Second order Definition and 602 Threads

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 (elements of the domain of discourse); second-order logic, in addition, also quantifies over relations. For example, the second-order sentence



∀
P

∀
x
(
P
x
∨
¬
P
x
)


{\displaystyle \forall P\,\forall x(Px\lor \neg Px)}
says that for every formula P, and every individual x, either Px is true or not(Px) is true (this is the law of excluded middle). 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 (often called simply the "domain" or the "universe"). The domain is a set over which individual elements may be quantified.

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  2. A

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  3. VoteSaxon

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  4. V

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  6. B

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  9. M

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  16. Alexandre

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  17. F

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  18. L

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  19. S

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  20. S

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  21. C

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  22. T

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  23. B

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  24. mr_sparxx

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  29. _N3WTON_

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  30. C

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  31. V

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  32. Y

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  34. D

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  38. F

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  39. M

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  44. nomadreid

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