Common Wisdom in Knowledge Representation

1
Common Wisdom in Knowledge Representation

• A body of formally represented knowledge is
  based on a conceptualization the objects,
  concepts, and other entities that are assumed to
  exist in some area of interest and the
  relationships that hold among them.
• -- (Genesereth Nilsson, 1987, my boldface)

2
Main Ideas

• Two important knowledge representation
  structures, classes and predicates, have more in
  common than it first appears.
• Indeed, these two structures might profitably
  unified under a single paradigm.
• This paradigm also has ties with the syntax and
  semantics of natural language.

3
A Common Way of Representing Nouns and Adjectives
big(x)
black(x)
hairy(x)
dog(x)
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Interesting Tendency with Nouns
animal
number
book
dog
shoe
5
and Adjectives
black
big
hairy
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Adjectives that Compete for the Same Attribute
purple
black
brown
blue
7
Strange Things Afoot

• A big dog is smaller than a small car.
• A dull razor is a sharp implement.
• People can be male or female integers cant (not
  strange, but relevant).

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Explanation
Hypothesis 1 An English noun invokes a schema,
which determines which attributes (adjective
groups) are appropriate, and equips each
attribute a distribution of normal and possible
values.
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Example of Class Specification

• class chihuahua
• attributes
• size normally 1-8 pounds, centering on 3-5
  pounds.
• color white to black, centering on orange-brown
• coat short to long, distributed bimodally
• sex male, female.

10
Parallels between English and Object Design
11
Verbs and Prepositions

• Hypothesis 2 Verbs and prepositions naturally
  lend themselves to formalization as logical
  predicates.
• Examples
• Tim gave the ball to Tom gave(tim, ball,
  tom).
• Tim is Toms brother brother(tim, tom).
• Tim is in Room 303 in(tim, room_303).

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Upshot
Two knowledge representation structures, classes
and predicates, together account fairly well for
the semantics of content words of English, as
well as most work in ontologies.
13
Minor Drawbacks in the Common Syntax for
Predicates

• parent_of(tim, tom) is semantically equivalent,
  but not syntactically equivalent, to
  child_of(tom, tim).
• brother_of(tim, tom) is semantically equivalent,
  but not syntactically equivalent, to
  brother_of(tom, tim).
• In predicates with many arguments, it is
  difficult to remember their order.
• Arity of predicates is fixed, making it
  cumbersome to introduce extra or optional
  arguments.
• These annoyances can be traced to the fact that
  our arguments have places rather than names,
  suggesting

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A Slight Variation

• Give arguments names instead of places!

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Example of Predicate Specification

• Predicate Gift Act
• Arguments
• donor person or agency
• gift any object
• recipient person or agency

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Possible Syntax

• gift_act(x), donor(x, tom), gift(x, ball),
  recipient(x, tim).
• offspring_relation(y), parent(y,tim),
  child(y,tom).
• brotherhood(z), member(z, tim), member(z, tom).

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Pros and Cons

• More characters to type ?.
• Eliminates artificial distinctions imposed by
  argument order.
• Allows higher order reasoning without higher
  order syntax.
• Hmmm looks familiar ?

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Example of Predicate Specification (again)

• Predicate Gift Act
• Arguments
• donor person or agency
• gift any object
• recipient person or agency

19
Example of Class Specification (again)

• class chihuahua
• attributes
• size normally 1-8 pounds, centering on 3-5
  pounds.
• color white to black, centering on orange-brown
• coat short to long, distributed bimodally
• sex male, female.

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Parallels Between Classes and Predicates

• Classes have
• attributes,
• attribute types,
• objects,
• existence.

• Predicates have
• arguments,
• a domain,
• facts,
• truth.

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A Schema for Schemata

• Schemata have
• slots (required and optional),
• allowed values,
• instances,
• satisfaction.

22
Another Possible Syntax

• gift_act x
• x.donor tom
• x.gift ball
• x.recipient tim

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person tom, tim offspring_relation y y.parent
tom y.child tim
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• person tom, tim
• brotherhood z
• membership x1
• x1.set z
• x1.member tim
• membership x2
• x2.set z
• x2.member tom

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Potential Windfalls

• Shared understanding of multiple forms of
  knowledge representation.
• Shared syntax for object oriented and logic
  programming (and semantic networks).
• Ontologies have only one type of basic element.
• Softens mental blocks to other uses of schemata
  (scripts, etc.).