Bertrand Russell Puzzle

Question

Solve the following Caliban problem, translating each clue 'loyally' into Prolog, i.e. as loyally as possible.

As a simple exercise in abstraction suppose that four meaningless symbols a, b, c, and d correspond in one order or another to the equally meaningless symbols w, x, y, and z, and suppose further that

If a is not x, then c is not y.
If b is either y or z, then a is x.
If c is not w, then b is z.
If d is y, then b is not x.
If d is not x, then b is x.

In what order do the two sets of symbols correspond?

I tried the following code:

vban(L) :-
       L=[[a,C1],[b,C2],[c,C3],[d,C4]],

       ( member(C1,[w,y,z]) -> member(C3,[w,x,z])),
       ( member(C2,[y,z]) -> member(C1,[x])),
       ( member(C3,[x,y,z]) -> member(C2,[z])),
       ( member(C4,[y]) -> member(C2,[w,y,z])),
       ( member(C4,[w,y,z]) -> member(C2,[x])).

But it shows fail.Any help would be appreciated.

Answer 1

Using CLP(B) in SICStus Prolog or SWI:

:- use_module(library(clpb)).
:- use_module(library(lists)).
:- use_module(library(clpfd)).

corresponding(Matrix) :-
        Matrix = [[ _,AX, _, _],
                  [ _,BX,BY,BZ],
                  [CW, _,CY, _],
                  [ _,DX,DY, _]],
        maplist(card1, Matrix),
        transpose(Matrix, TMatrix),
        maplist(card1, TMatrix),
        sat(~AX =< ~CY),
        sat(BY + BZ =< AX),
        sat(~CW =< BZ),
        sat(DY =< ~BX),
        sat(~DX =< BX).

card1(Vs) :- sat(card([1], Vs)).

Example query:

?- corresponding(Vs), 
   pairs_keys_values(Pairs, [t,a,b,c,d], [[w,x,y,z]|Vs]),
   maplist(writeln, Pairs).

Yielding (1 denotes corresponding elements):

t-[w,x,y,z]
a-[0,0,1,0]
b-[0,1,0,0]
c-[1,0,0,0]
d-[0,0,0,1]

and bindings for Vs and Pairs.