Numeric state variables in constraint

We extend a planning algorithm to cover simple forms of arithmetics. The operator preconditions can refer to the values of numeric variables and the operator postconditions can modify the values of numeric variables. The basis planning algorithm is based on techniques from propositional satissability testing and does not restrict to forward or backward chaining. When several operations aaect a numeric variable by increasing and decreasing its value in parallel, the eeects have to be combined in a meaningful way. This problem is especially acute in planning algorithms that maintain an incomplete state description of every time point of a plan execution. The approach we take requires that for operators that are executed in parallel, all linearizations of the operations to total orders behave equivalently. We provide an eecient and general solution to the problem.