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Michael Thielscher

A Theory of Dynamic Diagnosis

The article mentioned above has been submitted to the Electronic Transactions on Artificial Intelligence, and the present page contains the review discussion. Click here for more explanations and for the webpage of theauthor, Michael Thielscher.

Overview of interactions

N:o Question Answer(s) Continued discussion
1 3.11  Rob Miller
3.11  Michael Thielscher
2 23.12  Marie-Odile Cordier
9.1  Michael Thielscher
3.5  Anonymous Reviewer 2
7.5  Michael Thielscher
3 27.12  Wolfgang Nejdl
9.1  Michael Thielscher
4 3.5  Anonymous Reviewer 2
7.5  Michael Thielscher

Q1. Rob Miller (3.11):

Michael, a question regarding the relative likelihoods of different components failing:

It seems to me that, in the absence of specific domain knowledge to the contrary, it's right to prefer explanations of system failure which are minimal in terms of the number of failures of individual components, other things being equal (this is one aspect of how your main example works, if I've understood correctly). But you also mention that good diagnosis is able to "take into account a priori knowledge of differences in the likelihood of components to break" (an example might be the knowledge that relays are more likely to fail than resistors). Could you say a little more about this in relation to your approach? Would you perhaps use more than one  ab  predicate, with some sort of prioritised minimisation between the predicates?

A1. Michael Thielscher (3.11):


My theory does indeed respect domain knowledge of the kind you mention. This knowledge is formally represented by a partial ordering among the instances of the (unique)  ab  predicate--which is equivalent to your suggestion of allowing a priority hierarchy of different  ab  predicates. The notion of preferred models (Definition 10) reflects a given partial ordering in that more unlikely instances of  ab  are preferably minimized. As a consequence, the axiomatization of the theory by means of the Fluent Calculus (Section 5) employs Brewka's prioritized extension to classical Default Logic.

Q2. Marie-Odile Cordier (23.12):

I have three main comments on this paper :

1) The example on page 4-6 is quite interesting and highlights very clearly what happens when dealing with interactive faults ( ab(r1 causes  ab(re1 when  s1  is closed). But, I did not really agree with the conclusion the author is drawing from it.

What it clearly highlighted, in my opinion, is that "minimizing abnormality" cannot be used when dealing with interactive faults. Most research papers on diagnostics suppose implicitly that faults are independent and equiprobable, and in these cases, "minimizing abnormalities" is a good way of selecting the most probable diagnoses. However, as soon as you are dealing with interactive faults the preferred diagnoses have no good reason (no probabilistic foundation) to be the minimal ones. In the example, the probability of  ab(re2, knowing  ab(r2 and  closed(s2 is equal to 1 whatever the probability of  re2  is of being faulty from its own. Then,  d1  has to preferred rather than  d2  and  d3 .

The key point is that "minimization" (minimizing abnormalities) is not a good preference strategy in case of interactive faults. This seems to me to be the very reason why one doesn't get the expected results in this example.

Another point concerns when this "preferring" step has to be done. The author argues that it has to be done at the starting point and uses the example as a justification. I don't contest this fact (see below), but I contest that it follows from the example.

From the following example, it can be seen that "minimizing abnormalities" is not a correct solution even if it is done at the starting state. Let us suppose that it is known that  closed(s1,  closed(s2,  closed(s3 and  off(light are true in the initial state. Whatever the action might be, for example "open s1" or the empty action, you are going to prefer a state where  ab(re1 is true rather than the one where  ab(r1 and  ab(re1 are true, which is not at all justified from a probabilistic point of view. It is even problematic from a diagnostic point of view, for replacing  re1  by an unfaulty relay (instead of replacing  r1 ) will lead to breaking  re1  again as soon as you will close  s1 . In fact, example 1 (page 20) exhibits similar results which are not satisfying by forgetting  ab(r1 and  ab(r2 as possible faults.

2) The term "dynamic diagnosis" is used throughout the paper to denote diagnosis on systems on which you are performing actions (tests). As far as I understand, the systems are supposed to be static ones; they are not supposed to evolve by their own; they don't have any proper dynamic behaviour. The only way to make them change is to perform actions. This is the reason why you can predict the resulting state by looking only to the effects of the action. Unpredictable events are not taken into account, for exemple faults (or more simply evolutions of the system) that occur during the sequence of actions.

The term "dynamic diagnosis" is then misleading, at least for the diagnostic community for which dynamic diagnosis usually means diagnosing systems evolving in time by themselves, without explicit exogeneous events making them change.

In this context, the problem which is proposed is very similar to that of postdiction : knowing some observed facts resulting from an action (or a sequence of actions), you want to infer the actual state of the system. Faults cannot happen during the sequence of actions, and then dealing with an action or a sequence of actions makes no difference.

Consequently, it is quite justified to apply the "preference step" on the initial point. You have to determine the most probable sequences of steps (or histories, scenarii, trajectories?) starting from initial states, leading to some final states in which observations are true, and corresponding to a given sequence of actions. There are no unknown events; there is no uncertainty in the actions; no uncertainty wrt their effects; the only uncertainties concern the initial states. The preference between sequences depends directly on preferences on initial states, which explains why the "preference step" concerns the initial states.

This scheme is a restricted case of a most general scheme in which you take into account the possible occurences of events (as faults) interleaved with the actions, the probability of such events, and the probability of an action to produce some effects. Selecting some of these scenarii according to preference criteria corresponds to what we called "event-based diagnosis" in [Cordier 94]. It is also close to McIlraith's approach; see [McIlraith 94], [McIlraith 97]. The main difference between these approaches is that we tried to define diagnostics independently of the mechanism used for modeling actions and changes, whereas Sheila's proposal is clearly dependent on the formalism used to model actions (situation calculus).

3) The last point concerns the ramification problem and the use of a causal model to predict the effects of an action. I realize that this point is not the main subject of this paper, since it is devoted to diagnostics. However, an important point related to this paper is to examine whether it can be applied when dealing with dynamic systems.

This theory of action based on causal relationships is very attractive as long as you are looking for the effects of an action or a sequence of actions, and as long as the concerned system has no proper evolution. Fluents which are not affected by an action are then supposed not to change, by virtue of a minimal change principle. But as soon as you are concerned with dynamical systems, (which is not really the case in the paper), such a causal model would probably not be sufficient and you will need a "transition model", describing the way things evolve along time. This happens for example if you want to model the dynamics of a system, or the possible events as faults that occur as you are monitoring a system, or the natural ageing of components.

An answer could be that there cannot be changes without causes, but most of the time you don't want to model these causal chains or you are not even able to model the primary causes of such evolutions (for example, the ageing of components or the sudden occurence of a fault), but you want nevertheless to take them into account as far as possible.

The basic idea of the proposal we made in [Cordier 95] was that a transition model (that is, a set of possible (partially ordered) transitions) is needed in order to decide what is the most plausible state after an update, or equivalently, an action. A causal model is certainly quite adequate when considering static systems reacting to actions. More than that, in my opinion, a causal model is a very nice formalism allowing to acquire the partial orderings that exist between transitions, in a natural way. There is probably a strong correspondence between your "influences" and our "partially ordered transitions" which would be worth studying more deeply. However, transitions seem to have a broader scope in that they allow to represent any changes from one world to a next one, whereas causal relations or influences are restricted to represent "causative changes" (changes for which one can exhibit the causes). This is a problem when dealing with dynamical systems.


Cordier 94Marie-Odile Cordier and Sylvie Thiébaux.
Event-based diagnosis of evolutive systems.
Proceedings of the 1994 DX Conference.
Also available as IRISA technical report Nr. 819 [entry].
Cordier 95Marie-Odile Cordier and Pierre Siégel.
Prioritized transitions for updates.
Proceedings of the 1995 ECSQARU Conference, pp. 142-151.
Also available as IRISA technical report Nr. 884 [entry].
McIlraith 94Sheila A. McIlraith.
Towards a theory of diagnosis, testing and repair.
Proceedings of the 1994 DX Conference, pp. 185-192.

McIlraith 97Sheila A. McIlraith.
Explanatory diagnosis: conjecturing actions to explain observations.
Proceedings of the 1997 DX Conference, pp. 69-77.

A2. Michael Thielscher (9.1):

I want to thank Marie-Odile for the very detailed comments, the pointers to related literature, and for the interesting questions. Let me answer the latter in turn.

The main matter of concern in my paper is to point out a crucial aspect of generalizing theories of diagnosis to what I call the dynamic case: Component failures, which usually are considered abnormal, may naturally arise in the course of time as direct or indirect effects of actions (or events, for that matter). As a consequence, it is inappropriate to simply apply minimization strategies that are suitable in the static case equally to all states that arise during the diagnosis process. Rather it is necessary to employ the `static' strategy only once, namely, initially. This allows to count as perfectly normal any component failure that is effected later on. Now, in the paper I have pursued one particular `static' minimization strategy, namely, where it is required that if there is a difference in the a priori likelihood of component failures, then it needs to be explicitly stated so. This is not the case in the scenario and reasoning process you described: The a priori likelihood of  ab(re1 is higher than that of  ab(r1. Hence, what you suggest is a more sophisticated static strategy, where differences in the a priori likelihood of abnormalities are derived from state constraints. This does not affect my argument: If diagnosis concerns a sequence of states, then again this more elaborated minimization strategy should be applied only once, thus allowing for component failures to be effected in the course of time.

Concerning the second remark, I admit that for the diagnosis community the term "dynamic" might be misleading, at least at first glance. To begin with, in the area of formalizing reasoning about actions and change it has become common to call "dynamic" any system that may exhibit different states in the course of time, no matter whether state changes are brought about by exogenous action or by natural events that happen inside the system. The striving motivation for me adopting this term was to contrast the contents of the paper to Reiter's work on diagnosis [j-aij-32-57]. But apart from that, many results have been established that show how approaches to reasoning about actions can be generalized to the case where actions are performed in self-evolving systems. (See, e.g., [c-ijcai-95-1956], [c-kr-96-2], [mb-Shanahan-97], to mention a few.) The gap between dynamic systems which idle unless actions are performed, and those that are self-evolving turned out less deep than one might have expected. In particular, the theory of causal relationships (and the axiomatization on the basis of the Fluent Calculus) has very recently been extended to allow for natural events aside from exogenous, volitional actions [Thielscher 98]. Combining this extension with the diagnosis approach pursued in the paper has yet to be achieved, but there seems to be no fundamental obstacle for so doing.

This leads to my answer to your third remark. An example taken from [Thielscher 98] is the following specification of the behavior of a simple timer by means of a causal relationship:

  (clock IS x+1) causes 
      (timer IS t-1) if (timer=t and t>0)
which says that whenever the global clock ticks, then the timer counts down until it reaches zero. This shows that causal relationships do not depend on the performance of actions but just on the occurrence of effects, which might just as well be the consequence of natural events inside the system. Now, the motivation for using a causal description rather than an explicit transition model is that only the former corresponds directly to a natural and "elaboration-tolerant" (see [c-fcs-98-198]) description of actions and events, effects and change. (Notice that via the theory of causal relationships, any causal description implicitly determines a transition model.) Generally, research in the area of commonsense reasoning about actions is largely motivated by the conceptual gap between a natural description of causes and effects, and the corresponding transition model. The Ramification Problem, for instance, has to be understood in this way, and so is of course an issue in case of self-evolving dynamic systems just as well (see again [Thielscher 98]).


c-fcs-98-198John McCarthy.
Elaboration tolerance. [abstract] [postscript]
Proc. Formalization of Commonsense Reasoning, 1998, pp. 198-216.
c-ijcai-95-1956Michael Thielscher.
The Logic of Dynamic Systems.
Proc. International Joint Conference on Artificial Intelligence, 1995, pp. 1956-1962.
c-kr-96-2Ray Reiter.
Natural Actions, Concurrency and Continuous Time in the Situation Calculus.
Proc. International Conf on Knowledge Representation and Reasoning, 1996, pp. 2-13.
j-aij-32-57Ray Reiter.
A theory of diagnosis from first principles.
Artificial Intelligence Journal, vol. 32 (1987), pp. 57-95.
b-Shanahan-97Murray Shanahan.
Solving the Frame Problem: A Mathematical Investigation of the Common Sense Law of Inertia.
MIT Press, 1997.
Thielscher 98Michael Thielscher.
How (not) to minmize events.
Submitted to the conference KR-98.

C2-1. Anonymous Reviewer 2 (3.5):

I have only one complaint which has been already raised by Marie-Odile Cordier during the discussion phase (point 2): the theory assumes that the system may change its status only because of some action. However, faults cannot happen during the execution of actions. Because of this, it is reasonable to "minimize abnormalities" in the initial state. However, are the assumptions reasonable? In your reply to Marie-Odile, you say that you see no fundamental obstacle in extending the theory to "natural events aside from exogenous, volitional actions". Some more words (a section with an example?) about how to do it will be of great help.

C2-2. Michael Thielscher (7.5):

I hope that the following remark constitutes a satisfactory reply to your question. This is the basic idea in the paper [5], which I mentioned in my answer to Cordier's question to which you refer: The happening of a (non-exogenous) event is considered a property of a world state and thus is formally treated as a fluent. Hence it can be (directly or indirectly) caused by actions or other events. In the aforementioned paper we have shown that minimization of event occurrences had better be conducted in the initial state only. Now, here is a (sketchy) idea for combining this approach with the present theory of dynamic diagnosis: Suppose we introduce binary fluents  Happens(et indicating that event  e  is expected to happen at time  t . If  Happens  is minimized initially (just like  Ab  is in the paper under discussion), then the occurrence of natural events, too, may serve as explanation for abnormalities. These explanations would `compete' with assumptions about initial abnormalities; additional, qualitative knowledge as to the a priori likelihood of both events and abnormalities may then be used to tell apart the most plausible diagnoses (along the lines of Definition 10 of the present paper).

Q3. Wolfgang Nejdl (27.12):

One basic remark about the title and intention of your paper:

When I first read your paper, I had some difficulties in connecting your work to the usual diagnosis literature, as you basically refer only to papers about reasoning about action and change (which is ok, considering the content, but should be changed, considering the title). Also, the current title is somewhat misleading, as the term "dynamic diagnosis" in the diagnosis community is usually reserved for systems which monitor and diagnose continuous and/or time-varying systems. I would have suggested something like "diagnosis and actions" or similar within the title.

Anyway, here are some more specific questions, which came into my mind, while I was trying to comprehend your approach.

1. It seems to me, that one main problem (chapter 2) you are considering are dependent failures like " ab(c1 implies  ab(c2", which are usually neglected in many papers. Could you elaborate more on the advantages of your formalism when these dependent failures are not present? In such a case, what exactly do you gain by including explicit causal relationships (considering that most diagnosis systems use just ordinary state constraints)?

2. A second thread which seems to emerge in chapter 4 is the integration of test actions. Have you thought about which test actions one should take, or is this only a side issue in this chapter?

3. Also, could you comment some more about the relationship of your approach to the one of Sheila McIlraith?

Best regards,

Wolfgang Nejdl

A3. Michael Thielscher (9.1):

Let me now give answers to the questions by Wolfgang Nejdl. One of them also concerns the use of the term "dynamic systems" and so has already been considered in the answer to the previous question. The references before refer to the bibliography of that answer.

As for the motivation for using causal relationships, this is entirely due to the dynamic aspect. The past decade or so of research in reasoning about actions has revealed that state constraints, being static in nature, may however also give rise to indirect effects of actions (or events)-- yet it is usually challenging to determine exactly to which effects. In fact, state constraints often lack information needed to tell `real' indirect effects from `phantom' effects, which would never occur in reality. Causal relationships do provide this necessary additional information. (See the first three sections of [j-aij-89-317] for a detailed introduction to this problem and for the motivation behind causal relationships.)

As for the problem of determining suitable test actions, this is indeed a side issue in the present paper. I merely want to show that the theory does in principle support the search for such actions. A detailed account would mean to develop a sophisticated search strategy and to make precise how the relative usefulness of possible actions is to be judged. This would clearly go beyond the scope of the present paper, but is definitely of interest and could very well be the topic of a follow-up paper.

Finally, to the relation to Sheila's approach. First of all, there is a difference from a very general point of view. Her approach starts with a particular axiomatization strategy, namely, the Situation Calculus. My intention was to focus on a high-level theory of dynamic diagnosis, prior to considering the problem of a suitable first-order axiomatization. The latter I have briefly tackled in the section on a (provably correct) Fluent Calculus-based axiomatization. At least for a large part of the high-level theory, Sheila's axiomatization may very well prove correct, too. Some more specific remarks as to differences in the expressiveness have been made in the discussion part of the paper. In addition to this it is worth mentioning that much work has been done on the pros and cons of Situation Calculus in general compared to alternative axiomatization strategies (among which are the Event- and the aforementioned Fluent Calculi; see, e.g., [mb-Shanahan-97] or [j-aij-89-317]).


j-aij-89-317Michael Thielscher.
Ramification and causality.
Artificial Intelligence, vol. 89 (1997), pp. 317-364.
mb-Shanahan-97Murray Shanahan.
Solving the Frame Problem: A Mathematical Investigation of the Common Sense Law of Inertia.
MIT Press, 1997.

Q4. Anonymous Reviewer 2 (3.5):

I would like if the theory were adjusted to cover this small "defect": According to the definition of "action law" (page 11) the set  C  and  E  of fluent literals must be consistent for any sequence of entities in the scope of the action. This simplifies the presentation of the theory. However, it does not cover simple action laws like when  Move(xft transforms  {Loc(xf)}  into  {Loc(xt), ¬ Loc(xf)} , in which the set  E  of effects is not consistent when you consider  t = f .

A4. Michael Thielscher (7.5):

The following straightforward generalization of Definition 2 could handle your example without affecting any other part of the theory. Rather than stipulating that action laws themselves satisfy the consistency criterion, the latter shall be a requirement of applicable instances of these laws. In this way the statement

  Move(x,f,t) transforms 
    {Loc(x,f),-Loc(x,t)} into {Loc(x,t),-Loc(x,f)}
would satisfy the definition of an action law, and actions of the form  Move(xff wouldn't admit a successor state, hence wouldn't be applicable. In the paper I kept the definition of action laws as simple as I possibly could in order not to complicate matters at a point which is not an issue of the paper (namely, the specification of direct effects of actions). Since the original definition does not constitute a technical error, I hope this comment is sufficient an answer.


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