First Order Logic - FOL

Propositional logic is declarative but not expressive, hence we have First Order Logic (FOL), also called Predicate Calculus

Has quantifiers, universal ∀x (usually use ->), existential ∃x (usually use ^)

∃x ∀y is not the same as ∀y ∃x

∃x ∀y Loves(x,y)
“There is a person who loves everyone in the world”
∀y ∃x Loves(x,y)
“Everyone in the world is loved by at least one person”

∀x Likes(x,IceCream) = ¬∃x ¬Likes(x,IceCream)

kinship domain:
object are people
Properties include gender and they are related by relations
such as parenthood, brotherhood,marriage
predicates: Male, Female (unary)
Parent,Sibling,Daughter,Son...
Function:Mother Father

{a/Shoot} <- substitution