Sorry, no online dictionaries contain the exact phrase non commutative logic.
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Reverse dictionary results:
1. commute
2. independent
3. field
4. lesion
5. scalar
6. abelian
7. monadic
8. monoid
9. noncausal
10. noncommutative
11. unary
12. computable
13. abelian group
14. algebra
15. commutative group
16. commutativity
17. commutator
18. back
19. individualism
20. insane
21. negative
22. accident
23. random
24. absolute
25. abstention
26. ahimsa
27. area
28. ato
29. atom
30. base
31. beggar
32. being
33. bias
34. corporal
35. diagonal
36. door
37. down
38. failure
39. fiction
40. general

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You can look up the words in the phrase individually using these links:   non ?   commutative ?   logic ?
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