Results 1 to 8 of 8

Thread: Inference Laws

  1. #1
    Join Date
    Feb 2009
    Posts
    2,155
    Mentioned
    4 Post(s)
    Quoted
    42 Post(s)

    Default Inference Laws

    I'm am completely stuck with this question in my homework.

    Code:
    Use resolution to show the hypotheses “Allen is a bad boy or Hillary is a good girl” and
    “Allen is a good boy or David is happy” imply the conclusion “Hillary is a good girl or
    David is happy.”
    Can anyone point me in the right direction?

  2. #2
    Join Date
    Sep 2008
    Location
    Not here.
    Posts
    5,422
    Mentioned
    13 Post(s)
    Quoted
    242 Post(s)

    Default

    "Allen is a bad boy or Hillary is a good girl" can be represented as (not a) or b
    "Hillary is a good girl or David is happy" can then be represented as a or c
    If you assume a is true then b must be true. If you assume a is false then c must be true. So either b or c is true.

    Edit: woah just read this. Hint, don't logic while playing league.
    Last edited by tls; 02-20-2015 at 05:38 AM.

  3. #3
    Join Date
    Feb 2011
    Location
    The Future.
    Posts
    5,600
    Mentioned
    396 Post(s)
    Quoted
    1598 Post(s)

    Default

    Helps to look at it in a table if you're stuck.

    Given: Allen is bad OR Hillary is good AND Allen is good OR David is happy IMPLIES Hillary is good OR David is happy
    Inference: ( ¬ A \/ H ) /\ ( A \/ D ) -> ( H \/ D )

    And you can then maybe simplify the expression from there and figure out what makes the expression true..
    Last edited by Brandon; 02-20-2015 at 05:41 AM.
    I am Ggzz..
    Hackintosher

  4. #4
    Join Date
    Dec 2007
    Posts
    289
    Mentioned
    4 Post(s)
    Quoted
    86 Post(s)

    Default

    Work backwards from the conclusion;
    "Hillary is a good girl or David is happy.”
    If we assume Hillary is a good girl then we know Allen is not a bad boy (implied good boy) because “Allen is a bad boy or Hillary is a good girl”.
    Now that we know Allen is an (implied) good boy we know David is (implied) unhappy because “Allen is a good boy or David is happy”.

    Therefore the conclusion "Hillary is a good girl or David is happy.” is sound.

  5. #5
    Join Date
    May 2014
    Posts
    633
    Mentioned
    8 Post(s)
    Quoted
    322 Post(s)

    Default

    Referring to Allen is bad as A':

    The thing boils down to A'+H and A+D. Treating everything(A,H,D) as non-empty sets/regions it's pretty easy to draw out the venn diagram and see that this is true on all the regions remaining (of course this method won't scale, but it could be helpful for building intuition about this stuff)

  6. #6
    Join Date
    Dec 2011
    Location
    Toronto, Ontario
    Posts
    6,424
    Mentioned
    84 Post(s)
    Quoted
    863 Post(s)

    Default

    Brandon nailed it. of course, you'll have to state that A represents Allan being good and H represents Hilary being good etc etc.

  7. #7
    Join Date
    Oct 2011
    Posts
    805
    Mentioned
    21 Post(s)
    Quoted
    152 Post(s)

  8. #8
    Join Date
    Jan 2012
    Location
    127.0.0.1
    Posts
    702
    Mentioned
    11 Post(s)
    Quoted
    76 Post(s)

    Default

    Quote Originally Posted by bg5 View Post
    Propably OP has done his homework already, but I was just curious if I can solve it with boolean algebra...

    but whuh, those 2 expressions are not equal:
    just means when the result is evaluated true, gives the hypothesis, so there would be 2 non equal as this is not assumed to be in the hypothesis

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •