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A Boolean expression is one of:
true variable unknown truth value atom universally quantified variable
logical NOT Expr + Expr logical OR Expr * Expr logical AND Expr # Expr exclusive OR Var
existential quantification Expr
disequality (same as #) Expr
less or equal (implication) Expr
greater or equal Expr < Expr less than Expr > Expr greater than
cardinality constraint (see below)
n-fold disjunction (see below)
n-fold conjunction (see below)
where Expr again denotes a Boolean expression.
The Boolean expression
card(Is,Exprs) is true iff the
number of true expressions in the list Exprs is a member of
the list Is of integers and integer ranges of the form
For example, to state that precisely two of the three variables X, Y
and Z are
true, you can use
*(Exprs) denote, respectively,
the disjunction and conjunction of all elements in the list Exprs
of Boolean expressions.
Atoms denote parametric values that are universally quantified. All universal quantifiers appear implicitly in front of the entire expression. In residual goals, universally quantified variables always appear on the right-hand side of equations. Therefore, they can be used to express functional dependencies on input variables.