- Predicate logic
In

mathematical logic ,**predicate logic**is the generic term for symbolicformal system s likefirst-order logic ,second-order logic ,many-sorted logic orinfinitary logic . This formal system is distinguished from other systems in that its formulas containvariable s 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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