Formulas in predicate logic/3 places

Formulas in predicate logic

List

list

$P(A,B,C)$ 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

full Hasse diagram with 46 vertices

substructures
(The diagonals repeat a Hasse diagram with 2-dimensional matrices.) diagonal diagonal in solid sides in solid sides top sides bottom

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.