Sorry, no online dictionaries contain the exact phrase illogical inference.
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Reverse dictionary results:
1. non sequitur
2. illegitimate
3. inconsequent
4. logical
5. balderdash
6. illogicality
7. unsound
8. fallacious
9. illogic
10. inconsequential
11. irrational
12. rationalize
13. sophism
14. faulty
15. paralogism
16. analogy
17. argumentation
18. conclude
19. conclusion
20. consequence
21. consequent
22. consequential
23. corollary
24. deduction
25. deductive
26. ergotism
27. follow
28. hence
29. illation
30. imply
31. inconsequence
32. infer
33. intellect
34. legitimate
35. line
36. logic
37. logically
38. premise
39. presumption

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