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]
Predicate logic is a system of mathematical logic. It uses predicates to express the state of certain things. It is different from other systems of logic because it has the concept of quantifiers. This means, that it can also express things about quantity.
The best-known quantifiers are the existence quantifier (∃). The existence quantifier says that there is at least one (thing) that matches the predicate or formula. The other well-known quantifier is called universal quantifier (∀). It says that all the things match a certain predicate or formula.
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