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Formulas in predicate logic/3 places

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Formulas in predicate logic


list
as "A whishes B to love C."
example sentence sketch formula pairs coord var bin rank
Someone wants that someone loves someone. ∃x ∃y ∃z Pxyz

e123
777
777 444 3 111 6
For everyone there is someone who
wants them to be loved by someone.
∀z ∃x ∃y Pxyz

a3 e12
733
337 442 3 110 5
For everyone there is someone who
wants them to love someone.
∀y ∃x ∃z Pxyz

a2 e13
376
673 424 3 101 5
Everyone wants someone to love someone. ∀x ∃y ∃z Pxyz

a1 e23
667
766 244 3 011 5
There is a y for which for every z exists an x that wants y to love z.
There is someone so that for every other person exists someone
who wants them to love that other person.
∃y ∀z ∃x Pxyz

e2 a3 e1
731
137 431 3 110 4
There is someone who wants that everyone is loved by someone. ∃x ∀z ∃y Pxyz

e1 a3 e2
713
317 341 3 110 4
There is a z for which for every y exists an x that wants y to love z.
There is someone so that for every other person exists someone
who wants them to be loved by that other person.
∃z ∀y ∃x Pxyz

e3 a2 e1
374
473 413 3 101 4
Someone wants everyone to love someone. ∃x ∀y ∃z Pxyz

e1 a2 e3
176
671 314 3 101 4
There is someone whom everyone wishes to be loved by someone. ∃z ∀x ∃y Pxyz

e3 a1 e2
647
746 143 3 011 4
There is someone whom everyone wishes to love someone. ∃y ∀x ∃z Pxyz

e2 a1 e3
467
764 134 3 011 4
Someone wishes someone to love everyone. ∃x ∃y ∀z Pxyz

e12 a3
711
117 330 3 110 3
Someone wishes someone to be loved by everyone. ∃x ∃z ∀y Pxyz

e13 a2
174
471 303 3 101 3
There are y and z, and every x wants that y loves z.
There are two people, and everyone
wants one of them to love the other one.
∃y ∃z ∀x Pxyz

e23 a1
447
744 033 3 011 3
For every pair of people (y, z) there is some person x who wants y to love z.
For every two people a and b there is someone who wants a to love b
and someone who wants b to love a.
∀y ∀z ∃x Pxyz

a23 e1
330
033 411 3 100 3
Everyone wants everyone to be loved by someone. ∀x ∀z ∃y Pxyz

a13 e2
603
306 141 3 010 3
Everyone wants everyone to love someone. ∀x ∀y ∃z Pxyz

a12 e3
066
660 114 3 001 3
For everyone there is someone who wants them to love everyone. ∀y ∃x ∀z Pxyz

a2 e1 a3
310
013 310 3 100 2
For everyone there is someone who wants them to be loved by everyone. ∀z ∃x ∀y Pxyz

a3 e1 a2
130
031 301 3 100 2
Everyone wishes someone to love everyone. ∀x ∃y ∀z Pxyz

a1 e2 a3
601
106 130 3 010 2
For everyone there is someone whom everyone wants to love them. ∀z ∃y ∀x Pxyz

a3 e2 a1
403
304 031 3 010 2
Everyone wishes someone to be loved by everyone. ∀x ∃z ∀y Pxyz

a1 e3 a2
064
460 103 3 001 2
For everyone there is someone whom everyone wants them to love. ∀y ∃z ∀x Pxyz

a2 e3 a1
046
640 013 3 001 2
Someone wants that everyone loves everyone. ∃x ∀y ∀z Pxyz

e1 a23
110
011 200 3 100 1
There is someone whom everyone wishes
to love everyone.
∃y ∀x ∀z Pxyz

e2 a13
401
104 020 3 010 1
There is someone whom everyone wishes
to be loved by everyone.
∃z ∀x ∀y Pxyz

e3 a12
044
440 002 3 001 1
Everyone wants everyone to love everyone. ∀x ∀y ∀z Pxyz

a123
000
000 000 3 000 0
Someone wants to love someone. ∃x ∃y Pxxy

e(12)3
577
775 334 2 111 5
For everyone there is someone who wants to love them. ∀y ∃x Pxxy

a3 e(12)
533
335 332 2 110 4
Everyone wants to love someone. ∀x ∃y Pxxy

a(12) e3
266
662 224 2 001 4
Someone wants to love everyone. ∃x ∀y Pxxy

e(12) a3
511
115 220 2 110 2
There is someone whom everyone wants to love. ∃y ∀x Pxxy

e3 a(12)
244
442 112 2 001 2
Everyone wants to love everyone. ∀x ∀y Pxxy

a(12)3
200
002 110 2 000 1
Someone wants to be loved by someone. ∃x ∃y Pxyx

e(13)2
757
757 343 2 111 5
For everyone there is someone who wants to be loved by them. ∀y ∃x Pxyx

a2 e(13)
356
653 323 2 101 4
Everyone wants to be loved by someone. ∀x ∃y Pxyx

a(13) e2
623
326 242 2 010 4
Someone wants to be loved by everyone. ∃x ∀y Pxyx

e(13) a2
154
451 202 2 101 2
There is someone by whom everyone wants to be loved. ∃y ∀x Pxyx

e2 a(13)
421
124 121 2 010 2
Everyone wants to be loved by everyone. ∀x ∀y Pxyx

a(13)2
020
020 101 2 000 1
Someone wishes someone
to love themselves.
∃x ∃y Pxyy

e1(23)
775
577 433 2 111 5
Everyone wishes someone
to love themselves.
∀x ∃y Pxyy

a1 e(23)
665
566 233 2 011 4
For everyone there is someone who wishes them
to love themselves.
∀y ∃x Pxyy

a(23) e1
332
233 422 2 100 4
There is someone whom everyone wishes
to love themselves.
∃y ∀x Pxyy

e(23) a1
445
544 022 2 011 2
Someone wishes everyone
to love themselves.
∃x ∀y Pxyy

e1 a(23)
112
211 211 2 100 2
Everyone wishes everyone
to love themselves.
∀x ∀y Pxyy

a1(23)
002
200 011 2 000 1
Someone wants to love themselves. ∃x Pxxx

e(123)
555
555 244.5 1 111 4
Everyone wants to love themselves. ∀x Pxxx

a(123)
222
222 143.5 1 000 2

Implications

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substructures
diagonal
Someone wants to love someone.Everyone wants to love someone.Someone wants to love themselves.For everyone there is someone who wants to love them.There is someone whom everyone wants to love.Everyone wants to love themselves.Someone wants to love everyone.Everyone wants to love everyone.
Someone wants to be loved by someone.Everyone wants to be loved by someone.Someone wants to love themselves.For everyone there is someone who wants to be loved by them.There is someone by whom everyone wants to be loved.Everyone wants to love themselves.Someone wants to be loved by everyone.Everyone wants to be loved by everyone.
Someone wishes someone to love themselves.For everyone there is someone who wishes them to love themselves.Someone wants to love themselves.Everyone wishes someone to love themselves.Someone wishes everyone to love themselves.Everyone wants to love themselves.There is someone whom everyone wishes to love themselves.Everyone wishes everyone to love themselves.
sides top
Someone wants that someone loves someone.For everyone there is someone who wants them to love someone.Someone wants to love someone.Everyone wants someone to love someone.Someone wants everyone to love someone.Everyone wants to love someone.There is someone whom everyone wishes to love someone.Everyone wants everyone to love someone.
Someone wants that someone loves someone.Everyone wants someone to love someone.Someone wants to be loved by someone.For everyone there is someone who wants them to be loved by someone.There is someone whom everyone wishes to be loved by someone.Everyone wants to be loved by someone.There is someone who wants that everyone is loved by someone.Everyone wants everyone to be loved by someone.
Someone wants that someone loves someone.For everyone there is someone who wants them to be loved by someone.Someone wishes someone to love themselves.For everyone there is someone who wants them to love someone.There is someone so that for every other person exists someone who wants them to love that other person.For everyone there is someone who wishes them to love themselves.There is someone so that for every other person exists someone who wants them to be loved by that other person.For every two people ''a'' and ''b'' there is someone who wants ''a'' to love ''b'' and someone who wants ''b'' to love ''a''.


weak orderings
Weak orderings ordered by refinement — Finer ones are on the outside, so arrows would go to the inside.
Implications correspond to the ordering by refinement.
Implications are in the opposite direction.