1 / 20

INTRO LOGIC

INTRO LOGIC. Translations in PL 4. DAY 18. Chapter 7 Polyadic Predicate Logic. Examples of Polyadic Predication. Jay. respects. Kay. Jay. respects. some F. Jay. respects. every F. some F. respects. Kay. every F. respects. Kay. some F. respects. some G. some F. respects.

rahim-koch
Download Presentation

INTRO LOGIC

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. INTRO LOGIC Translations in PL4 DAY 18

  2. Chapter 7 Polyadic Predicate Logic

  3. Examples of Polyadic Predication Jay respects Kay Jay respects some F Jay respects every F some F respects Kay every F respects Kay some F respects some G some F respects every G every F respects some G every F respects every G

  4. Example 1 Jay respects someone there is someone who is respected by Jay there is some x : x is respected by Jay Jay respects x x Rjx R is always read in “active voice”

  5. Example 1 - redone Jay respects someone there is someone whom Jay respects there is someone : Jay respects him (her) there is some x : Jay respects x x Rjx

  6. Example 2 everyone respects Kay no matter who you are you respect Kay no matter who x is x respects Kay x Rxk

  7. Example 3 no-one respects Jay there is no one who respects Jay there is no x : x respects Jay x Rxj

  8. Example 4 everyone respects everyone no matter who you are you respect everyone no matter who x is x respects everyone x x respects everyone no matter who you are x respects you no matter who y is x respects y y Rxy x y Rxy

  9. Example 5 someone respects someone there is someone who respects someone there is some x : x respects someone x x respects someone there is someone whom x respects there is some y : x respects y y Rxy x y Rxy

  10. Example 6 no one respects everyone there is no one who respects everyone there is no x : x respects everyone x x respects everyone no matter who you are x respects you no matter who y is x respects y y Rxy x y Rxy

  11. Example 7 no one is respected by everyone there is no one who is R’ed by everyone there is no x : x is R’ed by everyone everyone respects x x everyone respects x no matter who you are you respect x no matter who y is y respects x y Ryx x y Ryx

  12. A Scope Ambiguity • everyone respects someone is ambiguous everyone respects someone or other vs. everyone respects someone (the same one) = there is someone whom everyone respects

  13. What is the Difference? • Situation 1 • Jay Jay • Kay Kay • Elle Elle does everyone respect someone? YES is there someone whom everyone respects? NO

  14. What is the Difference? (cont.) • Situation 2 • Jay Jay • Kay Kay • Elle Elle does everyone respects someone? YES is there someone whom everyone respects? YES NOTE: the latter implies the former

  15. Example 8 everyone respects someone (or other) no matter who you are you respect someone no matter who x is x respects someone x x respects someone there is someone whom x respects there is some y : x respects y y Rxy x y Rxy

  16. Example 9 everyone respects someone (the same) there is some one whom everyone respects there is some x : everyone respects x x everyone respects x no matter who you are you respect x no matter who y is y respects x y Ryx x y Ryx

  17. Example 10 there is some one who respects no one there is some x : x respects no one x x respects no one there is no one whom x respects there is no y : x respects y y Rxy x y Rxy

  18. Example 11 there is some one whom no one respects there is some x : no one respects x x no one respects x there is no one who respects x there is no y : y respects x y Ryx x y Ryx

  19. Example 12 Jay doesn’t respect anyone no matter who you are Jay does not respect you no matter who x is Jay does not respect x x Jay does not respect x Rjx x  Rjx

  20. THE END

More Related