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
add a comment |Â
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
Thanks for your corrections @Bernard - did you also check the calculations?
â user3352632
Aug 26 at 20:42
It's beyond my capabilities, unfortunately.
â Bernard
Aug 26 at 20:45
add a comment |Â
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
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
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?
â user3352632
Aug 26 at 20:42
It's beyond my capabilities, unfortunately.
â Bernard
Aug 26 at 20:45
add a comment |Â
Thanks for your corrections @Bernard - did you also check the calculations?
â user3352632
Aug 26 at 20:42
It's beyond my capabilities, unfortunately.
â Bernard
Aug 26 at 20:45
Thanks for your corrections @Bernard - did you also check the calculations?
â user3352632
Aug 26 at 20:42
Thanks for your corrections @Bernard - did you also check the calculations?
â user3352632
Aug 26 at 20:42
It's beyond my capabilities, unfortunately.
â Bernard
Aug 26 at 20:45
It's beyond my capabilities, unfortunately.
â Bernard
Aug 26 at 20:45
add a comment |Â
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Thanks for your corrections @Bernard - did you also check the calculations?
â user3352632
Aug 26 at 20:42
It's beyond my capabilities, unfortunately.
â Bernard
Aug 26 at 20:45