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PHIL012 Class Notes
1/12/2001
Outline
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Announcements, web page
Names and Predicates
Sentences, claims, and truth value
Atomic sentences
Homework Problems
Assignment for Monday (1/15)
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.
Language
“Name1”
“Name2”
World
Object1
Object2
“Pegasus”
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.
Good
Language
“The Morning Star”
“The Evening Star”
“Venus”
World
Bad
Language
“John”
World
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”
– “Can’tStandBrittanySpears” or simply
“BrittanyHater”
“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.
“Arities”of Predicates in Tarski’s 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”
“Arities”of Predicates in Tarski’s 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.
Names and Predicates
Language
World
Name
Object
Predicate
Property
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.
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.
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.
Homework Problems
Assignment for Monday (1/15)
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Meet with your groups at least once.
Read LFOL 2.4-2.7 if you haven’t 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 Tarski’s World