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- Introduction:
- Terms represent specific objects in the world and can be constants, variables or functions.
- Predicate Symbols refer to a particular relation among objects.
- Quantifiers and Variables allow us to refer to a collection of objects without explicitly naming each object.
- Functions allow us to refer to objects indirectly (via some relationship).
- Sentences represent facts, and are made of of Terms, Quantifiers and Predicate Symbols.
- Expressions:
- Predicates:
- Brother, Sister, Mother , Father
- Objects:
- Bill, Hillary, Chelsea, Roger
- Operations:
- Predicates:
- Facts:
- Father(Bill, Chelsea)
- Mother(Hillary, Chelsea)
- Brother(Bill, Roger)
- ~Father(Bill, Chelsea)
- Universal Quantification:
- For All:
- All Cats are Mammals.
- All Bill's Children are Hillary's too.
- Existential Quantification:
- There Exists:
- There exists an x, x is a Cat, and x is Mean.
- There exists an x, x's Father is Bill, and x's Mother is Hillary.
- Nested Quantification:
- All x and y, "x is y's Father" means "y is x's Child."
- All x, there exists a y, x Loves y. (Everybody loves y.)
- All x, x passes TOEIC test, or x is an English speaker.
- Example:
- Marcus was a man.
- Marcus was a Pompeian.
- All Pompeians were Romans.
- Caesar was a ruler.
- All Romans were either loyal to Caesar or hated him.
- Everyone is loyal to someone.
- Men only try to assassinate rulers they are not loyal to.
- Marcus tried to assassinate Caesar.
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