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1988-Why Things Go Wrong: a Formal Theory of Causal Reasoning

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From: AAAI-88 Proceedings. Copyright ©1988, AAAI (www.aaai.org). All rights reserved. Why Things Go Wrong: A Formal Theory of Causal Reasoning Leora Morgenstern and Lynn Andrea Stein Department of Computer Science Brown University Box 1910, Providence, RI 02912 Abstract 19861 [Shoham, 19871, [Kautz, 19861, [Lifschitz, 19861 [Lif- schitz, 19871, [Haugh, 19871). All of these solutions, how- This paper presents a theory of generalized tem- ever, while adequate for the Yale Shooting Problem itself, poral reasoning. We focus on the related prob- handle either forward or backward projection incorrectly, lems of and/or work only within a very limited temporal ontol- 1. Temporal Projection-determining all the ogy. Thus, they cannot serve as the basis for a theory of facts true in a chronicle, given a partial de- generalized temporal reasoning. scription of that chronicle, and In this paper, we present a solution to the problems 2. Explanation-figuring out what went wrong of both forward and backward temporal projection, based if an unexpected outcome occurs. upon the concept that actions happen only if they have to happen. We then show how our model lends itself to a We present a non-monotonic temporal logic based very natural characterization of the concept of an adequate on the notion that actions only happen if they explanation for an unexpected outcome. are motivated. We demonstrate that this the- In the next section, we survey the solutions that have ory handles generalized temporal projection cor- been proposed to the YSP, and explain why they can- rectly, and in particular, solves the Yale Shooting not handle general temporal projection accurately. We Problem and a related class of problems. We then then present our theory of default temporal reasoning and show how our model lends itself to a very natu- demonstrate that it can handle the Yale Shooting Problem ral characterization of the concept of an adequate as well as the problems that give other theories difficulty. explanation for an unexpected outcome. Finally, we extend our theory of temporal projection to a theory of explanation. 1 Introduction A theory of generalized temporal reasoning is a crucial 2 Previous Approaches to the part of any theory of commonsense reasoning. Agents who Prediction Problem are capable of tasks ranging from planning to story un- derstanding must be able to predict from their knowledge 2.31 Default Reasoning and the Yale of the past what will happen in the future, to decide on Shooting Problem what must have happened in the past, and to furnish a satisfactory explanation when a projection fails. The frame problem-the problem of determining which This paper present a theory that is capable of such rea- facts about the world stay the same when actions are soning. We focus on the related problems of performed-is an immediate consequence of the attempt to 1. Temporal Projection-determining all of the facts subsume temporal reasoning within first order logic. Mc- that are true in some chronicle, given a partial de- Carthy and Hayes first discovered this problem when they scription of that chronicle, and developed the situation calculus ([McCarthy and Hayes, 19691); however, it is not restricted to the situation calcu- 2. Explanation-determining what went wrong if an un- lus and in fact arises in all reasonably expressive tempo- expected outcome occurs. ral ontologies ([McDermott, 19871). In order to deal with Most AI researchers in the area of temporal reasoning the frame problem, McCarthy and Hayes suggested using have concentrated their efforts on parts of the temporal frame axioms to specify the facts that don’t change when projection task: in particular, on the problem of forward certain actions are performed; critics (e.g. [McDermott, temporal projection, or prediction ([McCarthy and Hayes, 19841) have argued that such an approach is unsatisfactory 19691, [McDermott, 19821, [Hayes, 19851, [Shoham, 19871). given the difficulty of writing such axioms, the intractabil- Standard logics are unsuitable for the prediction task be- ity of a theory containing so many axioms, and the fact cause of such difficulties as the frame problem. Straightfor- that frame axioms are often false. This last point is es- ward applications of non-monotonic logic to temporal log- pecially relevant for temporal ontologies which allow for its (suggested by [McDermott, 19821, [McCarthy, 19801) concurrent actions. are also inadequate, as [Hanks and McDermott, 19861 [McDermott, 19821 introduced the notion of a persis- demonstrated through the Yale Shooting Problem. tence: the time period during which a property typically Several solutions to the Yale Shooting Problem, using persists. He argued that we reason about what is true in extensions of default logic, have been proposed ([Shoham, the world, not via frame axioms, but through our knowl- 518 Knowledge Representation edge of the persistences of various properties. Such rea- The expected model-in which Fred is dead-is prefer- soning is inherently non-monotonic. able to the unexpected model-in which Fred is alive, These considerations led [McDermott, 19821 to argue since, in the unexpected model, it would be known that that temporal reasoning is best formalized within a non- at some point before 5, something happened to unload the monotonic logic. The discovery of the Yale Shooting Prob- gun. In fact, in all chronologically maximally ignorant lem ([Hanks and McDermott, 1986]), however, demon- models for this set of axioms, the gun is loaded at time 5, strated that this might not always yield desirable results. and therefore, Fred is dead. The Yale Shooting Problem can briefly be described as Solutions based upon forward reasoning strategies have follows: Assume that a gun is loaded at time 1, and the two drawbacks. In the first place, agents perform both gun is fired (at Fred) at time 5. We know that if one loads backward and forward reasoning. In fact, agents typically a gun at time j, it is loaded at time j+ll that if a loaded do backward reasoning when performing backward tempo- gun is fired at a person at time j, the person is dead at time ral projection. Consider, for example, a modification of the j+l, that if a gun is loaded at j, it will typically be loaded Yale Shooting Problem, where we are told that Fred is alive at time j+l (“loaded” persists for as long as possible), and at time 6. We should know that the gun must somehow that if a person is alive at time j, he will typically be alive have become unloaded between times 2 and 5; however, at time j+l (“alive” persists for as long as possible). we should not be able to say exactly when this happened. We would like to predict that Fred is dead at time 6. Rel- In contrast to this intuition, the systems of Shoham and ative to standard non-monotonic logics ([McDermott and Kautz would predict that the gun became unloaded be- Doyle, 19801, [McCarthy, 19801, [Reiter, 1980]), however, tween time 4 and time 5. This is because things stay the the chronicle description supports (at least) two models: same for as long as possible.2 the expected one, in which one reasons by default that the A second objection to the strategy of chronological min- gun is loaded at time 5, and in which Fred is dead at time 6, imization is that it does not seem to address the real con- and the unexpected model in which one reasons by default cerns underlying the Yale Shooting Problem. We don’t that Fred is alive at time 6, and in which, therefore, the reason that Fred is dead at time 6 because we reason for- gun must be unloaded at time 5. Standard non-monotonic ward in time. We conclude that Fred is dead because we logic gives us no way of preferring the expected, intuitively are told of an action that causes Fred’s death, but are not correct model to the unexpected model. told of any action that causes the gun to be unloaded. Like the frame problem, the Yale Shooting Problem was 2.2.2 Circumscribing Over Causes first presented within the situation calculus framework, but is not restricted to that particular ontology ([McDermott, [Lifschitz, 19871 and [Haugh, 19871 independently pro- 19871). posed solutions which were not based upon forward rea- soning strategies. We present Lifschitz’s; again criticisms of his theory apply to both. Lifschitz’s solution is based 2.2 Proposed Solutions to the YSP and on the intuition that “all changes in the values of flu- Their Limitations ents are caused by actions.” Lifschitz introduces a pred- In their original discussion of the Yale Shooting Problem, icate causes(act,f,v), where action act causes fluent f to Hanks and McDermott argued that the second, unexpected take on value v, and a predicate precond(f,act). Success model seems incorrect because we tend to reason forward is defined in terms of precond, affects in terms of causes in time and not backward. The second model seems to and success. He circumscribes over both the causes and reflect what happens when we reason backward. Such rea- precond predicates; circumscribing over causes solves the soning, they argued, is unnatural: the problem with non- frame problem. 3 Things are only caused when there are monotonic logic is that there is no way of preferring the axioms implying that they are caused. Necessary pre- forward reasoning models to the backward reasoning mod- conditions for an action are satisfied only when the ax- els. ioms force this to be the case. Actions are successful ex- actly when all preconditions hold; actions affect the val- 2.2.1 Chronological Minimization ues of fluents if and only if some successful action causes The first wave of solutions to the Yale Shooting Problem the value to change.
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