Monotonicity of Indexicals

A range R is monotone in S iff the value of R in S' is contained in the value of R in S, for every extension S' of S. A range R is anti-monotone in S iff the value of R in S is contained in the value of R in S', for every extension S' of S. By abuse of notation, we will say that X in R is (anti-)monotone iff R is (anti-)monotone.

The consistency or entailment of a constraint C expressed as indexicals X in R in a store S is checked by considering the relationship between D(X,S) and S(R), together with the (anti-)monotonicity of R in S. The details are given in Execution of Propagating Indexicals and Execution of Checking Indexicals.

The solver checks (anti-)monotonicity by requiring that certain variables occurring in the indexical be ground. This sufficient condition can sometimes be false for an (anti-)monotone indexical, but such situations are rare in practice.