|The Word "Only" in Logical Translation|
Joined: May 08, 2011
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Posted Jul 5, 2012 - 2:21 AM:
Subject: The Word "Only" in Logical Translation
Joined: May 21, 2005
Location: United States
Total Topics: 33
Total Posts: 843
Posted Jul 5, 2012 - 2:44 AM:
"Only boys can play football in college."
Anything that plays football in college is a boy. I.e., ∀x(playsincollege(x,football) → boy(x)).
"The only requirement for being class president is that the student is a senior."
Perhaps: Any student who is class president is a senior, and any property that is a prerequisite for being class president is seniority. I.e., ∀x(student(x) → ((classpresident(x) → senior(x)) ∧ ∀P(prerequisiteforpresidency(P) → P=senior))).
"Mrs. Johnson said that only one student would get a candy prize today for writing the best poem in class."
There exists some student who recently wrote or soon will write the best poem in class, and who will get a candy prize today, and whose receiving of this prize will be in honor of writing the best poem in class, and who is identical with every student who will receive the candy prize in question today.
A simplified version: There exists some S (i.e., student) who is P and Q and R, and every student who is Q and R is that student. ∃x(Sx ∧ (Px ∧ (Qx ∧ (Rx ∧ ∀y(Sy → ((Qy ∧ Ry) → x=y))))))
Edited by Raugust on Jul 5, 2012 - 2:49 AM