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INTRODUCTION. THE QUALIFICATION PROBLEM

(McCarthy 1959) proposed a program with ``common sense'' that would represent what it knows (mainly) by sentences in a suitable logical language. It would decide what to do by deducing a conclusion that it should perform a certain act. Performing the act would create a new situation, and it would again decide what to do. This requires representing both knowledge about the particular situation and general common sense knowledge as sentences of logic.

The ``qualification problem'', immediately arose in representing general common sense knowledge. It seemed that in order to fully represent the conditions for the successful performance of an action, an impractical and implausible number of qualifications would have to be included in the sentences expressing them. For example, the successful use of a boat to cross a river requires, if the boat is a rowboat, that the oars and rowlocks be present and unbroken, and that they fit each other. Many other qualifications can be added, making the rules for using a rowboat almost impossible to apply, and yet anyone will still be able to think of additional requirements not yet stated.

Circumscription is a rule of conjecture that can be used by a person or program for ``jumping to certain conclusions''. Namely, the objects that can be shown to have a certain property P by reasoning from certain facts A are all the objects that satisfy P. More generally, circumscription can be used to conjecture that the tuples <x,y ... ,z> that can be shown to satisfy a relation P(x,y, ... ,z) are all the tuples satisfying this relation. Thus we circumscribe the set of relevant tuples.

We can postulate that a boat can be used to cross a river unless ``something'' prevents it. Then circumscription may be used to conjecture that the only entities that can prevent the use of the boat are those whose existence follows from the facts at hand. If no lack of oars or other circumstance preventing boat use is deducible, then the boat is concluded to be usable. The correctness of this conclusion depends on our having ``taken into account'' all relevant facts when we made the circumscription.

Circumscription formalizes several processes of human informal reasoning. For example, common sense reasoning is ordinarily ready to jump to the conclusion that a tool can be used for its intended purpose unless something prevents its use. Considered purely extensionally, such a statement conveys no information; it seems merely to assert that a tool can be used for its intended purpose unless it can't. Heuristically, the statement is not just a tautologous disjunction; it suggests forming a plan to use the tool.

Even when a program does not reach its conclusions by manipulating sentences in a formal language, we can often profitably analyze its behavior by considering it to believe certain sentences when it is in certain states, and we can study how these ascribed beliefs change with time. See (McCarthy 1979a). When we do such analyses, we again discover that successful people and programs must jump to such conclusions.

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John McCarthy
Tue May 14 00:04:52 PDT 1996