PHIL012 Class Notes 1/12/2001. Outline Announcements, web page Names and Predicates Sentences,...
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Transcript of PHIL012 Class Notes 1/12/2001. Outline Announcements, web page Names and Predicates Sentences,...
PHIL012 Class Notes
1/12/2001
Outline
• 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 World
“Name1” Object1
“Name2” 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.
Language World
“The Morning Star”
“Venus”
“The Evening Star”
Good
Bad
Language World
“John”
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”
• 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.
“Arities”of Predicates in Tarski’s World
Names and PredicatesLanguage 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)
• 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