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

    Question in Proof of second order condition with linear constraints

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  2. L

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  3. U

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  4. P

    Partial second order differential proof

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  5. D

    Solving second order linear homogeneous differential equation HELP?

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  6. C

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  7. T

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  8. D

    Second order differential equation

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  9. Telemachus

    Solving second order non homogeneous diff. equation by a particular method

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  10. Telemachus

    Second order non homogeneous diff. equation at constant coefficients

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  11. Telemachus

    Question about second order differential equation

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  12. J

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  13. C

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  14. C

    Trying to solve a second order ODE

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  15. C

    Second order ODE application question

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  16. P

    Second order pole positions and rise time

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  17. S

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  18. D

    Second order linear differential equation

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  19. M

    Wronskian and Second Order Differential Equations

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  20. C

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  21. A

    Second Order Differential Equation

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  22. S

    Problem with Second Order Differential Equation

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  23. D

    System of coupled second order differential equations.

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  24. M

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  25. P

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  26. P

    How Do You Solve a Second Order Linear ODE with Non-Constant Coefficients?

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  27. 0

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  28. P

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  29. A

    Using matlab/mathematica to solve a second order diff.eq.

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  30. 0

    Inhomogeneous Second Order ODE

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  31. M

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  32. J

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  33. J

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  34. D

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  35. J

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  36. R

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  37. T

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  38. M

    Solving Linear Second Order PDE with Mixed Derivative Term?

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  39. O

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  40. N

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  41. L

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  42. J

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  43. M

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  44. N

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  45. A

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  46. J

    Second Order Differential Equation - Can't solve

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  47. P

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  48. M

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  49. D

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  50. T

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