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. S

    How can Euler differential equations be solved using a substitution?

    Second order diff.eq. help?? well i am trying to find a solution to this diff. eq, but i get stuck somewhere. \ 4x^{2}y''+y=0 I first took this substitution y'=p, y"=p' so the diff. eq becomes of this form \ 4x^{2}p'+p=0 i think this can be done with the separable of variables...
  2. S

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  3. J

    Reducible Second Order Differential Equation: Ind. and First Derivative Missing

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  4. J

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  5. I

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  6. KleZMeR

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  7. I

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  8. O

    Solve second order differential equation

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  9. D

    Second Order Differential Equation

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  10. Schrodinger's Dog

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  11. maverick280857

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  12. V

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  13. V

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  14. V

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  15. W

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  16. T

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  17. G

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  18. G

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  19. K

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  20. K

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  21. N

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  22. X

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  23. P

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  24. Z

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  25. H

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  26. S

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  27. R

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  28. J

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  29. F

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  30. P

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  31. S

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  32. M

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  33. B

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  34. S

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  35. E

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  36. O

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  37. J

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  38. D

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  39. J

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  41. T

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  43. E

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  44. E

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  45. B

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  46. P

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  47. S

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  48. E

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  49. L

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  50. N

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