Predicate logic


Predicate logic

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

Footnotes

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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