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# THE NEED FOR NONMONOTONIC REASONING

After reading the story, one is prepared to answer negatively the question of whether there was someone else besides Mr. Hug and the robbers present. However, sentences describing such another person could be added to the story without contradiction. Our basis for the negative answer is that we can construct a model of the facts stated in the story without such a person, and we are applying Occam's razor in order to not multiply entities beyond necessity. This could be attributed to the fact that the New York Times tells the whole story when it can, but I think that by putting Occam's razor into the system, we can get this result without having to formalize the New York Times.

This suggests introducing the notion of the minimal completion of a story expressed in the predicate calculus. The minimal completion of the story is also a set of sentences in the predicate calculus, but it contains sentences asserting things like ``The set of people in the store while the robbers were trying to crush Mr. Hug consists of Mr. Hug and the robbers.'' These sentences are to be obtained from the original set by the application of a process formalizing Occam's razor. This process works from a set of sentences and is not logical deduction although it might be accomplished by deduction in a meta-language that contained sentences about sets of sentences. As I have pointed out elsewhere, the process cannot be deduction, because it generates sentences that contradict sentences that are consistent with the original set of sentences.

A number of the questions given in the previous section have answers that can be formally deduced from the minimal completion but not from the original list.

It has been suggested that probabilistic reasoning should be used to exclude the presence of other people rather than Occam's razor. The problem with this is that the number of additional entities that are not logically excluded is limited only by one's imagination so that it is not clear how one could construct a probabilistic model that took these possibilities into account only to exclude them as improbable. If one wants to introduce probabilities, it might make more sense to assign a probability to the correctness of the minimal completion of a New York Times story based on its past record in finding the relevant facts of robberies.

Another problem in constructing the completion is the isolation of the story from the rest of the world. The members of the Police Emergency Squad all have mothers (living or dead), but we don't want to bring them into the completion--not to speak of bringing in more remote ancestors all of whom can be asserted to exist on the basis of axioms about people.

Next: CONCLUSION Up: AN EXAMPLE FOR Previous: THE USE OF LOGICAL

John McCarthy
Tue May 14 09:36:52 PDT 1996