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predicate logic

predicate logic

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Then it is necessary to include the usual axioms of equality from predicate logic as axioms about this defined symbol. en.wikipedia.org

These include propositional logic and monadic predicate logic, which is first-order logic restricted to unary predicate symbols and no function symbols. en.wikipedia.org

These three additional rules extend the propositional system to axiomatise classical predicate logic. en.wikipedia.org

Some authors refer to predicate logic with identity to emphasize this extension. en.wikipedia.org

In mathematical logic, a sentence of a predicate logic is a boolean-valued well-formed formula with no free variables. en.wikipedia.org

It is also known as first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic. en.wikipedia.org

Type theory extends this identification to predicate logic by introducing dependent types, that is types which contain values. en.wikipedia.org

Its semantics is based on first order predicate logic. en.wikipedia.org

This requires that the logic have a suitable notion of elementary substructure, for example by using the normal definition of a structure from predicate logic. en.wikipedia.org

They successfully transferred key properties of description, modal, and temporal logic to predicate logic. en.wikipedia.org

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