26 - Reasoning and Representation

Summary

Nonmonotonic or Defeasible Reasoning

Those AI researchers called logicists, who favor the use of logical languages for representing knowledge and the use of logical methods for reasoning, acknowledge one problem with ordinary logic; namely, it is monotonic. By that they mean that the set of logical conclusions that can be drawn from a set of logical statements does not decrease as more statements are added to the set. If one could prove a statement from a given knowledge base, one could still prove that same statement (with the very same proof!) when more knowledge is added.

Yet, much human reasoning does not seem to work that way – a fact well noticed (and celebrated) by AI's critics. Often, we jump to a conclusion using the facts we happen to have, together with reasonable assumptions, and then have to retract that conclusion when we learn some new fact that contradicts the assumptions. That style of reasoning is called nonmonotonic or defeasible (meaning “capable of being made or declared null and void”) because new facts might require taking back something concluded before.

One can even find examples of nonmonotonic reasoning in children's stories. In That's Good! That's Bad!, by Margery Cuyler, a little boy floats high into the sky holding on to a balloon his parents bought him at the zoo. “Wow! Oh, that's good,” the story goes.