- Email: [email protected]
History of circumscription
Artificial Intelligence 59 (1993) 23-26 Elsevier
23
ARTINT 1020
History of circumscription John McCarthy Computer Science Department, Stanford University, Stanford, CA 94305, USA
Introduction
My 1980 circumscription paper should be considered as part of a sequence of three papers [7-9] which introduced successively more expressive forms of circumscription. Circumscription is one way of making nonmonotonic reasoning formal in the sense of mathematical logic. My 1959 paper [6] contains some hints about the need for nonmonotonic reasoning, but it seems to me that I thought about it in terms of what facts the theorem proving and problem solving mechanism took into account rather than in terms of putting the nonmonotonic reasoning in the logic itself. Others, especially Marvin Minsky [10] thought about the need for nonmonotonic reasoning as an objection to the use of mathematical logic. Here I will assume that formalized nonmonotonic reasoning in general and circumscription in particular are good ideas. Arguments for the proposition are given in the papers. That being the case, we need to ask why it wasn't invented much earlier, any time after the work of Frege [2] and Pierce. It seems to me that the basic reason is that everyone thought about logic as being confined to absolutely correct reasoning. The fact that nonmonotonic reasoning, which generates conjectures, requires formal tools of the same character as deductive reasoning was not obvious. In fact, I and the others who started formal nonmonotonic reasoning sort of backed into the idea that the very same tools were appropriate. My opinion is that formalizing nonmonotonic reasoning won't be the final step in applying logic to understanding thought and making computers think well. Formalizing contexts, so far just begun, is another step.
Correspondence to: J. McCarthy, Computer Science Department, Stanford University, Stanford, CA 94305, USA. E-mail: [email protected].
0004-3702/93/$ 06.00 (~) 1993 - - Elsevier Science Publishers B.V. All rights reserved
24
J. McCarthy
1. W h a t else are we all missing?
The ideas of nonmonotonic reasoning in general have had a mixed reception. (1) The most vigorous uses of circumscription and other nonmonotonic formalisms have been in expressing common-sense facts and reasoning. The frame, qualification, and ramification problems all involve nonmonotonic reasoning in their general forms. Circumscription and default logic have been applied to them, but unfortunately the most obvious and apparently natural axiomatizations tend to have unintended models, and this has been observed in several examples, especially the Yale Shooting Problem (Hanks and McDermott [3]). This has led to revised formalizations which work but don't seem so natural. It isn't clear whether there is a problem with the systems of nonmonotonic reasoning or whether we simply don't yet have the right axiom sets. Anyway the existing formalizations don't have enough of what I call elaboration tolerance. The idea is that formalizations should follow human fact representation in being modifiable primarily by extension rather than by replacement of axioms. Thus the axioms that allow a program to plan an airplane trip don't take into account either the possibility of losing a ticket or the necessity of wearing clothes. However, a human can modify a plan to take into account either of these requirements should they become relevant but would not revise its general ideas about planning airplane trips to take them into account explicitly. I have an axiomatization of airplane travel that handles losing the ticket nicely, i.e. no axioms about the consequences of losing a ticket or buying a replacement are used in the planning, but if a sentence asserting the loss of a ticket is added, then the original plan can no longer be shown to work and a revised plan involving buying a replacement ticket can be shown to work. The ideas will need to be extended to handle the need to wear clothes. Etherington, Kraus and Perlis [1] have discussed another problem--the fact that asserting the existence of nonflying birds spoils using the usual axiomatization to show that Tweety flies. Their solution, introducing the notion of scope is obviously in the right direction, but multiple scopes will be required. We hope to handle this using formalized contexts. (2) Mathematical logicians have mainly seen circumscription and the other forms of nonmonotonic reasoning as a worthwhile addition to their subject matter. For example, Kolaitis and Papadimitriou [4] discuss the collapsibility of circumscription and its computability, and Lehmann and Magidor [5] discuss general axioms for nonmonotonic logics. (3) Researchers interested in applications of logic to AI have also worked on the mathematical logical foundations of nonmonotonic reasoning and its relation to other fields of computer science, e.g. logic programming.
History of circumscription
25
Others have applied nonmonotonic logical formalisms to axiomatization and reasoning in common-sense domains--mainly to formalization of the results of action. Today the main treatments of the frame, qualification, and ramification problems use nonmonotonic reasoning formalisms. (4) People taking a probabilistic, i.e. Bayesian, approach to AI have mostly misunderstood nonmonotonic logic. Probabilities and nonmonotonic logic are complementary rather than rival formalisms. Nonmonotonic methods, e.g. circumscription, are necessary to form the propositions to which probabilities are to be assigned. For example, suppose a person knows of some things wrong with his car and intends to get them fixed. The proposition that there is nothing else wrong with his car is most conveniently formed by circumscribing the predicate "is wrong with the car". After forming it, he can assign a probability to it. However, he may plan to use the car after the known things have been fixed without ever using probabilities in any conscious way. Maybe none of the nonmonotonic formalizations discussed in AI actually assign probabilities, because they can be treated either as infinitesimal or near 1. However, suppose we want to formalize a domain where nontrivial numerical probabilities are relevant. Suppose also that the propositions to which probabilities are usefully assigned are not given in advance, i.e. that there is nothing else wrong with the car. Then it will be necessary to combine nonmonotonic logical formalisms with probabilities, and if a computer program is to do the job by itself then it will have to combine the formalisms. Actually, humans do nonmonotonic reasoning all the time in forming the propositions to which they later attach probabilities. However, as long as this part of the problem is done by people and not by computers, it can be treated informally. (5) Some of the most confused people about formalized nonmonotonic reasoning and the problems for which AI people use it have been philosophers. This seems to come from trying to fit it into categories that philosophers have previously studied.
References [ 1] D.W. Etherington, S. Kraus and D. Perlis, Nonmonotonicity and the scope of reasoning, Artifl Intell. 52 (1991) 221-261. [2] G. Frege, Begriffsschrift (1879). [3] S. Hanks and D. McDermott, Nonmonotonic logic and temporal projection, Artif IntelL 33 (3) (1987) 379-412. [4] Kolaitis and Papadimitriou (198x). [5] D. Lehmann and M. Magidor, Rational logic and their models: a study in cumulative logic, Tech. Rept. TR 88-16, Leibniz Center for Computer Science, Department of Computer Science, Hebrew University, Jerusalem (1988).
26
J. McCarthy
[6] J. McCarthy, Programs with common sense, in: Proceedings Teddington Conference on the Mechanization of Thought Processes (Her Majesty's Stationery Office, London, 1959). [7] J. McCarthy, Epistemological problems of artificial intelligence, in: ProceedingslJCAI-77, Cambridge, MA (1977). [8] J. McCarthy, Circumscription--a form of non-monotonic reasoning, Artif Intell. 13 (1-2) (1980) 27-39. [9] J. McCarthy, Applications of circumscription to formalizing common sense knowledge, Artiflntell. 28 (1986) 89-116. [10] M. Minsky, A framework for representing knowlege, in: P.H. Winston, ed., Psychology of Computer Vision (McGraw-Hill, New York, 1975).
23
ARTINT 1020
History of circumscription John McCarthy Computer Science Department, Stanford University, Stanford, CA 94305, USA
Introduction
My 1980 circumscription paper should be considered as part of a sequence of three papers [7-9] which introduced successively more expressive forms of circumscription. Circumscription is one way of making nonmonotonic reasoning formal in the sense of mathematical logic. My 1959 paper [6] contains some hints about the need for nonmonotonic reasoning, but it seems to me that I thought about it in terms of what facts the theorem proving and problem solving mechanism took into account rather than in terms of putting the nonmonotonic reasoning in the logic itself. Others, especially Marvin Minsky [10] thought about the need for nonmonotonic reasoning as an objection to the use of mathematical logic. Here I will assume that formalized nonmonotonic reasoning in general and circumscription in particular are good ideas. Arguments for the proposition are given in the papers. That being the case, we need to ask why it wasn't invented much earlier, any time after the work of Frege [2] and Pierce. It seems to me that the basic reason is that everyone thought about logic as being confined to absolutely correct reasoning. The fact that nonmonotonic reasoning, which generates conjectures, requires formal tools of the same character as deductive reasoning was not obvious. In fact, I and the others who started formal nonmonotonic reasoning sort of backed into the idea that the very same tools were appropriate. My opinion is that formalizing nonmonotonic reasoning won't be the final step in applying logic to understanding thought and making computers think well. Formalizing contexts, so far just begun, is another step.
Correspondence to: J. McCarthy, Computer Science Department, Stanford University, Stanford, CA 94305, USA. E-mail: [email protected].
0004-3702/93/$ 06.00 (~) 1993 - - Elsevier Science Publishers B.V. All rights reserved
24
J. McCarthy
1. W h a t else are we all missing?
The ideas of nonmonotonic reasoning in general have had a mixed reception. (1) The most vigorous uses of circumscription and other nonmonotonic formalisms have been in expressing common-sense facts and reasoning. The frame, qualification, and ramification problems all involve nonmonotonic reasoning in their general forms. Circumscription and default logic have been applied to them, but unfortunately the most obvious and apparently natural axiomatizations tend to have unintended models, and this has been observed in several examples, especially the Yale Shooting Problem (Hanks and McDermott [3]). This has led to revised formalizations which work but don't seem so natural. It isn't clear whether there is a problem with the systems of nonmonotonic reasoning or whether we simply don't yet have the right axiom sets. Anyway the existing formalizations don't have enough of what I call elaboration tolerance. The idea is that formalizations should follow human fact representation in being modifiable primarily by extension rather than by replacement of axioms. Thus the axioms that allow a program to plan an airplane trip don't take into account either the possibility of losing a ticket or the necessity of wearing clothes. However, a human can modify a plan to take into account either of these requirements should they become relevant but would not revise its general ideas about planning airplane trips to take them into account explicitly. I have an axiomatization of airplane travel that handles losing the ticket nicely, i.e. no axioms about the consequences of losing a ticket or buying a replacement are used in the planning, but if a sentence asserting the loss of a ticket is added, then the original plan can no longer be shown to work and a revised plan involving buying a replacement ticket can be shown to work. The ideas will need to be extended to handle the need to wear clothes. Etherington, Kraus and Perlis [1] have discussed another problem--the fact that asserting the existence of nonflying birds spoils using the usual axiomatization to show that Tweety flies. Their solution, introducing the notion of scope is obviously in the right direction, but multiple scopes will be required. We hope to handle this using formalized contexts. (2) Mathematical logicians have mainly seen circumscription and the other forms of nonmonotonic reasoning as a worthwhile addition to their subject matter. For example, Kolaitis and Papadimitriou [4] discuss the collapsibility of circumscription and its computability, and Lehmann and Magidor [5] discuss general axioms for nonmonotonic logics. (3) Researchers interested in applications of logic to AI have also worked on the mathematical logical foundations of nonmonotonic reasoning and its relation to other fields of computer science, e.g. logic programming.
History of circumscription
25
Others have applied nonmonotonic logical formalisms to axiomatization and reasoning in common-sense domains--mainly to formalization of the results of action. Today the main treatments of the frame, qualification, and ramification problems use nonmonotonic reasoning formalisms. (4) People taking a probabilistic, i.e. Bayesian, approach to AI have mostly misunderstood nonmonotonic logic. Probabilities and nonmonotonic logic are complementary rather than rival formalisms. Nonmonotonic methods, e.g. circumscription, are necessary to form the propositions to which probabilities are to be assigned. For example, suppose a person knows of some things wrong with his car and intends to get them fixed. The proposition that there is nothing else wrong with his car is most conveniently formed by circumscribing the predicate "is wrong with the car". After forming it, he can assign a probability to it. However, he may plan to use the car after the known things have been fixed without ever using probabilities in any conscious way. Maybe none of the nonmonotonic formalizations discussed in AI actually assign probabilities, because they can be treated either as infinitesimal or near 1. However, suppose we want to formalize a domain where nontrivial numerical probabilities are relevant. Suppose also that the propositions to which probabilities are usefully assigned are not given in advance, i.e. that there is nothing else wrong with the car. Then it will be necessary to combine nonmonotonic logical formalisms with probabilities, and if a computer program is to do the job by itself then it will have to combine the formalisms. Actually, humans do nonmonotonic reasoning all the time in forming the propositions to which they later attach probabilities. However, as long as this part of the problem is done by people and not by computers, it can be treated informally. (5) Some of the most confused people about formalized nonmonotonic reasoning and the problems for which AI people use it have been philosophers. This seems to come from trying to fit it into categories that philosophers have previously studied.
References [ 1] D.W. Etherington, S. Kraus and D. Perlis, Nonmonotonicity and the scope of reasoning, Artifl Intell. 52 (1991) 221-261. [2] G. Frege, Begriffsschrift (1879). [3] S. Hanks and D. McDermott, Nonmonotonic logic and temporal projection, Artif IntelL 33 (3) (1987) 379-412. [4] Kolaitis and Papadimitriou (198x). [5] D. Lehmann and M. Magidor, Rational logic and their models: a study in cumulative logic, Tech. Rept. TR 88-16, Leibniz Center for Computer Science, Department of Computer Science, Hebrew University, Jerusalem (1988).
26
J. McCarthy
[6] J. McCarthy, Programs with common sense, in: Proceedings Teddington Conference on the Mechanization of Thought Processes (Her Majesty's Stationery Office, London, 1959). [7] J. McCarthy, Epistemological problems of artificial intelligence, in: ProceedingslJCAI-77, Cambridge, MA (1977). [8] J. McCarthy, Circumscription--a form of non-monotonic reasoning, Artif Intell. 13 (1-2) (1980) 27-39. [9] J. McCarthy, Applications of circumscription to formalizing common sense knowledge, Artiflntell. 28 (1986) 89-116. [10] M. Minsky, A framework for representing knowlege, in: P.H. Winston, ed., Psychology of Computer Vision (McGraw-Hill, New York, 1975).