Branches History Index

◀ ▲ ▶Branches / Logic / Chapter: Classifying the Logical Calculi - Variables, Formulas, Predicates and Signatures

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.

Table of Contents

  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

Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs

References

Bibliography

  1. Hoffmann, Dirk W.: "Grenzen der Mathematik - Eine Reise durch die Kerngebiete der mathematischen Logik", Spektrum Akademischer Verlag, 2011
  2. Beierle, C.; Kern-Isberner, G.: "Methoden wissensbasierter Systeme", Vieweg, 2000