Prolog SAT Solver

Question

I\'m trying to build a simple Prolog SAT solver. My idea is that the user should enter the boolean formula to be solved in CNF (Conjuctive Normal Form) using Prolog lists, f

Answer 1

One can use CLP(FD) to solve SAT. Just start with a CNF and then observe that a clause:

x1 v .. v xn 

Can be represented as a constraint:

x1 + .. + xn #> 0

Further for a negative literal:

~x

Simply use:

1-x

You need to restrict the variables to the domain 0..1 and invoke labeling. As soon as labeling returns some value for the variables, you know that your original formula is satisfiable.

Here is an example run, running the test of Joe Lehmann:

Welcome to SWI-Prolog (Multi-threaded, 64 bits, Version 6.5.2)
Copyright (c) 1990-2013 University of Amsterdam, VU Amsterdam

?- use_module(library(clpfd)).

?- L = [X,Y,Z], L ins 0..1, X+1-Y #> 0, 1-X+1-Y #> 0, X+Z #> 0, label(L).
X = Y, Y = 0,
Z = 1 ;
X = 1,
Y = Z, Z = 0 ;
X = Z, Z = 1,
Y = 0.

Bye

Constraint Logic Programming over Finite Domains
http://www.swi-prolog.org/man/clpfd.html