Sorry, no online dictionaries contain the exact phrase monadic first-order logic.
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Reverse dictionary results:
1. unary
2. monadology
3. amoeba
4. atom
5. entelechy
6. ion
7. monad
8. monadism
9. unit
10. abstract
11. dyadic
12. immanent
13. many
14. propositional
15. semiotic
16. subsistent
17. transcendental
18. leading
19. prime
20. prominent
21. subordinate
22. ameba
23. atemporal
24. deme
25. monadical
26. monadiform
27. monas
28. pantastomata
29. plastid
30. plastide
31. categorial
32. combinatory
33. depersonalized
34. existent
35. intensional
36. microcosmic
37. multiple
38. nonspatial
39. ontic
40. organismic

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You can look up the words in the phrase individually using these links:   monadic ?   first-order ?   logic ?
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