PHIL012 Class Notes

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PHIL012 Class Notes

• 1/12/2001

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Outline

• Announcements, web page
• Names and Predicates
• Sentences, claims, and truth value
• Atomic sentences
• Homework Problems
• Assignment for Monday (1/15)

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Names

• A name in a formal language refers to an object
  in the world.
• In FOL the object must exist. That is, every
  name must refer to an actual object.

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Language
World
Name1
Object1
Name2
Object2
Pegasus
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Names Continued

• No Name can name more than one object.
• In other words, every name must have a unique
  reference.
• Or, every name in FOL must be a rigid
  designator.
• An object can have more than one name or even be
  unnamed.

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Good
Language
World
The Morning Star
The Evening Star
Venus
7
Bad
Language
World
John
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Predicates

• Predicates in FOL refer to properties of objects
  in the world or relations between objects.
• Examples of Predicates
• IsBlue or simply Blue
• IsMarriedTo or simply Married
• CantStandBrittanySpears or simply
  BrittanyHater

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Arity

• Each predicate refers to a fixed number of
  objects.
• In other words, each predicate will take a fixed
  number of names as arguments or parameters.
• We refer to the number of arguments a predicate
  takes as its arity
• Note that this is not the same thing as an
  argument made up of sentences that makes a claim.

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Aritiesof Predicates in Tarskis World

• Arity 1 Cube, Tet, Dodec, Small, Medium, Large
• Example Cube(a) - a is the name of an object
  that has the property of being a cube.
• Arity 2 Smaller, Larger, LeftOf, RightOf,
  BackOf, FrontOf
• Example Smaller(a,b) - This says that an object
  named by a is smaller than an object named by
  b

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Aritiesof Predicates in Tarskis World

• Arity 3 Between
• Example Between(a,b,c) - An object named by a
  is between objects named by b and c.
• Remember Predicates must have a precise meaning
  in FOL.

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Names and Predicates
Language
World
Name
Object
Predicate
Property
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Sentences and Claims

• A sentence in FOL, like in English, makes a
  claim.
• A claim is a statement about a state of affairs
  in the world.
• Claims have truth value.
• That is, claims are either true or false.

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Claims and Truth Value

• A claim is true if it represents an actual state
  of affairs with regard to objects in the world.
  It is false if it does not.
• Consider the sentence expressing the claim Mary
  like Jim Likes(Mary,Jim).
• This sentence and this claim will be true just in
  case Mary actually does like Jim and false if she
  does not.

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Atomic Sentences

• An atomic sentence is a predicate followed by the
  correct number of names, such as Tet(a),
  Between(a,b,c), and Large(b).
• An atomic sentence is the simplest type of
  sentence that makes a claim.
• In other words, an atomic sentence is the
  smallest unit of FOL that can have a truth value.

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Homework Problems
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Assignment for Monday (1/15)

• Meet with your groups at least once.
• Read LFOL 2.4-2.7 if you havent already.
• Continue working LFOL probs. 2.1-2.10
• Work LFOL problems 2.11-2.17
• For practice, sample the exercises in chapter 1
  of Tarskis World