Excerpt from Constraint Propagation on Real-Valued Quantities For many applications, it is possible to restrict the nature of facts and inferences in the quantity knowledge base to a particular kind, which we will call simple quantitative inference. In simple inference, the program is given a set of facts about particular quantities, and it is asked to use these facts to deduce the value of some quantity. Typically, the input facts do not constrain the queried quantity to have a single value, so the program will return a range of possible values. For example, we might tell the program, Joe is younger than Mary and older than Sue. Mary is between forty and fifty. Sue is less than twenty years younger than Mary. If we now ask, How many years old is Joe? The system should answer, Between twenty and fifty. Formally, we can characterize the problem here as follows: We are given a conjunction of variable-free clauses, and we are asked for the range of values possible for a given term if all the formulas are satisfied.

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