Terminology for free variables











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Suppose you have a proof along the lines of



$$begin{array} {rc}
text{Assume:} & x > 2 \
& vdots \
& text{Some logic stuff} \
& vdots \
text{Conclude:} & x > 1 \
end{array}$$



Two common ways for this to be interpreted are (1) $(forall x~.~x > 2) to (forall x~.~x > 1)$ and (2) $forall x~.~(x > 2 to x > 1)$. Logics that intend the first way include PRA and Hilbert style FOL. Logics that intend the second way include Fitch style Natural Deduction.



Is there common terminology to distinguish the two approaches to interpreting how the free variables are shared between propositions in a proof? Or if you have reason to think there are no such common terms, what would you suggest?






logic terminology quantifiers sequent-calculus







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    up vote
    2
    down vote

    favorite












    Suppose you have a proof along the lines of



    $$begin{array} {rc}
    text{Assume:} & x > 2 \
    & vdots \
    & text{Some logic stuff} \
    & vdots \
    text{Conclude:} & x > 1 \
    end{array}$$



    Two common ways for this to be interpreted are (1) $(forall x~.~x > 2) to (forall x~.~x > 1)$ and (2) $forall x~.~(x > 2 to x > 1)$. Logics that intend the first way include PRA and Hilbert style FOL. Logics that intend the second way include Fitch style Natural Deduction.



    Is there common terminology to distinguish the two approaches to interpreting how the free variables are shared between propositions in a proof? Or if you have reason to think there are no such common terms, what would you suggest?






    logic terminology quantifiers sequent-calculus







    share|cite|improve this question
























      up vote
      2
      down vote

      favorite









      up vote
      2
      down vote

      favorite











      Suppose you have a proof along the lines of



      $$begin{array} {rc}
      text{Assume:} & x > 2 \
      & vdots \
      & text{Some logic stuff} \
      & vdots \
      text{Conclude:} & x > 1 \
      end{array}$$



      Two common ways for this to be interpreted are (1) $(forall x~.~x > 2) to (forall x~.~x > 1)$ and (2) $forall x~.~(x > 2 to x > 1)$. Logics that intend the first way include PRA and Hilbert style FOL. Logics that intend the second way include Fitch style Natural Deduction.



      Is there common terminology to distinguish the two approaches to interpreting how the free variables are shared between propositions in a proof? Or if you have reason to think there are no such common terms, what would you suggest?






      logic terminology quantifiers sequent-calculus







      share|cite|improve this question













      Suppose you have a proof along the lines of



      $$begin{array} {rc}
      text{Assume:} & x > 2 \
      & vdots \
      & text{Some logic stuff} \
      & vdots \
      text{Conclude:} & x > 1 \
      end{array}$$



      Two common ways for this to be interpreted are (1) $(forall x~.~x > 2) to (forall x~.~x > 1)$ and (2) $forall x~.~(x > 2 to x > 1)$. Logics that intend the first way include PRA and Hilbert style FOL. Logics that intend the second way include Fitch style Natural Deduction.



      Is there common terminology to distinguish the two approaches to interpreting how the free variables are shared between propositions in a proof? Or if you have reason to think there are no such common terms, what would you suggest?






      logic terminology quantifiers sequent-calculus




      logic terminology quantifiers sequent-calculus






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked 18 hours ago









      DanielV

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