Independence of Negative Constraints

The independence of negative constraints is a recurring phenomenon in logic programming. This property has in fact a natural interpretation in the context of linear programming that we exploit here to address problems of canonical representations of positive and negative linear arithmetic constraints. Independence allows us to design polynomial time algorithms to decide feasibility and to generate a canonical form, thus avoiding the combinatorial explosion that the presence of negative constraints would otherwise induce. This canonical form allows us to decide by means of a simple syntactic check the equivalence of two sets of constraints and provides the starting point for a symbolic computation system. It has, moreover, other applications and we show in particular that it yields a completeness theorem for constraint propagation and is an appropriate tool to be used in connection with constraint based programming languages.