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← 12-03 More Logic

12-03 More Logic

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Showing Revision 2 created 07/28/2014 by Udacity Robot.

  1. In this exercise, I'm going to give you some English sentences
  2. and then some first-order logic sentences
  3. and ask you does the first-order logic sentence
  4. correctly encode the English sentence, does it incorrectly encode it,
  5. or is it just an error that is not a legitimate sentence
  6. in first-order logic?
  7. The first English sentence is "Paris and Nice are both in France."
  8. Here's one possible translation.
  9. Paris and Nice are in France.
  10. Here's another.
  11. Paris is in France, and Nice is in France.
  12. Tell us if each of these is a correct encoding of English,
  13. incorrect, or if it's erroneous first-order logic syntax.
  14. The second sentence in English is "There is a country that borders Iran and Syria."
  15. Here are the possible translations.
  16. There exists a c, and we're going to use the predicate capital C
  17. to mean C when the argument is a country.
  18. So, there exists a c such that C of c,
  19. and we're going to use the predicate B to mean 2 objects border each other.
  20. So, c borders Iran, and c borders Syria.
  21. That's one translation. Here's the other translation.
  22. There exists a c if C is a country,
  23. then c borders Iran and c borders Syria.
  24. And the final English sentence is no 2 bordering countries
  25. can have the same map color, and we're going to use the predicate MC for map color.
  26. Here's one possibility for all x and y.
  27. X is a country, and y is a country.
  28. And x and y border each other.
  29. That implies it's not the case that the map color
  30. of x equals the map color of y.
  31. And I should say we're using map color here as a function, not as a predicate.
  32. Here's another possibility.
  33. For all x and y, it's not the case that x is a country,
  34. or it's not the case that y is a country,
  35. or it's not the case that x and y border,
  36. or it's not the case that the map color of x
  37. is equal to the map color of y.