While propositional logic assumes the world contains facts, first-order logic assumes the world contains objects, relations, functions, like natural language.
Syntax Constants: Poly, 2, refer to objects Predicates: brother, larger than, refer to relations functions: sqrt, refer to functional relations variables: x, y connectives: ^ $\Rightarrow$ equality: = quantifiers: $\exists$, $\forall$ Sentences atomic sentence = predicate(term1, …, termN) or term1 = term2. where term = function(term1, …, termN) or constant or variable complex sentences are made from atomic sentences using connectives Universal quantification $\forall $ Typically, $\Rightarrow$ is the main connective with $\forall$, avoid $\wedge$.