Скачать или смотреть What is Second-order logic?, Explain Second-order logic, Define Second-order logic

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~~~ Second-order logic ~~~

Title: What is Second-order logic?, Explain Second-order logic, Define Second-order logic
Created on: 2018-11-18
Source Link: https://en.wikipedia.org/wiki/Second-...

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Description: In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory. First-order logic quantifies only variables that range over individuals ; second-order logic, in addition, also quantifies over relations. For example, the second-order sentence ∀ P ∀ x {\displaystyle \forall P\,\forall x} says that for every unary relation P of individuals, and every individual x, either x is in P or it is not . Second-order logic also includes quantification over sets, functions, and other variables as explained in the section Syntax and fragments. Both first-order and second-order logic use the idea of a domain of discourse . The domain is a set over which individual elements may be quantified.

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