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Math Help - Don't even understand what it is trying to say: Predicate calculus

  1. #1
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    Don't even understand what it is trying to say: Predicate calculus

    Hi, I have a question (natural deduction),

    and the question says :

    construct a natural deduction proof, where y is not free in A. What does it mean by 'where y is not free in A'?

    This question shall not use algebraic laws. Just introduction and elimination rules.

    Thank you.
    Last edited by gomdohri; August 11th 2012 at 04:06 PM.
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  2. #2
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    Re: Don't even understand what it is trying to say: Predicate calculus

    Quote Originally Posted by gomdohri View Post
    What does it mean by 'where y is not free in A'?
    You need to consult your source (textbook or lecture notes). They must have a definition. Or see here in Wikipedia.

    Do you need a Fitch-style or tree-like natural deduction derivation?

    Informally, the derivation looks as follows.

    1. Assume E y. ( A -> P(y)).
    2. Assume A.
    3. From 1 take y and the proof of A -> P(y) (existential elimination).
    4. From 2 and 3 conclude P(y) by MP.
    5. From 4 conclude Ey. P(y).
    6. Close the assumption A from 2.

    Note that to prove the converse implication you need to use the rule of double-negation elimination or the law of excluded middle.

    Edit: After you construct a formal derivation, make sure you understand where the assumption that y is not free in A is used. This is the point of the exercise. If you need help with this, feel free to ask.
    Last edited by emakarov; August 11th 2012 at 07:57 AM.
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