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Reviewer: James Delgrande

This book describes a specific, formal approach to the problems of representing and reasoning about time and causation as they arise within the general framework of artificial intelligence. The book consists essentially of Shoham's doctoral dissertation and is part of the MIT Press Series in Artificial Intelligence, whose purpose is to provide “timely, detailed information” concerning recent AI research. Given this goal, it is not surprising that the book is neither a survey nor an introduction to the area (despite its subtitle), but rather provides a specific account of how such problems may be addressed. As such, it succeeds in being not only timely and detailed, but also interesting, thoughtful, and well written. It is not, however, intended for the neophyte. Consequently, a familiarity with work in temporal reasoning in AI is assumed and a familiarity with modal logics and nonmonotonic reasoning would be helpful. The book is written in a clear, economical style; if anything, it is perhaps a little overbrief in places. Decisions are at times simply stated, with minimal motivation or supporting argument. Similarly, there are times when an additional example or two would have helped to clarify a point. On the other hand, the author has clearly thought long and hard about the various issues and a full discussion of all of them might have lengthened the book unreasonably. The book can be divided into four major parts. The first part is concerned with developing a general logic of time; the second part presents a general model-theoretic approach to nonmonotonic reasoning. Given this, in the third part the author shows how the qualification problem and the problem of extended prediction may be resolved. Last, an account of the notion of causation deriving from these considerations is given. For the first part (chapter 2), a variant of McDermott's temporal logic is adopted as a vehicle for expressing temporal constructs: time points are taken as primitive, and propositions are identified with sets of intervals (pairs of points) over which they are true. The central construct in the language is the formula TRUE( u 1, u 2, p), where u 1 and u 2 are time point symbols, and p is a possibly negated primitive proposition. This formula is read as “ p is true over the interval &angl0; u 1, u 2 &angr0; .” The semantics is based on a limited ontology and avoids introducing events, properties, facts, and other such entities as primitive objects; these entities are introduced by definition instead. As a result, the logic rests on a conceptually clean foundation that is at the same time very general. The resultant formal systems appear sufficiently broad to capture most aspects of temporal reasoning. Thus, for example, no commitment is made as to whether time is discrete or not, or branching or not. This generality, however, seems to leave the systems open to the criticism that the semantics is perhaps too general or too loose and thus may admit unintuitive models. For example, in an interpretation, ?is any binary relation. While we can presumably assume that ?is at least a partial order, it would seem that we might want to add further constraints on this relation and, moreover, claim that these constraints are crucial in any temporal logic. For instance, we might want to say that any two time points are connected via a path through ?or its inverse. In addition, these systems are not used in their full generality; rather, most of the book assumes a much more constrained system wherein points of time are isomorphic to the integers. The second part of the book presents an approach for developing and analyzing nonmonotonic systems based on model-theoretic considerations. The general idea is elegant, simple, and, consequently, highly appealing. In brief, one orders the models of a logic by some preference criterion, and a interpretation M is said to preferentially satisfy a sentence A just when A is true in that interpretation and there is no less preferred M? satisfying A. Circumscription, for example, is shown to fit into this framework, and Reiter's system for default reasoning is shown to fit with a little coaxing. Again, however, the treatment given here is brief (which is perfectly understandable, given that the purpose of the dissertation was not to address nonmonotonicity per se) and leaves a number of questions unanswered. For example, the preference criterion is assumed to be a strict partial ordering, and so if M < M?, then we cannot have M? < M. (There would appear to be good arguments, however, for allowing both M ?9T M? and M? ?9T M (or models that are equally preferred).) The third part (chapters 4 and 5) addresses the problems of qualification and extended prediction. The first of these deals with the apparent requirement that, for reasoning in a realistic domain, an inordinate number of conditions must be satisfied before a conclusion is forthcoming. Thus, before concluding that a loaded gun makes a noise when the trigger is pulled, one would need first to ensure that the gun was not immersed in water, that there was air to carry the sound, etc. For this problem, the notion of a causal theory is introduced: a causal theory is a set of sentences (&Fgr; ? 9T&THgr;) :.F:6WWS :9Y&fgr;, where &fgr; is a sentence of the form TRUE( t 1, t 2, p) or ¬ TRUE( t 1, t 2, p), &Fgr; (roughly) is a conjunction of sentences that must be known to be satisfied, and &THgr; (roughly) is a conjunction of sentences whose negation is not known. Assuming that certain reasonable constraints are met, Shoham shows how temporal nonmonotonic consequents can be determined and, moreover, can be determined in O( n log n) time. Thus, while this formulation is not totally general, it does lead to very good complexity bounds. For the problem of extended prediction, which amounts to the difficulty of easily yet accurately predicting things over extended periods of time, Shoham extends Hayes's notion of space-time histories. The idea introduced here (again, roughly) is that of potential histories, entities that by default extend into the future until explicitly blocked. Again, the author shows how a particular model can be efficiently constructed. In the final part (chapter 6), it is argued that the preceding work provides a sound basis for a new account of causation. The sentence “ TRUE( t 1, t 2, p) directly causes TRUE( t 3, t 4, q)” is taken to be true in a causal theory just when that theory contains a causal rule (:9Y TRUE( t 1,:- Ct 2, p) ? 9T&THgr;) :.F:6WWS :9Y TRUE:- A( t 3, t 4, q), where &THgr; is a conjunction of conditions where the negation of none of the conjuncts is known, and where various reasonable conditions concerning temporal precedence hold. Thus, if one does indeed pull the trigger of a loaded gun, and one does not know that there is no air, or that there is no firing pin, etc., then one can conclude that pulling the trigger causes a noise in the next time instant. This account of causation has a certain appeal, but it is unclear to what extent it provides a full account of this phenomenon. First, only primitive propositions can be “caused” by something. A second limitation is that this account appears to admit some counterintuitive statements of causation. It is thus possible to assert that some condition causes some other condition, where the second condition already happens to be true. Hence, in this account, if I painted a fire hydrant red, which was already red, I could nonetheless claim that I caused the hydrant to be red. Stranger examples can be constructed as well. For instance, statements that happen to be known to be true can seemingly have arbitrary causes. For example, I have a friend, Art, who is an avid drummer. If we assume that he catches a cold, it seems that we can equally well assert “catching the cold on Saturday caused Art's blocked sinuses” and “drumming on Saturday caused Art's blocked sinuses.” Last, it can be observed that any theorem may be “caused” in any causal theory. Thus we could assert, for example, that “Art's drumming last Saturday caused De Morgan's laws on Sunday.” A conceivable way around these difficulties is to simply exclude such statements from causal theories. This solution just defers the problem, however, since we now have to decide which statements should be admitted into these theories. However, if we could make this decision, then the suggested approach would allow us to reason about causality; it just would not furnish us with a definition. To summarize, this is a highly interesting and useful book for researchers in AI, particularly those interested in temporal reasoning and related areas. The adoption of a formal framework leads to a clear, principled investigation and solution of recalcitrant and fundamental problems in temporal reasoning. The notion of model preference is appealing, not just for its potential applications in temporal reasoning, but as an approach to the problem of nonmonotonicity in general. Causal theories and potential histories provide a satisfying resolution to problems of reasoning about temporal phenomena. The section on causality, while perhaps not providing a general definition of the phenomenon, does allow one to decide when something causes something else, given a prior set of statements of causality.

Reviewer: Peter Naur

The author demonstrates his one hundred pages of formal developments in terms of a single example, called the shooting scenario. This concerns the basis for arguing whether when a gun is fired a loud bang will be heard. For this purpose a so-called causal theory is developed, including as its most significant part the following lines of formal description (shown identically on pages 107, 117, 130, and 131): :.OC :.HB :9Y(t.loaded) ? :9Y(t. fire) ? 9L :6WW:9S(t.air) ? 9L :6WW:9S(t.firingpin) ? 9L :6WW:9S(t.no-marshmallow-bullets) ? 9L . . . :6WW:9S . . . other mundane conditions :3WS9L :9Y(t+1,noise), for all t :.HT :.0E Roughly these lines state that if at time t the gun is loaded, fired, surrounded by air, provided with a proper firing pin, and loaded with bullets not made of marshmallow, and in addition other mundane conditions are also satisfied, then at time t+1 a noise will be heard. That this is a non-solution, however, is made visible most prominently by the appearance of the “other mundane conditions” clause. This clause clearly will have to take care of the rest of the world. But the world cannot be captured in terms of predicates. This has been tried and given up before, notably by Carnap (as discussed by Quine [1]). In terms of the present example the clause would have to state explicitly anything that the bullets cannot be made of, besides marshmallow. No finite clause could do that. The author's definition of causality depends on the same type of formal description as the one dismissed here, and shares its deficiency. It is outside the scope of the present review to enter into issues of other activities called AI by their practitioners. Some of my views in this direction can be found elsewhere (see [2] and [3]).

Reviewer: Yoav Shoham

It appears that Naur has not read my dissertation carefully, and has misunderstood the parts he did read. One gets the feeling that he is attacking not only my own work, but a major line of research which lies primarily within artificial intelligence (AI). The review does not suffer as much from Naur's obvious unfamiliarity with AI issues as it does from his unawareness of this gap. If his review merits comment, it is only because of the respectable forum in which it appears, and my admiration of Naur's early contributions to computer science. Naur seems to be making three main points: 1.The dissertation addresses two distinct issues: reasoning in logic about mechanics, and defining causation. 2.The former is ridiculous for ignoring the lessons of physics, and indeed the dissertation contributes nothing to our understanding of mechanics. 3.The latter misses the point of what causation is really about. The short answer is that the dissertation addresses not two distinct issues but several related ones, that mechanics is not one of them, and that Naur's discussion of causation completely ignores my definition of it. In a bit more detail the answer is as follows. The main task I consider in the dissertation is that of making defensible predictions in any domain, including stock market behavior and interpersonal relationships (page 1). The fundamental problem is that when we, people, make predictions, we are forced to make many assumptions, without which it would become prohibitive to make any predictions. For example, when we fire a loaded gun, we predict that a loud noise will follow, even though we have not checked for the many possible-but-unlikely conditions that violate this prediction (the gun is missing a firing pin, there is no air to carry the sound, etc.). The same limitations will apply to our resource-limited robots. The billiard balls example merely illustrates the issues. There too we must make assumptions, such as about there not being additional balls around, about no one drilling holes in the table, and so on. Physics, of course, has nothing to say about this assumption making. Incidentally, the main example in the dissertation is not the billiard balls one, but the gun-firing scenario. In this case Newtonian physics are not relevant for prediction purposes in any practical sense. Curiously, Naur makes no mention of it. The dissertation clarifies these problems and proposes a solution to them. In particular, it identifies the qualification problem and the extended-prediction problem (which subsume the so-called frame problem). At the end of his review Naur confuses the frame problem with the qualification problem. Perhaps that is why he considers the former unsolved, whereas in fact it is solved in chapter 5. Along the way, the dissertation makes independent contributions to both temporal logic and nonmonotonic logic, both very active research areas nowadays. Naur views my discussion of causation as a separate issue, whereas in fact it is a natural outgrowth of the preceding analyses. In one paragraph he attempts to point to the right perspective on causation. Some of his intuitions are right—for example, that the concept is tied to “human context and situation.” However, it seems to me astounding, indeed appalling, that he ignores the fact that this is precisely my underlying premise (I am very explicit about it in Subsection 6.2 and in many other places thereafter). For example, it follows from my definition that firing a loaded gun causes noise, but only in the context of assumptions about the existence of firing pins, the absence of silencers, and so on. Some of Naur's other intuitions about causation I find misguided, such as about causation relying on the notion of intent. A debate on nonmonotonic temporal reasoning and on causation is welcome, but this is not the right forum. I am a big fan of exposing one field to the criticism of others—for the scrutiny, for example, of AI by those in other branches of computer science or in psychology or philosophy. We in AI are facing hard problems, and input from all smart people can be invaluable. Such feedback, however, requires an effort of the outsider to understand the problems in the new field, which may render some deeply entrenched presuppositions inadequate. In any case, dismissing by “it has no merit” a piece of work on which two LICS papers, one AAAI paper, a prize-winning ECAI paper, and an IJCAI paper and several journal articles were all based, serves no useful purpose.

Reviewer: Peter Naur

The main part of this dissertation is the development, in several stages, of logical formalisms for expressing issues related to situations involving several items that react with one another over a period of time. This field of interest is illustrated in terms of scenarios involving rolling and colliding billiard balls. A later section discusses causation as an additional issue of these formalisms. To this reviewer the decisive issue in this presentation is the starting premise—the assumption that significant insight into the events taking place when solid bodies, such as billiard balls, move about can be obtained solely by calculations with truth values, that is, by reasoning. This essential assumption becomes evident on page 9, where it is suggested that, in dealing with moving objects, “precise numerical information (such as the precise distance between two billiard balls) is unnecessary and unavailable.” It seems to this reviewer astounding, indeed appalling, that at this time in history, 300 years after Newton, such a view of motions and mechanics can be entertained. How can anyone dealing at all seriously with time and motion be unaware that the motions of the heavenly bodies, including their encounters in eclipses, are calculated very successfully as a matter of astronomical routine, and that the motions of aircraft are being calculated continuously in airport control systems, to mention just two examples. How can anyone present one hundred pages of formalism in order to arrive at a non-solution of the problem solved with high efficiency by Newtonian mechanics__?__ For despite the author's claims about its efficiency, what emerges after these hundred pages is a non-solution. Causation, the second issue taken up by the author, fares no better than mechanics. The author quotes seven lines from Bertrand Russell's discussion of cause, which establishes quite clearly that causes have no place in physics and astronomy, but then joins several other authors who quote Russell without grasping his message. It occurs to none of these authors that meaningful talk of causes, like meaningful talk of anything else, is a matter of context and situation. A typical context and situation would be that of a serviceman being called in to fix a broken television receiver. The cause here might be a defective line cord, for example. Spelled out in more detail, the context is that of a person dealing with a thing involving several issues or parts, which are intended by the person to serve a particular function. The situation is that the thing fails in its intended function, and we are then entitled to ask for the cause of the failure. It is meaningful to ask why something fails to function according to our intent. To ask why something functions properly makes no sense, since the circumstances that lead to the present situation of the world are beyond enumeration. In the book under review this latter notion gives rise to what is called the frame problem. The reader is misled by this euphemism into expecting that it will be solved. It will not. It is a sad reflection on the state of computer science that the present work can not only be published as a book, but be accepted as a Ph.D. dissertation by Yale University. It has no merit.