tag:blogger.com,1999:blog-6642011.post108998432281732173..comments2021-09-15T09:59:44.957-04:00Comments on Philosophy, et cetera: Logic TranslationsRichard Y Chappellhttp://www.blogger.com/profile/16725218276285291235noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-6642011.post-1128206858863796892005-10-01T18:47:00.000-04:002005-10-01T18:47:00.000-04:00Great blog,I surf a lot a day, and want to tell yo...Great blog,<BR/>I surf a lot a day, and want to tell you yours is cool:<BR/><A HREF="http://email.eqqu.com/?klinkecs01" REL="nofollow">Free Email Pays</A>Legacy Userhttps://www.blogger.com/profile/14847245800960234414noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-1093754517395578632004-08-29T00:41:00.000-04:002004-08-29T00:41:00.000-04:00I take it that "eating out" is the opposite of "ea...I take it that "eating out" is the opposite of "eating at home", so this would turn the truth functional translation into:<br />(~H & M) v (H & A)<br />As you point out, one should perhaps add "& (M->~A)" at the end of the formula.<br />In first order logic, I would suggest substituting M for Wfm (Fred will eat with Martha) and A (Fred eats alone) for ~Vx(Wfx & ~x=f) (there exists no x such that x is different from Fred and x will eat with Fred, i.e., no one apart from Fred will eat with Fred). My proposed translation is, therefore:<br />(~H & Wfm) v (H & ~Vx(Wfx & ~x=f)).<br /><br />On the question of how to translate sentences into formulae, I would say that it very much depends on the problem at hand. We are usually interested in working with the logical structure, and this is what needs to be respected in the translation, but this greatly depends on the problem we are trying to solve.<br />Alex Beta | Email | Homepage | 18th Jul 04 - 12:19 am | #<br /><br />----------------<br /><br />Thanks for the comment. Just a couple of quick points:<br /><br /><I>I take it that "eating out" is the opposite of "eating at home"</I>Well, conceptually perhaps, but not logically. Note that ~H simply means "It is not the case that Fred will eat at home". <B>But this will be true if Fred simply doesn't eat at all!</B> So we cannot use ~H to denote 'eating out', it is too broad.<br /><br />Also, I think you might have a minor typo in your translation of "Fred eats alone". Rather than beginning with "~Vx(...)", we would require "Vx~(...)" which is equivalent to "~Ex(...)".<br /><br />That is, where you say "not all x...", we rather want to be saying "not any x", i.e. "for all x, not..."<br />Richard | Email | Homepage | 18th Jul 04 - 12:58 am | #<br /><br />----------<br /><br />I completely agree with the fact that H and O might not be opposites. As you correctly note, this is not the case if we do not assume that Fred will eat, but this depends on the nature of the problem. If we had found this sentence in a logic puzzle where you are supposed to determine where Fred will eat, my assumption that H and O where opposites would probably have been acceptable. As the context was lacking, the assumption was made explicitly ("I take it that...").<br /><br />My proposed formula in first order logic does not contain a typo, it just happens to contain an unfortunate choice of notation. You use "V" to represent "for all..." and "E" to represent "there exists...". I was using the convention of representing "there exists..." with a large disjunction "V" and for "for all x" I chose "(x)." Despite the misunderstanding that this might have caused, you have guessed my intention correctly.<br />Alex Beta | Email | Homepage | 18th Jul 04 - 8:40 am | #<br /><br />-------------<br /><br />Oh, fair enough. Thanks for clarifying that :)<br />Richard | Email | Homepage | 18th Jul 04 - 12:32 pm | #Richard Y Chappellhttps://www.blogger.com/profile/16725218276285291235noreply@blogger.com