Results 1 to 9 of 9

Math Help - predicate calculus

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    12

    predicate calculus

    please help with the following problem

    Consider the following statements:

    Every file in MyDocuments is encrypted or hidden. Every encrypted
    file in MyDocuments is secure. Every secure file in MyDocuments
    contains secrets. There is a file in MyDocuments which does not contain
    secrets. Therefore there is a file in MyDocuments which is hidden.

    Choose an appropriate universal set and collection of predicates, and express this argument in the language of predicate calculus.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,554
    Thanks
    785
    Let the universal set be the set of all files in MyDocuments. What about choosing the collection of predicates, e.g., E(x) means "x is envrypted"? Can you do that?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2009
    Posts
    12
    i am trying the problem. please check if its ok or not.


    Let
    U, the set of all files in MyDocuments

    we define the following functions

    E(x), indicates if file x is encrypted
    H(x), indicates if file x is hidden
    Secure(x), indicates if file x is secure
    Secret(x), indicates if file x contains secrets

    we can now write the given statements using predicate and logical connectives

    x ∈ U: E(x) ∨ H(x)
    x ∈ U: E(x) ⇒Secure(x)
    x ∈ U: Secure(x) Secret(x)
    ∃x ∈ U: ( Secret(x) ) ⇒ ∃x ∈ U: H(x)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,554
    Thanks
    785
    I agree with what you wrote, except that the last line looks like one formula, i.e., one assumption. The claim to be proved should be clearly separated from all the assumptions.

    Let us know if you need help with constructing a formal or informal derivation, etc.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Dec 2009
    Posts
    12
    Quote Originally Posted by emakarov View Post
    I agree with what you wrote, except that the last line looks like one formula, i.e., one assumption. The claim to be proved should be clearly separated from all the assumptions.

    Let us know if you need help with constructing a formal or informal derivation, etc.
    I don't know what to do with the last line. would it be something like joining all the lines together like this? please help

    x ∈ U:(E(x) ∨ H(x)) ∧ ∀x ∈ U: (E(x) ⇒Secure(x)) ∧ x ∈ U:(Secure(x) Secret(x))∧ ∃x ∈ U: ( Secret(x) ) ⇒ ∃x ∈ U: H(x)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Dec 2009
    Posts
    12
    i need it to be done today. please help
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Nov 2009
    Posts
    10
    Hello ruleworld!

    Quote Originally Posted by ruleworld View Post
    i am trying the problem. please check if its ok or not.


    Let
    U, the set of all files in MyDocuments

    we define the following functions

    E(x), indicates if file x is encrypted
    H(x), indicates if file x is hidden
    Secure(x), indicates if file x is secure
    Secret(x), indicates if file x contains secrets

    we can now write the given statements using predicate and logical connectives

    x ∈ U: E(x) ∨ H(x)
    x ∈ U: E(x) ⇒Secure(x)
    x ∈ U: Secure(x) Secret(x)
    ∃x ∈ U: ( Secret(x) ) ⇒ ∃x ∈ U: H(x)
    In the last line of the quote you write \exists x\in U:\neg (Secret(x))\Longrightarrow \exists x\in U: H(x), so it looks like this statement is given. Actually \exists x\in U:\neg (Secret(x)) is one of the givens and \exists x\in U: H(x) is the conclusion.

    Emakarov meant that this should be clear for everybody who reads your text. Thus I suggest you write it for example like this

    given
    given
    given
    .
    .
    .
    given
    -------
    conclusion

    In this form the readers can see which are the givens and what the conlcusion is.

    Best wishes,
    Sebastian
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,554
    Thanks
    785
    Yes, that was my idea.

    If one wants to express the whole problem as one formula (for example, in order to feed it to an automatic theorem prover and see if it is derivable), then the long implication given by OP is also correct. I would only put extra parentheses to avoid ambiguity and possibly add some indentation, something like this:

    (∀x ∈ U: (E(x) ∨ H(x))) ∧
    (∀x ∈ U: (E(x) ⇒ Secure(x))) ∧
    (∀x ∈ U: (Secure(x) ⇒ Secret(x))) ∧
    (∃x ∈ U: (Secret(x))) ⇒
    ∃x ∈ U: H(x)

    Bloody editor: I don't know how to indent the last line by a couple of spaces.

    Last edited by emakarov; December 13th 2009 at 06:45 AM. Reason: formatting
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Dec 2009
    Posts
    12
    Thanks very much for ur help Emakarov and Seppel.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. derivations in predicate calculus
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: April 23rd 2010, 07:44 AM
  2. Predicate calculus - propositions
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: August 2nd 2009, 08:50 PM
  3. Predicate Calculus
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 21st 2009, 05:19 PM
  4. Predicate Calculus Question
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: May 20th 2009, 05:39 PM
  5. Predicate Calculus help
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: March 6th 2009, 10:19 PM

Search Tags


/mathhelpforum @mathhelpforum