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## INTRO LOGIC

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**INTRO LOGIC**Translations in PL6 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 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**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**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 )**Review – 2 Quantifiers, 1 Predicate**everyone respects everyone xy Rxy someone respects someone xy Rxy no-one respects everyone xy Rxy no-one is respected by everyone xy Ryx everyone respects someone (or other) xy Rxy there is someone whom everyone R’s xy Ryx there is someone who respects no-one xy Rxy there is someone whom no-one respects xy Ryx**Review – 2 Quantifiers, 2 Predicates**every F respects everyone x ( Fx yRxy) some one respects some G xy ( Gy & Rxy) every F respects someone (or other) x ( Fx yRxy) no one respects every G xy ( Gy Rxy) there is some F who R’s everyone x ( Fx &yRxy) there is someone who R’s no G xy ( Gy &Rxy)**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))**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**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 )**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 )}**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 )}**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}**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)}**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}