Natural deduction proof - is this correct?
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I don't know of any means to check my work, can anyone point out if they're any mistakes?
proof-verification logic propositional-calculus first-order-logic natural-deduction
edited Nov 23 at 3:28
Graham Kemp
84.7k43378
asked Nov 23 at 2:00
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up vote
-4
down vote
favorite
I don't know of any means to check my work, can anyone point out if they're any mistakes?
proof-verification logic propositional-calculus first-order-logic natural-deduction
edited Nov 23 at 3:28
Graham Kemp
84.7k43378
asked Nov 23 at 2:00
esperski
2
It is prefered that you type things out rather than use an outside link. Text is searchable, and links may disappear.
– Graham Kemp
Nov 23 at 3:27
add a comment |
up vote
-4
down vote
favorite
up vote
-4
down vote
favorite
I don't know of any means to check my work, can anyone point out if they're any mistakes?
proof-verification logic propositional-calculus first-order-logic natural-deduction
edited Nov 23 at 3:28
Graham Kemp
84.7k43378
asked Nov 23 at 2:00
esperski
2
I don't know of any means to check my work, can anyone point out if they're any mistakes?
proof-verification logic propositional-calculus first-order-logic natural-deduction
proof-verification logic propositional-calculus first-order-logic natural-deduction
edited Nov 23 at 3:28
Graham Kemp
84.7k43378
asked Nov 23 at 2:00
esperski
2
edited Nov 23 at 3:28
Graham Kemp
84.7k43378
asked Nov 23 at 2:00
esperski
2
edited Nov 23 at 3:28
Graham Kemp
84.7k43378
edited Nov 23 at 3:28
Graham Kemp
84.7k43378
edited Nov 23 at 3:28
Graham Kemp
84.7k43378
84.7k43378
asked Nov 23 at 2:00
esperski
2
asked Nov 23 at 2:00
esperski
2
asked Nov 23 at 2:00
esperski
2
2
It is prefered that you type things out rather than use an outside link. Text is searchable, and links may disappear.
– Graham Kemp
Nov 23 at 3:27
add a comment |
It is prefered that you type things out rather than use an outside link. Text is searchable, and links may disappear.
– Graham Kemp
Nov 23 at 3:27
It is prefered that you type things out rather than use an outside link. Text is searchable, and links may disappear.
– Graham Kemp
Nov 23 at 3:27
It is prefered that you type things out rather than use an outside link. Text is searchable, and links may disappear.
– Graham Kemp
Nov 23 at 3:27
add a comment |
1 Answer
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Yes. You are putting the deductions before their sub-proofs and the naming convention is not quite what I'm used to, but that looks okay.
To check, in my prefered format that would be:
$$smalldeffitch#1#2{quadbegin{array}{|l}#1\hline #2end{array}}fitch{1.~lnot (pto q)qquadtextsf{Premise}}{fitch{2.~lnot(plandlnot q)qquadtextsf{Assumption}}{3.~lnot(pto q)qquadtextsf{Reiteration (1)}}\4.~ lnot(plandlnot q)tolnot(pto q)qquadtextsf{Conditional Introduction (2-3)}\fitch{5.~lnot(plandlnot q)qquadtextsf{Assumption}}{fitch{6.~pqquadtextsf{Assumption}}{fitch{7.~lnot qqquadtextsf{Assumption}}{8.~plandlnot qqquadtextsf{Conjunction Introduction (6,7)}}\9.~lnot qto( plandlnot q)qquadtextsf{Conditional Introduction (7-8)}\fitch{10.~lnot qqquadtextsf{Assumption}}{11.~lnot (plandlnot q)qquadtextsf{Reiteration (5)}}\12.~lnot qtolnot(plandlnot q)qquadtextsf{Conditional Introduction (10-11)}\13.~lnotlnot qqquadtextsf{Negation Introduction (9,12)}\14.~qqquadtextsf{Double Negation Elimination (13)}}\15.~pto qqquadtextsf{Conditional Introduction (6-14)}}\16.~lnot(plandlnot q)to (pto q)qquadtextsf{Conditional Introduction (5-15)}\17.~lnotlnot(plandlnot q)qquadtextsf{Negation Introduction (4,16)}\18.~plandlnot qqquadtextsf{Double Negation Elimination (17)}\blacksquare}$$
answered Nov 23 at 3:20
Graham Kemp
84.7k43378
add a comment |
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1 Answer
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Yes. You are putting the deductions before their sub-proofs and the naming convention is not quite what I'm used to, but that looks okay.
To check, in my prefered format that would be:
$$smalldeffitch#1#2{quadbegin{array}{|l}#1\hline #2end{array}}fitch{1.~lnot (pto q)qquadtextsf{Premise}}{fitch{2.~lnot(plandlnot q)qquadtextsf{Assumption}}{3.~lnot(pto q)qquadtextsf{Reiteration (1)}}\4.~ lnot(plandlnot q)tolnot(pto q)qquadtextsf{Conditional Introduction (2-3)}\fitch{5.~lnot(plandlnot q)qquadtextsf{Assumption}}{fitch{6.~pqquadtextsf{Assumption}}{fitch{7.~lnot qqquadtextsf{Assumption}}{8.~plandlnot qqquadtextsf{Conjunction Introduction (6,7)}}\9.~lnot qto( plandlnot q)qquadtextsf{Conditional Introduction (7-8)}\fitch{10.~lnot qqquadtextsf{Assumption}}{11.~lnot (plandlnot q)qquadtextsf{Reiteration (5)}}\12.~lnot qtolnot(plandlnot q)qquadtextsf{Conditional Introduction (10-11)}\13.~lnotlnot qqquadtextsf{Negation Introduction (9,12)}\14.~qqquadtextsf{Double Negation Elimination (13)}}\15.~pto qqquadtextsf{Conditional Introduction (6-14)}}\16.~lnot(plandlnot q)to (pto q)qquadtextsf{Conditional Introduction (5-15)}\17.~lnotlnot(plandlnot q)qquadtextsf{Negation Introduction (4,16)}\18.~plandlnot qqquadtextsf{Double Negation Elimination (17)}\blacksquare}$$
answered Nov 23 at 3:20
Graham Kemp
84.7k43378
add a comment |
up vote
0
down vote
Yes. You are putting the deductions before their sub-proofs and the naming convention is not quite what I'm used to, but that looks okay.
To check, in my prefered format that would be:
$$smalldeffitch#1#2{quadbegin{array}{|l}#1\hline #2end{array}}fitch{1.~lnot (pto q)qquadtextsf{Premise}}{fitch{2.~lnot(plandlnot q)qquadtextsf{Assumption}}{3.~lnot(pto q)qquadtextsf{Reiteration (1)}}\4.~ lnot(plandlnot q)tolnot(pto q)qquadtextsf{Conditional Introduction (2-3)}\fitch{5.~lnot(plandlnot q)qquadtextsf{Assumption}}{fitch{6.~pqquadtextsf{Assumption}}{fitch{7.~lnot qqquadtextsf{Assumption}}{8.~plandlnot qqquadtextsf{Conjunction Introduction (6,7)}}\9.~lnot qto( plandlnot q)qquadtextsf{Conditional Introduction (7-8)}\fitch{10.~lnot qqquadtextsf{Assumption}}{11.~lnot (plandlnot q)qquadtextsf{Reiteration (5)}}\12.~lnot qtolnot(plandlnot q)qquadtextsf{Conditional Introduction (10-11)}\13.~lnotlnot qqquadtextsf{Negation Introduction (9,12)}\14.~qqquadtextsf{Double Negation Elimination (13)}}\15.~pto qqquadtextsf{Conditional Introduction (6-14)}}\16.~lnot(plandlnot q)to (pto q)qquadtextsf{Conditional Introduction (5-15)}\17.~lnotlnot(plandlnot q)qquadtextsf{Negation Introduction (4,16)}\18.~plandlnot qqquadtextsf{Double Negation Elimination (17)}\blacksquare}$$
answered Nov 23 at 3:20
Graham Kemp
84.7k43378
add a comment |
up vote
0
down vote
up vote
0
down vote
Yes. You are putting the deductions before their sub-proofs and the naming convention is not quite what I'm used to, but that looks okay.
To check, in my prefered format that would be:
$$smalldeffitch#1#2{quadbegin{array}{|l}#1\hline #2end{array}}fitch{1.~lnot (pto q)qquadtextsf{Premise}}{fitch{2.~lnot(plandlnot q)qquadtextsf{Assumption}}{3.~lnot(pto q)qquadtextsf{Reiteration (1)}}\4.~ lnot(plandlnot q)tolnot(pto q)qquadtextsf{Conditional Introduction (2-3)}\fitch{5.~lnot(plandlnot q)qquadtextsf{Assumption}}{fitch{6.~pqquadtextsf{Assumption}}{fitch{7.~lnot qqquadtextsf{Assumption}}{8.~plandlnot qqquadtextsf{Conjunction Introduction (6,7)}}\9.~lnot qto( plandlnot q)qquadtextsf{Conditional Introduction (7-8)}\fitch{10.~lnot qqquadtextsf{Assumption}}{11.~lnot (plandlnot q)qquadtextsf{Reiteration (5)}}\12.~lnot qtolnot(plandlnot q)qquadtextsf{Conditional Introduction (10-11)}\13.~lnotlnot qqquadtextsf{Negation Introduction (9,12)}\14.~qqquadtextsf{Double Negation Elimination (13)}}\15.~pto qqquadtextsf{Conditional Introduction (6-14)}}\16.~lnot(plandlnot q)to (pto q)qquadtextsf{Conditional Introduction (5-15)}\17.~lnotlnot(plandlnot q)qquadtextsf{Negation Introduction (4,16)}\18.~plandlnot qqquadtextsf{Double Negation Elimination (17)}\blacksquare}$$
answered Nov 23 at 3:20
Graham Kemp
84.7k43378
Yes. You are putting the deductions before their sub-proofs and the naming convention is not quite what I'm used to, but that looks okay.
To check, in my prefered format that would be:
$$smalldeffitch#1#2{quadbegin{array}{|l}#1\hline #2end{array}}fitch{1.~lnot (pto q)qquadtextsf{Premise}}{fitch{2.~lnot(plandlnot q)qquadtextsf{Assumption}}{3.~lnot(pto q)qquadtextsf{Reiteration (1)}}\4.~ lnot(plandlnot q)tolnot(pto q)qquadtextsf{Conditional Introduction (2-3)}\fitch{5.~lnot(plandlnot q)qquadtextsf{Assumption}}{fitch{6.~pqquadtextsf{Assumption}}{fitch{7.~lnot qqquadtextsf{Assumption}}{8.~plandlnot qqquadtextsf{Conjunction Introduction (6,7)}}\9.~lnot qto( plandlnot q)qquadtextsf{Conditional Introduction (7-8)}\fitch{10.~lnot qqquadtextsf{Assumption}}{11.~lnot (plandlnot q)qquadtextsf{Reiteration (5)}}\12.~lnot qtolnot(plandlnot q)qquadtextsf{Conditional Introduction (10-11)}\13.~lnotlnot qqquadtextsf{Negation Introduction (9,12)}\14.~qqquadtextsf{Double Negation Elimination (13)}}\15.~pto qqquadtextsf{Conditional Introduction (6-14)}}\16.~lnot(plandlnot q)to (pto q)qquadtextsf{Conditional Introduction (5-15)}\17.~lnotlnot(plandlnot q)qquadtextsf{Negation Introduction (4,16)}\18.~plandlnot qqquadtextsf{Double Negation Elimination (17)}\blacksquare}$$
answered Nov 23 at 3:20
Graham Kemp
84.7k43378
edited Nov 23 at 3:26
answered Nov 23 at 3:20
Graham Kemp
84.7k43378
answered Nov 23 at 3:20
Graham Kemp
84.7k43378
answered Nov 23 at 3:20
Graham Kemp
84.7k43378
84.7k43378
add a comment |
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It is prefered that you type things out rather than use an outside link. Text is searchable, and links may disappear.
– Graham Kemp
Nov 23 at 3:27