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Thread: A question about inference rules of parthood relation symbol

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    A question about inference rules of parthood relation symbol

    There are some ways of regimenting plural quantificational statements like "There are some apples on the table" as:

    (∃xx)(∀u)(xx ≤ u → Au & Tu)

    which translates into "There exist some xx such that for every u, if xx is part of u, then u is an apple, and u is on the table" in semi-formal language mixed with logic and English.

    The symbol '≤' means '...is part of...', that is, the parthood relation. I think that the symbol of parthood must have inference rules like other logical symbols have.

    My question is "What are the inference rules of parthood relation symbol???"
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    Re: A question about inference rules of parthood relation symbol

    Quote Originally Posted by mosesquine View Post
    There are some ways of regimenting plural quantificational statements like "There are some apples on the table" as:
    (∃xx)(∀u)(xx ≤ u → Au & Tu)
    which translates into "There exist some xx such that for every u, if xx is part of u, then u is an apple, and u is on the table" in semi-formal language mixed with logic and English.
    The symbol '≤' means '...is part of...', that is, the parthood relation. I think that the symbol of parthood must have inference rules like other logical symbols have.

    My question is "What are the inference rules of parthood relation symbol???"
    I think that is topic is in category theory?
    If that is correct then this webpage will help.
    If not, I have no clue.
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    Newbie mosesquine's Avatar
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    Re: A question about inference rules of parthood relation symbol

    That webpage introducing inclusion based point-free geometry and connection theory is really helpful. However, what I want to get is an explanation of so-called introduction-rules and elimination-rules that can be used for natural deduction proofs. It's more like identity-introduction rule, identity-elimination rule in predicate logic, for parthood relation symbol.
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