Historical remarks on nonmonotonic reasoning, especially circumscription

Humans have always done nonmonotonic reasoning, but rigorous monotonic reasoning in reaching given conclusions has been deservedly more respected and admired. Euclid contains the first extended monoton-ically reasoned text available to a large public. I sus-pect that even Euclid did nonmonotonic reasoning in arguing for the postulates. It is unfortunate that the rigorous monotonic reasoning of Euclid has been de-emphasized in education, because Euclid generates in people who are not mathematically minded a respect for rigor. Conclusions derived by monotonic logical reasoning from precisely stated premises have always been the ideal. When people jump to conclusions, they are crit-icized for the gaps in their reasoning, because the con-clusions are not guaranteed to follow from the premises. Worse yet, the premises are often unstated. The inability to base all conclusions on logical reason-ing from precise and agreed premises has been long noted. There are two main reactions. One is to try to develop other principles of reasoning, and the other is to abandon logic- a big mistake. In my 1977 pa-per, Epistemological problems of artificial intelligence (McCarthy 1976). I referred to people saying logic was inadequate. I may have been referring to Marvin Min-sky’s 1975 paper and not getting around to looking it up. I think he was the first to use the phrase “non-monotonic reasoning”. Long before I wrote Epistemological problems..., I knew deduction wouldn’t suffice for AI. However, writ-ing that summarizing paper obliged me to say some-thing systematic about nonmonotonic reasoning and I introduced circumscription, perhaps with Occam’s ra-zor in mind. Here’s how I summarized it. The intuitive idea of circumscription is as fol-lows: We know some objects in a given class and we have some ways of generating more. We jump to the conclusion that this gives all the objects in the class. Thus we circumscribe the class to the objects we know how to generate. In (McCarthy 1986) I summarized the proposed uses of circumscription as follows