The basic idea is to represent each subplan as though it was developed in a context. These contexts will differ, either slightly or greatly. The terminology within each subcontext is likely to be specialized, and making the plans work together requires some generalization. For this purpose we use lifting formulas, i.e. formulas that relate the propositions and terms in subcontexts to propositions and terms in an outer context.

Here is an example. Assume that a route planner, like the route optimization program of the TRAINS project [3], and a supply planner, like the transportation scheduler developed at Kestrel [53], have been developed independently by different groups. Given a source and a destination, the route planner will find the best route between these places. It however, has no notion of which supplies need to be transported and no notion of time. The supply planner keeps track of the supplies of some economic system and informs us which supplies need to be moved at any given time. We assume that the supply planner has no knowledge about the routes that the supplies need to travel to reach their destination.

To fill in a work order we need to integrate the information produced by the supply planner with that of the route planner. Assume that the supply planner produces

informing us that equipment1 needs to be transported from Rome Air Force base in New York on 11/6/95, to Frankfurt on 1/20/96. The context constant denotes the context in which supply planner operates and reports its results. Now assume that the route planner tells us that the best route from Rome to Frankfurt is via New York City (NYC). This is represented in the context of the route planner, , by stating

Note that is a function returning a list which encodes the best route. Integrating this information inside the problem solving context, , we get

stating that equipment1 needs to be transported by the route Rome-NYC-Frankfurt departing on 11/6/95 and arriving on 1/20/96. This information can now be entered into the work order. Note that the same predicate symbol, , is used in different ways in two different contexts: its arity and its arguments are different in the context and in the context.

The context formalism enables us to capture this style of reasoning
in logic. We write *lifting axioms* which describe how the
information from different contexts can be integrated. In the above example
the lifting formula is

If the formula is true in the context of the supply planner, then the formula

holds in the problem solving context.
Intuitively, formula 70 expresses that if the supply planner
states that some items *x* need to be transported leaving *l*1 on *d*1
and arriving to *l*2 on *d*2, and if

is reported by the route planner as the best route from *l*1 to
*l*2, then the information which can be entered into the work order is

In other words, formula 70 specifies the integrating of a plan which involves the notions of time and supplies produced by the supply planner with the details involving a route produced the route planner. The lifting axiom 70 allows us to derive the plan given by formula 69 in the problem solving context from the plans given by formulas 67 and 68 in the contexts of their corresponding planners.

A term with a definite meaning in one context often needs translation when used in another context. Thus may mean Rome NY in a data base of US Air Force bases but needs translation when a formula is lifted to a context of worldwide geography. Lifting formulas similar to 70 can be used to do this type of translation.

Sun Jul 12 14:45:30 PDT 1998