In mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic. This formal system is distinguished from other systems in that its formulas contain variables which can be quantified. Two common quantifiers are the existential ∃ and universal ∀ quantifiers. The variables could be elements in the universe, or perhaps relations or functions over the universe. For instance, an existential quantifier over a function symbol would be interpreted as modifier "there is a function".

In informal usage, the term "predicate logic" occasionally refers to first-order logic. Some authors consider the predicate calculus to be an axiomatized form of predicate logic, and the predicate logic to be derived from an informal, more intuitive development.¹

Footnotes

1. ^ Among these authors is Stolyar, p. 166. Hamilton considers both to be calculi but divides them into an informal calculus and a formal calculus.

References

• A. G. Hamilton 1978, Logic for Mathematicians, Cambridge University Press, Cambridge UK ISBN 0-521-21838-1.

• Abram Aronovic Stolyar 1970, Introduction to Elementary Mathematical Logic, Dover Publications, Inc. NY. ISBN 0-486-64561

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