• Sentences are built up from terms and atoms:
  • A term (denoting a real-world individual) is a constant symbol, a variable symbol, or an n-place function of n terms. For example, x and f(x1, ..., xn) are terms, where each xi is a term.

  • An atom (which has value true or false) is either an n-place predicate of n terms, or, if P and Q are atoms, then ~P, P V Q, P ^ Q, P => Q, P <=> Q are atoms

  • A sentence is an atom, or, if P is a sentence and x is a variable, then (Ax)P and (Ex)P are sentences

  • A well-formed formula (wff) is a sentence containing no "free" variables. I.e., all variables are "bound" by universal or existential quantifiers. E.g., (Ax)P(x,y) has x bound as a universally quantified variable, but y is free.