Formulas in predicate logic/3 places

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Formulas in predicate logic Rdrup.svg


List[edit | edit source]

list
as "A whishes B to love C."
example sentence sketch formula pairs coord var bin rank
Someone wants that someone loves someone. Predicate logic; 3 variables; sketch e123.png ∃x ∃y ∃z Pxyz
Predicate logic; 3 variables; ordered partition e123.svg
e123
777
Predicate logic; 3 variables; pairs e123.svg
777 444 3 111 6
For everyone there is someone who
wants them to be loved by someone.
Predicate logic; 3 variables; sketch a3e12.png ∀z ∃x ∃y Pxyz
Predicate logic; 3 variables; ordered partition a3e12.svg
a3 e12
733
Predicate logic; 3 variables; pairs a3e12.svg
337 442 3 110 5
For everyone there is someone who
wants them to love someone.
Predicate logic; 3 variables; sketch a2e13.png ∀y ∃x ∃z Pxyz
Predicate logic; 3 variables; ordered partition a2e13.svg
a2 e13
376
Predicate logic; 3 variables; pairs a2e13.svg
673 424 3 101 5
Everyone wants someone to love someone. Predicate logic; 3 variables; sketch a1e23.png ∀x ∃y ∃z Pxyz
Predicate logic; 3 variables; ordered partition a1e23.svg
a1 e23
667
Predicate logic; 3 variables; pairs a1e23.svg
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.
Predicate logic; 3 variables; sketch e2a3e1.png ∃y ∀z ∃x Pxyz
Predicate logic; 3 variables; ordered partition e2a3e1.svg
e2 a3 e1
731
Predicate logic; 3 variables; pairs e2a3e1.svg
137 431 3 110 4
There is someone who wants that everyone is loved by someone. Predicate logic; 3 variables; sketch e1a3e2.png ∃x ∀z ∃y Pxyz
Predicate logic; 3 variables; ordered partition e1a3e2.svg
e1 a3 e2
713
Predicate logic; 3 variables; pairs e1a3e2.svg
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.
Predicate logic; 3 variables; sketch e3a2e1.png ∃z ∀y ∃x Pxyz
Predicate logic; 3 variables; ordered partition e3a2e1.svg
e3 a2 e1
374
Predicate logic; 3 variables; pairs e3a2e1.svg
473 413 3 101 4
Someone wants everyone to love someone. Predicate logic; 3 variables; sketch e1a2e3.png ∃x ∀y ∃z Pxyz
Predicate logic; 3 variables; ordered partition e1a2e3.svg
e1 a2 e3
176
Predicate logic; 3 variables; pairs e1a2e3.svg
671 314 3 101 4
There is someone whom everyone wishes to be loved by someone. Predicate logic; 3 variables; sketch e3a1e2.png ∃z ∀x ∃y Pxyz
Predicate logic; 3 variables; ordered partition e3a1e2.svg
e3 a1 e2
647
Predicate logic; 3 variables; pairs e3a1e2.svg
746 143 3 011 4
There is someone whom everyone wishes to love someone. Predicate logic; 3 variables; sketch e2a1e3.png ∃y ∀x ∃z Pxyz
Predicate logic; 3 variables; ordered partition e2a1e3.svg
e2 a1 e3
467
Predicate logic; 3 variables; pairs e2a1e3.svg
764 134 3 011 4
Someone wishes someone to love everyone. Predicate logic; 3 variables; sketch e12a3.png ∃x ∃y ∀z Pxyz
Predicate logic; 3 variables; ordered partition e12a3.svg
e12 a3
711
Predicate logic; 3 variables; pairs e12a3.svg
117 330 3 110 3
Someone wishes someone to be loved by everyone. Predicate logic; 3 variables; sketch e13a2.png ∃x ∃z ∀y Pxyz
Predicate logic; 3 variables; ordered partition e13a2.svg
e13 a2
174
Predicate logic; 3 variables; pairs e13a2.svg
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.
Predicate logic; 3 variables; sketch e23a1.png ∃y ∃z ∀x Pxyz
Predicate logic; 3 variables; ordered partition e23a1.svg
e23 a1
447
Predicate logic; 3 variables; pairs e23a1.svg
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.
Predicate logic; 3 variables; sketch a23e1.png ∀y ∀z ∃x Pxyz
Predicate logic; 3 variables; ordered partition a23e1.svg
a23 e1
330
Predicate logic; 3 variables; pairs a23e1.svg
033 411 3 100 3
Everyone wants everyone to be loved by someone. Predicate logic; 3 variables; sketch a13e2.png ∀x ∀z ∃y Pxyz
Predicate logic; 3 variables; ordered partition a13e2.svg
a13 e2
603
Predicate logic; 3 variables; pairs a13e2.svg
306 141 3 010 3
Everyone wants everyone to love someone. Predicate logic; 3 variables; sketch a12e3.png ∀x ∀y ∃z Pxyz
Predicate logic; 3 variables; ordered partition a12e3.svg
a12 e3
066
Predicate logic; 3 variables; pairs a12e3.svg
660 114 3 001 3
For everyone there is someone who wants them to love everyone. Predicate logic; 3 variables; sketch a2e1a3.png ∀y ∃x ∀z Pxyz
Predicate logic; 3 variables; ordered partition a2e1a3.svg
a2 e1 a3
310
Predicate logic; 3 variables; pairs a2e1a3.svg
013 310 3 100 2
For everyone there is someone who wants them to be loved by everyone. Predicate logic; 3 variables; sketch a3e1a2.png ∀z ∃x ∀y Pxyz
Predicate logic; 3 variables; ordered partition a3e1a2.svg
a3 e1 a2
130
Predicate logic; 3 variables; pairs a3e1a2.svg
031 301 3 100 2
Everyone wishes someone to love everyone. Predicate logic; 3 variables; sketch a1e2a3.png ∀x ∃y ∀z Pxyz
Predicate logic; 3 variables; ordered partition a1e2a3.svg
a1 e2 a3
601
Predicate logic; 3 variables; pairs a1e2a3.svg
106 130 3 010 2
For everyone there is someone whom everyone wants to love them. Predicate logic; 3 variables; sketch a3e2a1.png ∀z ∃y ∀x Pxyz
Predicate logic; 3 variables; ordered partition a3e2a1.svg
a3 e2 a1
403
Predicate logic; 3 variables; pairs a3e2a1.svg
304 031 3 010 2
Everyone wishes someone to be loved by everyone. Predicate logic; 3 variables; sketch a1e3a2.png ∀x ∃z ∀y Pxyz
Predicate logic; 3 variables; ordered partition a1e3a2.svg
a1 e3 a2
064
Predicate logic; 3 variables; pairs a1e3a2.svg
460 103 3 001 2
For everyone there is someone whom everyone wants them to love. Predicate logic; 3 variables; sketch a2e3a1.png ∀y ∃z ∀x Pxyz
Predicate logic; 3 variables; ordered partition a2e3a1.svg
a2 e3 a1
046
Predicate logic; 3 variables; pairs a2e3a1.svg
640 013 3 001 2
Someone wants that everyone loves everyone. Predicate logic; 3 variables; sketch e1a23.png ∃x ∀y ∀z Pxyz
Predicate logic; 3 variables; ordered partition e1a23.svg
e1 a23
110
Predicate logic; 3 variables; pairs e1a23.svg
011 200 3 100 1
There is someone whom everyone wishes
to love everyone.
Predicate logic; 3 variables; sketch e2a13.png ∃y ∀x ∀z Pxyz
Predicate logic; 3 variables; ordered partition e2a13.svg
e2 a13
401
Predicate logic; 3 variables; pairs e2a13.svg
104 020 3 010 1
There is someone whom everyone wishes
to be loved by everyone.
Predicate logic; 3 variables; sketch e3a12.png ∃z ∀x ∀y Pxyz
Predicate logic; 3 variables; ordered partition e3a12.svg
e3 a12
044
Predicate logic; 3 variables; pairs e3a12.svg
440 002 3 001 1
Everyone wants everyone to love everyone. Predicate logic; 3 variables; sketch a123.png ∀x ∀y ∀z Pxyz
Predicate logic; 3 variables; ordered partition a123.svg
a123
000
Predicate logic; 3 variables; pairs a123.svg
000 000 3 000 0
Someone wants to love someone. Predicate logic; 3 variables; sketch e(12)3.png ∃x ∃y Pxxy
Predicate logic; 3 variables; ordered partition e(12)3.svg
e(12)3
577
Predicate logic; 3 variables; pairs e(12)3.svg
775 334 2 111 5
For everyone there is someone who wants to love them. Predicate logic; 3 variables; sketch a3e(12).png ∀y ∃x Pxxy
Predicate logic; 3 variables; ordered partition a3e(12).svg
a3 e(12)
533
Predicate logic; 3 variables; pairs a3e(12).svg
335 332 2 110 4
Everyone wants to love someone. Predicate logic; 3 variables; sketch a(12)e3.png ∀x ∃y Pxxy
Predicate logic; 3 variables; ordered partition a(12)e3.svg
a(12) e3
266
Predicate logic; 3 variables; pairs a(12)e3.svg
662 224 2 001 4
Someone wants to love everyone. Predicate logic; 3 variables; sketch e(12)a3.png ∃x ∀y Pxxy
Predicate logic; 3 variables; ordered partition e(12)a3.svg
e(12) a3
511
Predicate logic; 3 variables; pairs e(12)a3.svg
115 220 2 110 2
There is someone whom everyone wants to love. Predicate logic; 3 variables; sketch e3a(12).png ∃y ∀x Pxxy
Predicate logic; 3 variables; ordered partition e3a(12).svg
e3 a(12)
244
Predicate logic; 3 variables; pairs e3a(12).svg
442 112 2 001 2
Everyone wants to love everyone. Predicate logic; 3 variables; sketch a(12)3.png ∀x ∀y Pxxy
Predicate logic; 3 variables; ordered partition a(12)3.svg
a(12)3
200
Predicate logic; 3 variables; pairs a(12)3.svg
002 110 2 000 1
Someone wants to be loved by someone. Predicate logic; 3 variables; sketch e(13)2.png ∃x ∃y Pxyx
Predicate logic; 3 variables; ordered partition e(13)2.svg
e(13)2
757
Predicate logic; 3 variables; pairs e(13)2.svg
757 343 2 111 5
For everyone there is someone who wants to be loved by them. Predicate logic; 3 variables; sketch a2e(13).png ∀y ∃x Pxyx
Predicate logic; 3 variables; ordered partition a2e(13).svg
a2 e(13)
356
Predicate logic; 3 variables; pairs a2e(13).svg
653 323 2 101 4
Everyone wants to be loved by someone. Predicate logic; 3 variables; sketch a(13)e2.png ∀x ∃y Pxyx
Predicate logic; 3 variables; ordered partition a(13)e2.svg
a(13) e2
623
Predicate logic; 3 variables; pairs a(13)e2.svg
326 242 2 010 4
Someone wants to be loved by everyone. Predicate logic; 3 variables; sketch e(13)a2.png ∃x ∀y Pxyx
Predicate logic; 3 variables; ordered partition e(13)a2.svg
e(13) a2
154
Predicate logic; 3 variables; pairs e(13)a2.svg
451 202 2 101 2
There is someone by whom everyone wants to be loved. Predicate logic; 3 variables; sketch e2a(13).png ∃y ∀x Pxyx
Predicate logic; 3 variables; ordered partition e2a(13).svg
e2 a(13)
421
Predicate logic; 3 variables; pairs e2a(13).svg
124 121 2 010 2
Everyone wants to be loved by everyone. Predicate logic; 3 variables; sketch a(13)2.png ∀x ∀y Pxyx
Predicate logic; 3 variables; ordered partition a(13)2.svg
a(13)2
020
Predicate logic; 3 variables; pairs a(13)2.svg
020 101 2 000 1
Someone wishes someone
to love themselves.
Predicate logic; 3 variables; sketch e1(23).png ∃x ∃y Pxyy
Predicate logic; 3 variables; ordered partition e1(23).svg
e1(23)
775
Predicate logic; 3 variables; pairs e1(23).svg
577 433 2 111 5
Everyone wishes someone
to love themselves.
Predicate logic; 3 variables; sketch a1e(23).png ∀x ∃y Pxyy
Predicate logic; 3 variables; ordered partition a1e(23).svg
a1 e(23)
665
Predicate logic; 3 variables; pairs a1e(23).svg
566 233 2 011 4
For everyone there is someone who wishes them
to love themselves.
Predicate logic; 3 variables; sketch a(23)e1.png ∀y ∃x Pxyy
Predicate logic; 3 variables; ordered partition a(23)e1.svg
a(23) e1
332
Predicate logic; 3 variables; pairs a(23)e1.svg
233 422 2 100 4
There is someone whom everyone wishes
to love themselves.
Predicate logic; 3 variables; sketch e(23)a1.png ∃y ∀x Pxyy
Predicate logic; 3 variables; ordered partition e(23)a1.svg
e(23) a1
445
Predicate logic; 3 variables; pairs e(23)a1.svg
544 022 2 011 2
Someone wishes everyone
to love themselves.
Predicate logic; 3 variables; sketch e1a(23).png ∃x ∀y Pxyy
Predicate logic; 3 variables; ordered partition e1a(23).svg
e1 a(23)
112
Predicate logic; 3 variables; pairs e1a(23).svg
211 211 2 100 2
Everyone wishes everyone
to love themselves.
Predicate logic; 3 variables; sketch a1(23).png ∀x ∀y Pxyy
Predicate logic; 3 variables; ordered partition a1(23).svg
a1(23)
002
Predicate logic; 3 variables; pairs a1(23).svg
200 011 2 000 1
Someone wants to love themselves. Predicate logic; 3 variables; sketch e(123).png ∃x Pxxx
Predicate logic; 3 variables; ordered partition e(123).svg
e(123)
555
Predicate logic; 3 variables; pairs e(123).svg
555 244.5 1 111 4
Everyone wants to love themselves. Predicate logic; 3 variables; sketch a(123).png ∀x Pxxx
Predicate logic; 3 variables; ordered partition a(123).svg
a(123)
222
Predicate logic; 3 variables; pairs a(123).svg
222 143.5 1 000 2

Implications[edit | edit source]


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.Predicate logic; 3 variables; some implications; hex diag 3.png
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.Predicate logic; 3 variables; some implications; hex diag 2.png
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.Predicate logic; 3 variables; some implications; hex diag 1.png
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.Predicate logic; 3 variables; some implications; hex side 3b.png
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.Predicate logic; 3 variables; some implications; hex side 2b.png
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''.Predicate logic; 3 variables; some implications; hex side 1b.png


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.