3.7.92. Entailment

Denotes the fact that the catalogue mentions a sufficient condition for the entailment of a constraint. Consider a constraint π’ž(V 1 ,V 2 ,...,V n ) and the potential sets of values π‘‘π‘œπ‘š(V 1 ),π‘‘π‘œπ‘š(V 2 ),...,π‘‘π‘œπ‘š(V n ) that can respectively be assigned to the domain variables V 1 ,V 2 ,...,V n . The constraint π’ž(V 1 ,V 2 ,...,V n ) is entailed if and only if π’ž(V 1 ,V 2 ,...,V n ) holds whatever values π‘£π‘Žπ‘™ 1 βˆˆπ‘‘π‘œπ‘š(V 1 ),π‘£π‘Žπ‘™ 2 βˆˆπ‘‘π‘œπ‘š(V 2 ),...,π‘£π‘Žπ‘™ n βˆˆπ‘‘π‘œπ‘š(V n ) will respectively be assigned variables V 1 ,V 2 ,...,V n .

Entailment is usually not considered as very important when designing a filtering algorithm, even if it can sometimes save waking again and again a constraint that will for sure be satisfied. From a modelling point of view, entailment detection is mandatory for coming up with the reified version of a constraint (see alsoΒ reified automaton constraint).