Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Horses have heads Symbolic Logic

  1. Feb 15, 2008 #1
    "Horses have heads" Symbolic Logic

    I was given this sentence to represent in first-order predicate calculus.
    The formula must use the following terms--horse, has, head--where:

    "horse" represents "x is a horse"
    "has" represents "x has a head"
    "head" represents "x is a head"

    Are these possibilities?
    1) (x)(horsex-->hasxhead) which means(?) "For all x, if x is a horse then x has a

    2) (x)(y)((horsex & heady)-->hasxy) which means(?) "For all x and for all y, if x is a horse and y is a head, then x has y"

    If not, how can "Horses have heads" be represented using these specification? Thank you.
  2. jcsd
  3. Feb 15, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    The second is not true- a horse does not have all heads!
    2) says "every horse has every head".
    The first looks to me like a correct statement.
  4. Feb 15, 2008 #3
    Thank you. I am not positive that (1) correctly represents the sentence.

    Regarding (2): you said the formula is stating "a horse has all heads" Does it really?
    If so, I don't understand how it says that. If it's saying a single horse has all entities (which is plural) that are heads, why wouldn't it say "all horses have all heads". That is, I don't understand why it would say a single horse has multiple heads as opposed to saying multiple, i.e. all, horses have multiple, i.e. all, heads.
    I suppose i'm asking if you can explain how (2) says what you claimed; how (2) is incorrect. Thank you.
  5. Feb 16, 2008 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    You said:
    Okay, here is a horse, x, standing just over that fence, and here is a head, y, between my shoulders. Does x have y? You did say "for all x and for all y".
  6. Feb 16, 2008 #5
    Just to get things straight, HORSE and HEAD are one-place predicates, and HAS is a two-place predicate, right?

    I think what you want is (Ax)[HORSEx --> (Ey)[HEADy & HASxy]].
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Horses have heads Symbolic Logic
  1. Logic Symbols (Replies: 12)