My Math Forum  

Go Back   My Math Forum > College Math Forum > Applied Math

Applied Math Applied Math Forum


Reply
 
LinkBack Thread Tools Display Modes
January 5th, 2014, 10:07 AM   #1
Newbie
 
Joined: Jan 2014

Posts: 1
Thanks: 0

predicate logic

translate the following sentences:

(i) Mary has a false passport. F(m,p) (F=False, m=Mary, p=Passport)
(ii) Peter likes nobody but himself.
(iii) Mary only dates Americans.
(iv) Smoking is dangerous. D(s) (D=dangerous, s=Smoking)
(v) Not everybody cooked their own dinner. ?x (C(x) --> D(x,x)) (C=cooked, D=dinner)
(vi) Sally wore a beautiful dress. ?x(S(x) ^ (W(x,d) ^ B(d))) (S=sally, W=wore, d=dress, B=beautiful)

Unsure of the translations, any help would be great!
skaur is offline  
 
January 6th, 2014, 05:51 PM   #2
Senior Member
 
Joined: Dec 2013
From: Russia

Posts: 327
Thanks: 108

Re: predicate logic

As a general remark, a translation into predicate logic depends completely on the chosen predicate symbols and constants. We could translate any sentence into just P if such symbol P is available.

Quote:
Originally Posted by skaur
(i) Mary has a false passport. F(m,p) (F=False, m=Mary, p=Passport)
I don't think having the predicate "false" apply to Mary is the most natural approach. I would suggest having a one-argument predicate F (false), a one-argument predicate P (passport; not a constant since there can be real and false passports), a two-argument predicate H(x,y) (x has y) and a constant m (Mary). Other choices of predicate symbols are possible.

Quote:
Originally Posted by skaur
(ii) Peter likes nobody but himself.
I suggest L(x,y) (x likes y) and a constant p (Peter).

Quote:
Originally Posted by skaur
(iii) Mary only dates Americans.
D(x, y) (x dates y), a unary A (American) and a constant m (Mary).

Quote:
Originally Posted by skaur
(iv) Smoking is dangerous. D(s) (D=dangerous, s=Smoking)
Seems OK.

Quote:
Originally Posted by skaur
(v) Not everybody cooked their own dinner. ?x (C(x) --> D(x,x)) (C=cooked, D=dinner)
I suggest B(x, y) (x belongs to y) to express "own" and C(x, y) (x cooked y).

Quote:
Originally Posted by skaur
(vi) Sally wore a beautiful dress. ?x(S(x) ^ (W(x,d) ^ B(d))) (S=sally, W=wore, d=dress, B=beautiful)
I would make Sally a constant rather than a predicate and quantify existentially over dresses.
Evgeny.Makarov is offline  
Reply

  My Math Forum > College Math Forum > Applied Math

Tags
logic, predicate



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Predicate Logic mohitpd Applied Math 0 October 26th, 2013 07:45 PM
Predicate Logic pavankumar.thati Applied Math 0 April 16th, 2013 09:26 AM
Resolution in Predicate logic Leila Applied Math 9 January 4th, 2011 05:54 AM
Predicate Logic translation. >_< pinkcheese Applied Math 0 November 22nd, 2010 08:40 PM
Sets and Predicate logic Zhai Applied Math 7 February 22nd, 2010 06:32 PM





Copyright © 2017 My Math Forum. All rights reserved.