What is Second order: Definition and 602 Discussions

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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  1. H

    Calculating Contact Time and Damping Coefficient for a Second Order System

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  2. F

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  3. V

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  4. H

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  5. B

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  6. whatisgoingon

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  7. K

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  8. T

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  9. T

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  11. sa1988

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  13. V

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  14. I

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  15. E

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  16. Dyatlov

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  17. J

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  18. K

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  19. A

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  20. J

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  21. tanvi nautiyal

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  22. A

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  23. Schwarzschild90

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  24. G

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  25. i_hate_math

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  27. faradayscat

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  28. T

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  29. E

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  30. L

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  31. kostoglotov

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  32. G

    MHB Solving Second Order ODE: True or False?

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  33. Andreol263

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  34. A

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  35. B

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  36. I

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  37. engnrshyckh

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  38. P

    Second Order Linear D.E W/ Constant Coefficients and Zero RHS

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  39. C

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  40. P

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  41. kostoglotov

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  42. S

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  43. M

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  44. Mark Brewer

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  45. PWiz

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  46. W

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  47. Roy Fokker

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  48. SteliosVas

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  49. Q

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  50. S

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