Applications

Here are some applications of the logical theory of contexts.

1. Conventional linguistic applications like the referents of pronouns can be treated using contexts as objects, but formalized contexts are also useful for more complex anaphora. For example, we need to relate the surgeon's ``Scalpel'' to the sentence ``Please hand me a number 3 scalpel''. See [Buv96]. These applications require associating contexts with sentences or parts of sentences.
2. Defining a theory in a narrow context in a way that permits it to be lifted to a richer outer context and applied. [McC93] discusses lifting a simple theory of above(x,y) as the transitive closure of on(x,y) to an outer situation calculus context that uses on(x,y,s) and above(x,y,s). A key formula of that paper is

    

   which relates the three argument situation calculus predicate on(x,y,s) and the two element predicate on(x,y) of the specialized theory of on and above. The use of contexts to implement ``microtheories'' in Cyc is described in [Guh91]. This allowed people entering knowledge about some phenomenon, e.g. automobiles, to do it in a limited context, but leave open the ability to use the knowledge in a larger context.

3. Defining a narrow context for a problem and importing facts that permit the problem to be solved by considering only a small set of possibilities. For example, in formulating the missionaries and cannibals problem a person or program must take a number of common sense facts into account, but ends up with a 32 state space, because all that is relevant in this context is the numbers of missionaries, cannibals and boats on each bank of the river.
4. Relating databases with different conventions [MB94]. Imagine that the Airforce and the General Electric Company have databases both of which include prices for the jet engines that the company sells the Airforce. However, suppose the databases don't agree on what the price covers, e.g. spare parts. We use one context for the Air Force database, another for the GE database, and a third context c0 that needs to relate information from both. Lifting formulas in the context true in c0 relate information in the different databases to the context in which reasoning is done, , e.g. they tell about the relation of the prices listed in and to the inclusion or not of spare parts.
5. Buvac and McCarthy have also discussed using context to combine aspects of plans generated by different planners not originally designed to work together--or plans originally intended to work together but which have drifted apart in the course of separate development.