Propositional logic does not allow any reasoning based on general rules, so its usefulness is limited. Predicate calculus generalizes propositional logic with variables, quantifiers, and functions.

Formulas are constructed from:

• Predicates have arguments, which are terms: P(x, f(a)). Predicates are true or false.
• Terms refer to objects in the application domain:
  • Variables: x, y, z
  • Constants: John, Mary, 3, a, b. Note that a constant is generally capitalized in English: Austin can be a constant, but dog cannot.
  • Functions: f(x) whose arguments are terms.
• Quantifiers: &forall (``for all'') and &exist (``there exists'' or ``for some'') quantify variables: &forall x, &exist y. If a variable is in the scope of a quantifier, it is bound; otherwise, it is free.

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