
  sub-or superclass of another concept and without
  any axioms, does not say anything about chairs.
• Concept names and their denotations are not
  necessarily the same.

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Common Mistakes

• Too many/too few subclasses
• Dont squeeze too many subclasses into a concept,
  dont stretch the hierarchy unnecessarily.
• More than a dozen subclasses might indicate the
  need for additional intermediate concepts.
• A single subclass is a sign of a modeling
  problem (or simply unnecessary).

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Common Mistakes

• Disjoint concepts
• Partitioning the ontology via disjoint concepts
  is useful for reasoning. But be careful!
• (disjointWith Dog Thing) is unwise

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Ontology What is there?Answer Everything

• Willard Van Orman Quine