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INTRO LOGIC

INTRO LOGIC. Translations in PL 6. DAY 20. EXAM #3. 25 translations from English into Predicate Logic 4 points each Only final formula is graded. Do intermediate work on scratch paper. EXAM TOPICS 1. Chapter 6. HW. #. example. un-quantified formulas. 6a. 2. JAY and KAY are HAPPY.

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INTRO LOGIC

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  1. INTRO LOGIC Translations in PL6 DAY 20

  2. EXAM #3 25 translations from English into Predicate Logic 4 points each Only final formula is graded. Do intermediate work on scratch paper.

  3. EXAM TOPICS 1 Chapter 6 HW # example un-quantified formulas 6a 2 JAY and KAY are HAPPY simple quantifiers 6b 2 everyone is HAPPY specified quantifiers 6c 2 every SENIOR is HAPPY ‘only’ 6f 1 only SENIORS are HAPPY conjunctive combinations 6e 1 every F S is HAPPY disjunctive combinations 6g 1 every A and B is C multiple quantification 6h 3 if everyone is F, then everyone is H ‘any’ 6i 1 if anyone is F, then everyone is H

  4. EXAM TOPICS 2 Chapter 7 HW # Example 1 quantifier, 1 predicate 7a 2 everyone RESPECTS KAY 1 quantifier, 2 predicates 2 KAY RESPECTS every STUDENT 2 quantifiers, 1 predicate 7b 2 everyone RESPECTS someone 2 quantifiers, 2 predicates 7c 2 no STUDENT RESPECTS everyone 2 quantifiers, 3 predicates 7d 2 every F RESPECTS some G complex predicates 7e 2 every one who RESPECTS every F RESPECTS every G

  5. Review – 1 Quantifier, 1 Predicate Jay respects some one x Rjx every one respects Kay x Rxk no-one respects Jay x Rxj Review – 1 Quantifier, 2 Predicates Jay respects some F x ( Fx & Rjx ) every F respects Kay x ( Fx  Rxk ) no F respects Jay x ( Fx & Rxj )

  6. 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

  7. Review – 2 Quantifiers, 2 Predicates every F respects everyone x ( Fx yRxy) some one respects some G xy ( Gy & Rxy) every F respects someone (or other) x ( Fx yRxy) no one respects every G xy ( Gy Rxy) there is some F who R’s everyone x ( Fx &yRxy) there is someone who R’s no G xy ( Gy &Rxy)

  8. Review – 2 Quantifiers, 3 Predicates every F respects every G x ( Fx y(Gy  Rxy)) some F respects some G x ( Fx &y(Gy & Rxy)) every F respects some G (or other) x ( Fx y(Gy & Rxy)) no F respects every G x ( Fx &y(Gy Rxy)) there is some F who R’s every G x ( Fx &y(Gy Rxy)) there is some F who R’s no G x ( Fx &y(Gy &Rxy))

  9. new material for day 5

  10. Complex Predicates Simple Predicates x is a Citizen Cx no further analysis required x is a Politician Px Complex Predicates x Respects him/herself x must be further analyzed x Respects everyone Jay Respects x no Citizen Respects x

  11. Example Analyses x Respects Kay Rxk Jay Respects x Rjx x Respects him/herself Rxx x Respects everyone y Rxy someone Respects x y Ryx x Respects at least one Pol y ( Py & Rxy ) x Respects every Pol y ( Py Rxy ) every Citizen Respects x y ( Cy  Ryx ) no Citizen Respects x y ( Cy & Ryx )

  12. Example 1 every citizenrespects at least one politician every citizen respects at least one politician every C is   you if you are C then you are  x { Cx  x } x R’s at least one P y ( Py & Rxy ) x{Cx y ( Py & Rxy )}

  13. Example 2 nopoliticianisrespected by every citizen no politician is respected by every citizen is no P  there is no one who is P and who is  } x Px & x { x is R’ed by every C every C Respects x y ( Cy Ryx ) x{Px&y ( Cy Ryx )}

  14. Example 3 everyone who respects every polisa moron every one who respects every P is a moron every  is M  you if you are  then you are M x x {  Mx } x R’s every Politician y ( Py Rxy ) x{y(Py Rxy)Mx}

  15. Example 4 every one who respects every Pol is respected by every Pol every one who R’s every P is respected by every P every  is   you if you are  then you are  x { x  x } x R’s every P x is R’ed by every P y ( Py Rxy ) y ( Py Ryx ) x{y(Py Rxy)y(Py Ryx)}

  16. Example 5 noone who respects every polrespects him/herself no one who R’s every P respects him/herself no  is  there is no one who is  and who is  there is no x : x is  x is  x x { & x } x R’s every P x R’s him/herself y (Py Rxy ) Rxx x{y ( Py Rxy )&Rxx}

  17. THE END

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