2. First-Order Logic
First-order logic extends propositional logic by allowing formulas to speak about objects, properties of objects, and relations between objects, rather than treating every statement as an indivisible unit. The language contains variables, constants, function symbols, predicate symbols, logical connectives, and quantifiers, and these symbols allow mathematical statements to be expressed with much greater internal structure than in propositional logic. The first part of the chapter defines terms, predicates, and formulas,...