Predicate logic

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For the specific term, see First-order 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.

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