INTRO LOGIC

1. INTRO LOGIC Translations in PL5 DAY 19

2. Review – 1 Quantifier, 1 Predicate Jay respects someone x Rjx Jay respects everyone x Rjx Jay respects no one  x Rjx some one respects Kay x Rxk everyone respects Kay x Rxk no-one respects Kay x Rxk

3. Review – 2 Quantifiers, 1 Predicate everyone respects everyone x y Rxy someone respects someone x y Rxy no-one respects everyone x y Rxy no-one is respected by everyone x y Ryx everyone respects someone (or other) x y Rxy there is someone whom everyone R’s x y Ryx there is someone who respects no-one x y Rxy there is someone whom no-one respects x y Ryx

4. New Material 1 quantifier, 2 predicates2 quantifiers, 2 predicates2 quantifiers, 3 predicates

5. Example 1 every student respects Kay no matter who you are IF you are a student, THEN you respect Kay no matter who x is IF x is a student, THEN x respects Kay x ( Sx  Rxk )

6. Example 2 no student respects Jay there is no-one who is a S and who R's j there is no x : x is a S and x R's j x ( Sx & Rxj)

7. Example 3 Jay respects some (at least one) student there is someone who is a S (whom) j respects who is a S and whom j R's there is someone x x is a S and j R's x x (Sx & Rjx)

8. Example 4 no-one respects every politician there is no one who respects every politician there is no x : x respects every politician x x respects every politician

9. Example 4b x x respects every politician no matter who you are IF you are P, THEN x R’s you no matter who y is IF y is P, THEN x R’s y y Py  Rxy y ( Py  Rxy ) x y ( Py  Rxy )

10. Example 5 every Student respects someone or other no matter who you are IF you are S, THEN you R someone no matter who x is IF x is S, THEN x R's someone x Sx  x R's someone x ( Sx  x R's someone )

11. Example 5b x ( Sx  x R's someone ) there is someone who is R'ed by x whom x R's there is some y x R's y y Rxy x ( Sx y Rxy )

12. Example 6 there is a politician whom no-one respects there is someone who is a P whom no-one R‘s who is P AND whom no-one R's there is some x : x is P AND no-one R's x x Px & no-one R's x x ( Px & no-one R's x )

13. Example 6b x ( Px & no one R's x ) there is no one who R’s x there is no y y R's x y Ryx x ( Px & y Ryx )

14. Example 7 there is a Politicianwhom every Citizen Respects there is someone who is a P whom every C R's who is P AND whom every C R's there is some x x is P AND every C R's x x Px & every C R's x x ( Px & every C R's x )

15. Example 7b x ( Px & every C R's x ) no matter who you are if you are C then you R x no matter who y is if y is C then y R’s x y Cy Ryx y ( Cy Ryx ) x ( Px & y ( Cy Ryx ) )

16. Example 8 every Citizen Respects some Politician (or other) no matter who you are if you are C, then you R some P no matter who x is if x is C, then x R's some P x Cx  x R's some P x ( Cx  x R's some P )

17. Example 8b x ( Cx  x R's some P ) there is someone who is a P R'ed by x who is a P AND who is R'ed by x who is P AND whom x R's there is some y y is P AND x R's y y Py & Rxy y ( Py & Rxy ) x ( Cx y ( Py & Rxy ) )

18. Example 9 there is a Citizen who Respects no Politician there is someone who is a C who R's no P who is a C AND who R's no P there is some x : x is a C AND x R's no P x Cx & x R's no P x ( Cx & x R's no P )

19. Example 9b x ( Cx & x R's no P ) there is no one who is a P AND who is R'ed by x there is no y : y is P AND y is R’ed by x y is P AND x R's y y Py & Rxy y ( Py & Rxy ) x ( Cx & y ( Py & Rxy ) )

20. THE END