Remarks and Acknowledgements

1. The English language elaborations don't refer to an original English text. If someone has read about the problem and understands it, he usually won't be able to quote the text he read. Moreover, if he tells the problem to someone else more than once, he is unlikely to use the same words each time. We conclude from this that that a person's understanding of MCP is represented in the brain in some other way than as an English text. For the purposes of this paper we don't need to speculate about how it is represented, since the formal elaboration tolerance applies to logical formulations.

2. Some commonly adopted conventions in theories of actions interfere with elaboration tolerance. An example is identifying situations or events with intervals of time. You can get away with it sometimes, but eventually you will be sorry. For example, you may want to say that a good move is one that leads to a better situation with
   
   $$Good(a,s) \equiv s <_{good} Result(a,s).$$
   
   

3. Elaboration tolerance and belief revision have much in common, but we are looking at the problem from the opposite direction from researchers in belief revision. Belief revision studies have mainly concerned the effect of adding or removing a given sentence, whereas our treatment of elaboration tolerance concerns what you must add or change to get the effect you want. Moreover, the effect of an elaboration can involve changing the first order language and not just replacing one expression in the language by another.

4. Elaboration tolerance is rather straightforward when the theory to be changed has the structure of a cartesian product, and the elaboration can be describes as giving some components of the product new values. [McC79b] discusses theories with cartesian product structures in connection with counterfactuals, and [McC62] discusses the semantics of assignment, i.e. the semantics of changing components of a state.

5. Murray Shanahan [Sha97] considers many issues of elaboration tolerance in his discussions of action formalisms. In particular, his solutions for the frame problem are considerably elaboration tolerant. I qualified the above, because I consider elaboration tolerance an open ended problem.

6. I suspect that elaboration tolerance requires a proper treatment of hypothetical causality and this involves counterfactual conditional sentences. Counterfactuals will be treated in a shortly forthcoming paper by Tom Costello and John McCarthy. For example, we need a non-trivial interpretation of ``If another car had come over the hill while you were passing, there would have been a head-on collision'' that is compatible with the fact that no car came. By non-trivial interpretation, I mean one that could have as a consequence that a person should change his driving habits, whereas no such conclusion can be reached from sentences of the form $p \rightarrow q$ when $p$ is false.

7. We can distinguish between a formalism admitting a particular elaboration and the consequences of the elaboration being entirely determined. For example, the Jesus Christ elaboration could be given alternate interpretations and not just the one about his ability to walk on water.

   Another example (suggested by Tom Costello) has the original story say that the capacity of the boat is one less than the number of missionaries. Then changing the number of missionaries and cannibals to 4 leaves the problem still solvable, even though the set of logical consequences of the sentences of the two formalisms is the same. This tells us that if we translate the English to logic and take all logical consequences, information that determines the effects of elaborations can be lost.

This paper has benefitted from discussions with Eyal Amir, Tom Costello, Aarati Parmar and Josephina Sierra. The present version is somewhat improved from the version presented at Common Sense-98 in January 1998. It may be further improved without warning.