A set of constraints
entails a constraint
is a valuation of the variables in the scopes of the constraints in
also satisfies the constraint
Some operations on constraints produce a new constraint that is a consequence of them.
Constraint composition operates on a pair of binary constraints
with a common variable.
that is satisfied by every evaluation of the two non-shared variables for which there exists a value of the shared variable
such that the evaluation of these three variables satisfies the two original constraints
Constraint projection restricts the effects of a constraint to some of its variables.
its projection to a subset
of its variables is the constraint
that is satisfied by an evaluation if this evaluation can be extended to the other variables in such a way the original constraint
Extended composition is similar in principle to composition, but allows for an arbitrary number of possibly non-binary constraints; the generated constraint is on an arbitrary subset of the variables of the original constraints.
of their variables, the extended composition of them is the constraint
satisfies this constraint if it can be extended to the other variables so that
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