Chapter: Classifying the Logical Calculi - Variables, Formulas, Predicates and Signatures

Signatures offer a way to classify logical calculi. They describe the vocabulary of a logical calculus formed by the strings of the underlying formal language. Usually, the vocabulary - a signature - consists of variables, functions, and predicates. We will now formally define what variables, formulas, predicates, and signatures are and then we will introduce logical calculi with different signatures, including propositional logic, first-order predicate logic and higher-order logics.

  1. Definition: Variable in a Logical Calculus
  2. Definition: Quantifier, Bound Variables, Free Variables
  3. Definition: Function, Arity and Constant
  4. Definition: Predicate of a Logical Calculus
  5. Definition: Signature

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