Sentence

is either:

• AtomicSentence
• ¬Sentence
• Sentence BinaryLogicalConnective Sentence
• Quantifier Variable, … Sentence

AtomicSentence

Predicate(Term, …)

Term

is either:

• Function(Term, …)
• Constant
• Variable

BinaryLogicalConnective

is either: (↔ - iff), (→ - implies), (∧ - and), (v - or)

Quantifier

∀𝑥 - universal quantifier

• ∀𝑥Predicate(𝑥) means that Predicate holds for ALL values of 𝑥 in the domain associated with that variable
• e.g. ∀𝑥 dolphin(𝑥) → mammal(𝑥)

∃𝑥 - existential quantifier

• ∃𝑥Predicate(𝑥) means that Predicate holds for SOME value of 𝑥 in the domain associated with that variable
• e.g. ∃𝑥 mammal(𝑥) → lays-eggs(𝑥)

Constant

represents objects in the world, such as: 𝐴, 𝑋₁, 𝐽𝑜ℎ𝑛

Variable

denoted as lowercase letters, such as: 𝑎, 𝑥, 𝑓𝑜𝑜

Predicate

• maps objects to boolean values
• is a Function that returns true or false, such as:
  • President(Obama, America) # was true, now false
  • President(Marcus, America) # false

Function

• does not return a boolean value
• specifies what a particular object is such as:
  • Human(Obama)
  • Mother(Anna)
• maps objects to objects
  • father-of(Mary) = John
  • color-of(Sky) = Blue