Sorry, no online dictionaries contain the exact phrase derives from logic.
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Reverse dictionary results:
1. rational
2. logical
3. reasoned
4. sensible
5. rationable
6. instrumentalness
7. qualification
8. reasonable
9. sane
10. cognisance
11. cognizance
12. cognizing
13. conusance
14. conusant
15. electiveness
16. instructiveness
17. presumptiveness
18. proficiency
19. reason
20. sensical
21. accommodation
22. aptitude
23. capacity
24. cogence
25. cognatus
26. cognisant
27. cognising
28. cognizably
29. colourable
30. competency
31. compliance
32. conformism
33. face validity
34. informativity
35. intentionality
36. materiality

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