Mixing
Help in removing assumptions in logic proofs
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When showing that X is provable from Y (Y ⊢ X) when do remove the assumptions we made? I can't seem to find a rule
discrete-mathematics logic
asked Feb 1 at 14:18
SergioSergio
11
$endgroup$
add a comment |
$begingroup$
When showing that X is provable from Y (Y ⊢ X) when do remove the assumptions we made? I can't seem to find a rule
discrete-mathematics logic
asked Feb 1 at 14:18
SergioSergio
11
$endgroup$
$begingroup$
Yes your completely right, my mistake, will edit even though it doesn't really affect the answer
$endgroup$
– Sergio
Feb 2 at 9:48
add a comment |
$begingroup$
When showing that X is provable from Y (Y ⊢ X) when do remove the assumptions we made? I can't seem to find a rule
discrete-mathematics logic
asked Feb 1 at 14:18
SergioSergio
11
$endgroup$
When showing that X is provable from Y (Y ⊢ X) when do remove the assumptions we made? I can't seem to find a rule
discrete-mathematics logic
discrete-mathematics logic
asked Feb 1 at 14:18
SergioSergio
11
asked Feb 1 at 14:18
SergioSergio
11
edited Feb 2 at 9:49
Sergio
asked Feb 1 at 14:18
SergioSergio
11
asked Feb 1 at 14:18
SergioSergio
11
asked Feb 1 at 14:18
SergioSergio
11
11
$begingroup$
Yes your completely right, my mistake, will edit even though it doesn't really affect the answer
$endgroup$
– Sergio
Feb 2 at 9:48
add a comment |
$begingroup$
Yes your completely right, my mistake, will edit even though it doesn't really affect the answer
$endgroup$
– Sergio
Feb 2 at 9:48
$begingroup$
Yes your completely right, my mistake, will edit even though it doesn't really affect the answer
$endgroup$
– Sergio
Feb 2 at 9:48
$begingroup$
Yes your completely right, my mistake, will edit even though it doesn't really affect the answer
$endgroup$
– Sergio
Feb 2 at 9:48
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
Some inference rules allow us to "discharge" assumptions; others do not.
See Natural Deduction : rules.
For example, the rule of Conjunction elimination : $dfrac {varphi land psi}{ varphi}$ does not allow us to discharge any assumption, while the rule of Conditional introduction : $dfrac {Gamma, varphi vdash psi}{Gamma vdash varphi to psi}$ does.
See also : Deduction theorem.
answered Feb 1 at 14:30
Mauro ALLEGRANZAMauro ALLEGRANZA
67.8k449117
$endgroup$
$begingroup$
Thank you for your input.
$endgroup$
– Sergio
Feb 2 at 9:49
add a comment |
Your Answer
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1 Answer
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active
oldest
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1 Answer
1
active
oldest
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oldest
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active
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votes
$begingroup$
Some inference rules allow us to "discharge" assumptions; others do not.
See Natural Deduction : rules.
For example, the rule of Conjunction elimination : $dfrac {varphi land psi}{ varphi}$ does not allow us to discharge any assumption, while the rule of Conditional introduction : $dfrac {Gamma, varphi vdash psi}{Gamma vdash varphi to psi}$ does.
See also : Deduction theorem.
answered Feb 1 at 14:30
Mauro ALLEGRANZAMauro ALLEGRANZA
67.8k449117
$endgroup$
$begingroup$
Thank you for your input.
$endgroup$
– Sergio
Feb 2 at 9:49
add a comment |
$begingroup$
Some inference rules allow us to "discharge" assumptions; others do not.
See Natural Deduction : rules.
For example, the rule of Conjunction elimination : $dfrac {varphi land psi}{ varphi}$ does not allow us to discharge any assumption, while the rule of Conditional introduction : $dfrac {Gamma, varphi vdash psi}{Gamma vdash varphi to psi}$ does.
See also : Deduction theorem.
answered Feb 1 at 14:30
Mauro ALLEGRANZAMauro ALLEGRANZA
67.8k449117
$endgroup$
$begingroup$
Thank you for your input.
$endgroup$
– Sergio
Feb 2 at 9:49
add a comment |
$begingroup$
Some inference rules allow us to "discharge" assumptions; others do not.
See Natural Deduction : rules.
For example, the rule of Conjunction elimination : $dfrac {varphi land psi}{ varphi}$ does not allow us to discharge any assumption, while the rule of Conditional introduction : $dfrac {Gamma, varphi vdash psi}{Gamma vdash varphi to psi}$ does.
See also : Deduction theorem.
answered Feb 1 at 14:30
Mauro ALLEGRANZAMauro ALLEGRANZA
67.8k449117
$endgroup$
Some inference rules allow us to "discharge" assumptions; others do not.
See Natural Deduction : rules.
For example, the rule of Conjunction elimination : $dfrac {varphi land psi}{ varphi}$ does not allow us to discharge any assumption, while the rule of Conditional introduction : $dfrac {Gamma, varphi vdash psi}{Gamma vdash varphi to psi}$ does.
See also : Deduction theorem.
answered Feb 1 at 14:30
Mauro ALLEGRANZAMauro ALLEGRANZA
67.8k449117
answered Feb 1 at 14:30
Mauro ALLEGRANZAMauro ALLEGRANZA
67.8k449117
answered Feb 1 at 14:30
Mauro ALLEGRANZAMauro ALLEGRANZA
67.8k449117
answered Feb 1 at 14:30
Mauro ALLEGRANZAMauro ALLEGRANZA
67.8k449117
67.8k449117
$begingroup$
Thank you for your input.
$endgroup$
– Sergio
Feb 2 at 9:49
add a comment |
$begingroup$
Thank you for your input.
$endgroup$
– Sergio
Feb 2 at 9:49
$begingroup$
Thank you for your input.
$endgroup$
– Sergio
Feb 2 at 9:49
$begingroup$
Thank you for your input.
$endgroup$
– Sergio
Feb 2 at 9:49
add a comment |
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$begingroup$
Yes your completely right, my mistake, will edit even though it doesn't really affect the answer
$endgroup$
– Sergio
Feb 2 at 9:48