First, let’s address some pros and cons of propositional logic

• Propositional logic is declarative: pieces of syntax correspond to facts
• Propositional logic allows partial/disjunctive/negated information
• Propositional logic is compositional: e.g. $B_{1,1} \land P_{1,2}$ is derived from the meaning of $B_{1,1}$ and of $P_{1,2}$
• Meaning in propositional logic is context-independent
• However, propositional logic has very limited expressive power

First-Order Logic

While propositional logic assumes world contains facts, first-order logic(like natural language) assumes the world contains

• Objects
• Relations
• Functions

Some basic elements of first-order logic includes

• Constants (2, UCLA, people’s name, ...)
• Predicates (>, is brother of, ...)
  • return true or false
• Functions (sqrt, left leg of, ...)
• Variables
• Connectives ($\land,\lor, \neg,\implies,...$)
• Equality (=)
• Quantifiers ($\forall, \exist$)

Atomic Sentences