INTRO LOGIC DAY 20 Translations in PL 6

INTRO LOGIC DAY 20 Translations in PL 6 1

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

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

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

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 ) 5

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 6

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

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 no G x ( Fx & y(Gy & Rxy) ) 8

new material for day 5 9

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

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 ) 11

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

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

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

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) } 15

Example 5 no one who respects every pol respects him/herself no one who R’s every P no is there is no one who is and who is there is no x : x is x { x respects him/herself x is & x x R’s every P x R’s him/herself y (Py Rxy ) Rxx } x { y ( Py Rxy ) & Rxx } 16

THE END 17