Natural deduction proof - is this correct?











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proof-verification logic propositional-calculus first-order-logic natural-deduction







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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







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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
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up vote
-4
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favorite









up vote
-4
down vote

favorite











1



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







share|cite|improve this question















1



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






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edited Nov 23 at 3:28









Graham Kemp

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asked Nov 23 at 2:00









esperski

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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


















  • 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










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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:



$$smalldeffitch#1#2{quadbegin{array}{|l}#1\hline #2end{array}}fitch{1.~lnot (pto q)qquadtextsf{Premise}}{fitch{2.~lnot(plandlnot q)qquadtextsf{Assumption}}{3.~lnot(pto q)qquadtextsf{Reiteration (1)}}\4.~ lnot(plandlnot q)tolnot(pto q)qquadtextsf{Conditional Introduction (2-3)}\fitch{5.~lnot(plandlnot q)qquadtextsf{Assumption}}{fitch{6.~pqquadtextsf{Assumption}}{fitch{7.~lnot qqquadtextsf{Assumption}}{8.~plandlnot qqquadtextsf{Conjunction Introduction (6,7)}}\9.~lnot qto( plandlnot q)qquadtextsf{Conditional Introduction (7-8)}\fitch{10.~lnot qqquadtextsf{Assumption}}{11.~lnot (plandlnot q)qquadtextsf{Reiteration (5)}}\12.~lnot qtolnot(plandlnot q)qquadtextsf{Conditional Introduction (10-11)}\13.~lnotlnot qqquadtextsf{Negation Introduction (9,12)}\14.~qqquadtextsf{Double Negation Elimination (13)}}\15.~pto qqquadtextsf{Conditional Introduction (6-14)}}\16.~lnot(plandlnot q)to (pto q)qquadtextsf{Conditional Introduction (5-15)}\17.~lnotlnot(plandlnot q)qquadtextsf{Negation Introduction (4,16)}\18.~plandlnot qqquadtextsf{Double Negation Elimination (17)}\blacksquare}$$






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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:



    $$smalldeffitch#1#2{quadbegin{array}{|l}#1\hline #2end{array}}fitch{1.~lnot (pto q)qquadtextsf{Premise}}{fitch{2.~lnot(plandlnot q)qquadtextsf{Assumption}}{3.~lnot(pto q)qquadtextsf{Reiteration (1)}}\4.~ lnot(plandlnot q)tolnot(pto q)qquadtextsf{Conditional Introduction (2-3)}\fitch{5.~lnot(plandlnot q)qquadtextsf{Assumption}}{fitch{6.~pqquadtextsf{Assumption}}{fitch{7.~lnot qqquadtextsf{Assumption}}{8.~plandlnot qqquadtextsf{Conjunction Introduction (6,7)}}\9.~lnot qto( plandlnot q)qquadtextsf{Conditional Introduction (7-8)}\fitch{10.~lnot qqquadtextsf{Assumption}}{11.~lnot (plandlnot q)qquadtextsf{Reiteration (5)}}\12.~lnot qtolnot(plandlnot q)qquadtextsf{Conditional Introduction (10-11)}\13.~lnotlnot qqquadtextsf{Negation Introduction (9,12)}\14.~qqquadtextsf{Double Negation Elimination (13)}}\15.~pto qqquadtextsf{Conditional Introduction (6-14)}}\16.~lnot(plandlnot q)to (pto q)qquadtextsf{Conditional Introduction (5-15)}\17.~lnotlnot(plandlnot q)qquadtextsf{Negation Introduction (4,16)}\18.~plandlnot qqquadtextsf{Double Negation Elimination (17)}\blacksquare}$$






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      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:



      $$smalldeffitch#1#2{quadbegin{array}{|l}#1\hline #2end{array}}fitch{1.~lnot (pto q)qquadtextsf{Premise}}{fitch{2.~lnot(plandlnot q)qquadtextsf{Assumption}}{3.~lnot(pto q)qquadtextsf{Reiteration (1)}}\4.~ lnot(plandlnot q)tolnot(pto q)qquadtextsf{Conditional Introduction (2-3)}\fitch{5.~lnot(plandlnot q)qquadtextsf{Assumption}}{fitch{6.~pqquadtextsf{Assumption}}{fitch{7.~lnot qqquadtextsf{Assumption}}{8.~plandlnot qqquadtextsf{Conjunction Introduction (6,7)}}\9.~lnot qto( plandlnot q)qquadtextsf{Conditional Introduction (7-8)}\fitch{10.~lnot qqquadtextsf{Assumption}}{11.~lnot (plandlnot q)qquadtextsf{Reiteration (5)}}\12.~lnot qtolnot(plandlnot q)qquadtextsf{Conditional Introduction (10-11)}\13.~lnotlnot qqquadtextsf{Negation Introduction (9,12)}\14.~qqquadtextsf{Double Negation Elimination (13)}}\15.~pto qqquadtextsf{Conditional Introduction (6-14)}}\16.~lnot(plandlnot q)to (pto q)qquadtextsf{Conditional Introduction (5-15)}\17.~lnotlnot(plandlnot q)qquadtextsf{Negation Introduction (4,16)}\18.~plandlnot qqquadtextsf{Double Negation Elimination (17)}\blacksquare}$$






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        up vote
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        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:



        $$smalldeffitch#1#2{quadbegin{array}{|l}#1\hline #2end{array}}fitch{1.~lnot (pto q)qquadtextsf{Premise}}{fitch{2.~lnot(plandlnot q)qquadtextsf{Assumption}}{3.~lnot(pto q)qquadtextsf{Reiteration (1)}}\4.~ lnot(plandlnot q)tolnot(pto q)qquadtextsf{Conditional Introduction (2-3)}\fitch{5.~lnot(plandlnot q)qquadtextsf{Assumption}}{fitch{6.~pqquadtextsf{Assumption}}{fitch{7.~lnot qqquadtextsf{Assumption}}{8.~plandlnot qqquadtextsf{Conjunction Introduction (6,7)}}\9.~lnot qto( plandlnot q)qquadtextsf{Conditional Introduction (7-8)}\fitch{10.~lnot qqquadtextsf{Assumption}}{11.~lnot (plandlnot q)qquadtextsf{Reiteration (5)}}\12.~lnot qtolnot(plandlnot q)qquadtextsf{Conditional Introduction (10-11)}\13.~lnotlnot qqquadtextsf{Negation Introduction (9,12)}\14.~qqquadtextsf{Double Negation Elimination (13)}}\15.~pto qqquadtextsf{Conditional Introduction (6-14)}}\16.~lnot(plandlnot q)to (pto q)qquadtextsf{Conditional Introduction (5-15)}\17.~lnotlnot(plandlnot q)qquadtextsf{Negation Introduction (4,16)}\18.~plandlnot qqquadtextsf{Double Negation Elimination (17)}\blacksquare}$$






        share|cite|improve this answer














        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:



        $$smalldeffitch#1#2{quadbegin{array}{|l}#1\hline #2end{array}}fitch{1.~lnot (pto q)qquadtextsf{Premise}}{fitch{2.~lnot(plandlnot q)qquadtextsf{Assumption}}{3.~lnot(pto q)qquadtextsf{Reiteration (1)}}\4.~ lnot(plandlnot q)tolnot(pto q)qquadtextsf{Conditional Introduction (2-3)}\fitch{5.~lnot(plandlnot q)qquadtextsf{Assumption}}{fitch{6.~pqquadtextsf{Assumption}}{fitch{7.~lnot qqquadtextsf{Assumption}}{8.~plandlnot qqquadtextsf{Conjunction Introduction (6,7)}}\9.~lnot qto( plandlnot q)qquadtextsf{Conditional Introduction (7-8)}\fitch{10.~lnot qqquadtextsf{Assumption}}{11.~lnot (plandlnot q)qquadtextsf{Reiteration (5)}}\12.~lnot qtolnot(plandlnot q)qquadtextsf{Conditional Introduction (10-11)}\13.~lnotlnot qqquadtextsf{Negation Introduction (9,12)}\14.~qqquadtextsf{Double Negation Elimination (13)}}\15.~pto qqquadtextsf{Conditional Introduction (6-14)}}\16.~lnot(plandlnot q)to (pto q)qquadtextsf{Conditional Introduction (5-15)}\17.~lnotlnot(plandlnot q)qquadtextsf{Negation Introduction (4,16)}\18.~plandlnot qqquadtextsf{Double Negation Elimination (17)}\blacksquare}$$







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Nov 23 at 3:26

























        answered Nov 23 at 3:20









        Graham Kemp

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