Is my Skolem normal form of $(forall x exists yexists zT(x,y)land S(y,z))land(lnotforall yP(y))$ correct?

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Is my skolem normal form of $(forall x exists y exists z T(x,y)land S(y,z))land (lnot forall yP(y))$ correct?



$$
beginarray
hline
( forall x exists y exists z ; T(x,y) land S(y,z) )
land (neg forall y ; P(y))
& leftarrowtextGiven formula
\
hline
( forall x exists y exists z ; T(x,y) land S(y,z))
land (neg forall y ; P(y))
& textRename variables and
\

& textchange quantors
\
hline
( forall x exists y exists z ; (T(x,y) land S(y,z)) )
land (exists v ; neg P(v))
& textRemove $()$ and move
\

& text$exists v$ to the left side
\
hline
forall x exists y exists z exists u
; T(x,y) land S(y,z) land neg P(u)
& textIt is in PNF. Do:
\

& exists y = i(x);
exists z = k(x);
\

& exists u = h(x)
\
hline
forall x ; T(x, i(x)) land Q(f(x), k(x)) land neg P(h(x))
& textIt is in SNF.
\
hline
endarray
$$
(Original picture of the calculation here.)




predicate-logic




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  • Thanks for your corrections @Bernard - did you also check the calculations?
    – user3352632
    Aug 26 at 20:42










  • It's beyond my capabilities, unfortunately.
    – Bernard
    Aug 26 at 20:45














up vote
0
down vote

favorite












Is my skolem normal form of $(forall x exists y exists z T(x,y)land S(y,z))land (lnot forall yP(y))$ correct?



$$
beginarray
hline
( forall x exists y exists z ; T(x,y) land S(y,z) )
land (neg forall y ; P(y))
& leftarrowtextGiven formula
\
hline
( forall x exists y exists z ; T(x,y) land S(y,z))
land (neg forall y ; P(y))
& textRename variables and
\

& textchange quantors
\
hline
( forall x exists y exists z ; (T(x,y) land S(y,z)) )
land (exists v ; neg P(v))
& textRemove $()$ and move
\

& text$exists v$ to the left side
\
hline
forall x exists y exists z exists u
; T(x,y) land S(y,z) land neg P(u)
& textIt is in PNF. Do:
\

& exists y = i(x);
exists z = k(x);
\

& exists u = h(x)
\
hline
forall x ; T(x, i(x)) land Q(f(x), k(x)) land neg P(h(x))
& textIt is in SNF.
\
hline
endarray
$$
(Original picture of the calculation here.)




predicate-logic




share|cite|improve this question






















  • Thanks for your corrections @Bernard - did you also check the calculations?
    – user3352632
    Aug 26 at 20:42










  • It's beyond my capabilities, unfortunately.
    – Bernard
    Aug 26 at 20:45












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Is my skolem normal form of $(forall x exists y exists z T(x,y)land S(y,z))land (lnot forall yP(y))$ correct?



$$
beginarray
hline
( forall x exists y exists z ; T(x,y) land S(y,z) )
land (neg forall y ; P(y))
& leftarrowtextGiven formula
\
hline
( forall x exists y exists z ; T(x,y) land S(y,z))
land (neg forall y ; P(y))
& textRename variables and
\

& textchange quantors
\
hline
( forall x exists y exists z ; (T(x,y) land S(y,z)) )
land (exists v ; neg P(v))
& textRemove $()$ and move
\

& text$exists v$ to the left side
\
hline
forall x exists y exists z exists u
; T(x,y) land S(y,z) land neg P(u)
& textIt is in PNF. Do:
\

& exists y = i(x);
exists z = k(x);
\

& exists u = h(x)
\
hline
forall x ; T(x, i(x)) land Q(f(x), k(x)) land neg P(h(x))
& textIt is in SNF.
\
hline
endarray
$$
(Original picture of the calculation here.)




predicate-logic




share|cite|improve this question














Is my skolem normal form of $(forall x exists y exists z T(x,y)land S(y,z))land (lnot forall yP(y))$ correct?



$$
beginarray
hline
( forall x exists y exists z ; T(x,y) land S(y,z) )
land (neg forall y ; P(y))
& leftarrowtextGiven formula
\
hline
( forall x exists y exists z ; T(x,y) land S(y,z))
land (neg forall y ; P(y))
& textRename variables and
\

& textchange quantors
\
hline
( forall x exists y exists z ; (T(x,y) land S(y,z)) )
land (exists v ; neg P(v))
& textRemove $()$ and move
\

& text$exists v$ to the left side
\
hline
forall x exists y exists z exists u
; T(x,y) land S(y,z) land neg P(u)
& textIt is in PNF. Do:
\

& exists y = i(x);
exists z = k(x);
\

& exists u = h(x)
\
hline
forall x ; T(x, i(x)) land Q(f(x), k(x)) land neg P(h(x))
& textIt is in SNF.
\
hline
endarray
$$
(Original picture of the calculation here.)





predicate-logic





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share|cite|improve this question




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edited Aug 26 at 20:47









Jendrik Stelzner

7,63121037




7,63121037










asked Aug 26 at 20:23









user3352632

827




827











  • Thanks for your corrections @Bernard - did you also check the calculations?
    – user3352632
    Aug 26 at 20:42










  • It's beyond my capabilities, unfortunately.
    – Bernard
    Aug 26 at 20:45
















  • Thanks for your corrections @Bernard - did you also check the calculations?
    – user3352632
    Aug 26 at 20:42










  • It's beyond my capabilities, unfortunately.
    – Bernard
    Aug 26 at 20:45















Thanks for your corrections @Bernard - did you also check the calculations?
– user3352632
Aug 26 at 20:42




Thanks for your corrections @Bernard - did you also check the calculations?
– user3352632
Aug 26 at 20:42












It's beyond my capabilities, unfortunately.
– Bernard
Aug 26 at 20:45




It's beyond my capabilities, unfortunately.
– Bernard
Aug 26 at 20:45















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