a template constraint is a proposition function that determines whether a given value can be assigned to a variable.
a constraint function is a conjunction that takes a set of boolean inputs produced by propositions over a given value, and returns a truth value that indicates whether those propositions hold true. every proposition must be true in order for the constraint to be true.

C(x)—> F1(x)^F2(x)^…^Fn(x)
x is a given input
y is a boolean output
C is a constraint function
F is a set of propositions
a selection function has the same general structure as a constraint, except for it’s head. where constraints apply a conjunction to a set of truth values, selection functions apply disjunctions. a constraint is true if every proposition holds true, while a selection is true if any proposition holds true. this distinction is essential because it represents a difference in the criteria needed to justify different decisions.
a general form of propositions that takes boolean sets as input is given by a function with a constant variable, and any time a proposition is called it finds the sum of boolean inputs and determines whether it outweighs the constant.
the truth of a proposition is therefore determined by the number of true inputs received and the number of true inputs required by the function to produce a true output.
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