A.8.12 Reification

The constraints in/2, #=/2, #\=/2, #</2, #>/2, #=</2, and #>=/2 can be reified, which means reflecting their truth values into Boolean values represented by the integers 0 and 1. Let P and Q denote reifiable constraints or Boolean variables, then:

#\ Q	True iff Q is false
P #\/ Q	True iff either P or Q
P #/\ Q	True iff both P and Q
P #\ Q	True iff either P or Q, but not both
P #<==> Q	True iff P and Q are equivalent
P #==> Q	True iff P implies Q
P #<== Q	True iff Q implies P

The constraints of this table are reifiable as well.

When reasoning over Boolean variables, also consider using CLP(B) constraints as provided by http://eu.swi-prolog.org/man/clpb.htmllibrary(clpb).