|Moderated by Erik Sandewall.|
Causality in Action Theories
mentioned above has been submitted to the Electronic
Transactions on Artificial Intelligence, and the present page
contains the review discussion. Click here for
explanations and for the webpage of theauthor, Camilla Schwind.
Overview of interactions
Given that an online open review is written not just for the author and editors, but also for other readers, some of whom may not even have a chance to read the paper yet, it seems to me a good idea to summarize the paper first.
This paper considers statements of the form "A causes B", and proposes
the following nine criteria to characterize them (in the following,
I shall use
1. Monotonicity: this concerns the question of whether
2. Transitivity: from
3. Contraposition: from
4. Reflexivity: Should
5. Conjunction of preconditions: from
6. Conjunction: from
7. Reasoning by cases: from
8. Right weakening: from
9. Left logical equivalence: from
It then proceeds to consider five theories of causation found in the area of reasoning about actions and classify them using these nine criteria.
It seems to me that this is a reasonable approach to take for comparing various theories of causation, and the only paper that I know of that attempts to connect commonsense notion of causation with recent formal theories of causation proposed in the area of reasoning about actions.
I have no idea how fruitful it would be to connect causal theories of actions to commonsense notion of causation. My following comments and questions are only about issues that in my opinion are relevant to reasoning about actions.
1. First of all, why these nine conditions? In the paper, these
conditions are often compared to the corresponding ones for material
implication in classical logic. But there are many other properties of
implication. For instance, if
2. A related but more important question is how revealing these conditions are. For instance, the paper shows that some particular interpretations of McCain and Turner's causal logic (McCain & Turner AAAI'97) and Lin's causal action theory (Lin IJCAI'95) are monotonic and transitive, contrary to the proposed criteria 1 and 2 above. Now how bad this is for the two logics in question? Does it tell us anything about the range of applications of these two logics?
3. These nine conditions are about statements of the form "A causes B".
But it seems to me that many theories of causation in the area of
reasoning about actions are not directly about this kind of statements.
For instance, Geffner (AAAI'91), Giordano et al (ECAI'98) and
Turner (AIJ 1999)
all use a modal operator, and Lin (IJCAI'95) uses a predicate
that has only
one argument for fluents. It makes a lot of difference whether to
represent 'A causes B' as, for example,
The author's answer to this question is available in postscript.
Q2. Hector Geffner (7.9):
Erik has asked me to comment on Camilla Schwind's paper "Causality in Action Theories". Here are few comments that I hope Camilla and others may find useful.
The paper is an assessment of four theories of action that handle causal relations, in terms of a set of nine inference rules; namely, monotonicity, transitivity, contraposition, reflexivity, etc. The paper discusses (briefly) which rules should be valid and why, and then analyzes which inference rules are valid in each proposal.
This type of analysis has been common in the study of the logics of conditionals in philosophy (e.g, Lewis, Stalnaker, Adams, Nute, Pollock, ..) and more recently in the study of non-monotonic consequence relations and belief revision in AI (e.g., Gabbay, Makinson, Kraus et al; Gardenfors, Katsuno and Mendelson, ..).
I think this is a principled and meaningul approach to assess entailment relations, in particular in an area where a lot of the discussion is often based on individual examples.
Yet when applying this type of analysis to causal reasoning, it's natural to ask questions like:
I'm not less sure about this, as the paper does not make a convincing argument about the choice of the rules. Indeed, to me, it looks that very few of the rules have to do with "causality", and most have to do with "plausible (non-monotonic) reasoning" in general. Indeed, monotonicity, transitivity, conjunction, cases, right weakening, and left logical equivalence, have been discussed before in the general non-mon setting. The arguments supporting the validity or invalidity of each of these rules in the general setting applies in the specific setting of non-monotonic causal reasoning. So they have little to do with "causal" reasoning in particular. The same could be said about the other three rules left.
I think for this analysis to be more insightful, the principles have to appeal to the distinction between causal and non-causal relations.
For example, something that could be called "Pearl's principle" (see his papers) says something like this:
The interesting point is that the same principle is NOT supposed to hold when "A causes B" is replaced by "A implies B". So, if reasonable, the principle says something that is true for "A causes B" that is NOT true for "A (logically or defeasibly) implies B".
Other "causality" principles could be formulated in a similar way (again, I'd suggest to look at Pearl's work).
I think that one could get further by analyzing and building on principles such as these -- that are based on the distinction between causal and non-causal relations -- than on more general principles of plausible reasoning. I've attempted something like this in an IJCAI-97 paper but with limited success.
Answer to Hector Geffner, who raised the following questions:
First, let me point out that my main purpose has been to compare existing approaches and not to define postulates. I prefer the term "comparison criteria". This is what I formulated and NOT postulates.
ad 1. The criteria have been formulated with respect to the comparison task of several action theories which integrated causality; in this respect they are relevant as I think.
ad 2. It happened to me to use other criteria, which are not in the list and which are more related to causality and update. Since NO one of the formalisms I reported could be compared along those criteria, I found it moderately interesting to include them.
I think indeed that causality is a nonmonotonic inference relation (see my criterion 1). But there are properties of nonmonotonic inference which I reject for causlity (e.g. reflexivity).
Q3. Judea Pearl (21.9):
I have some comments on recent ENRAC discussions of Camilla's paper, "Causality in Action Theories".
Axioms are good for detecting and summarizing differences among theories, but not so good as means of evaluating adequacy of theories. Camilla's list of axioms illustrates this observation relative to theories of causation. Even some of the most innocently-looking axioms on her list are not free from objections.
Take for example Right Weakening, with
The same goes for transitivity. If we ask a person on the street if causality is transitive, the answer would be: Of course. If we ask any causal analyst, the answer would be: Of course not. (e.g., my whistle causes Joe to shoot. When Joe shoots he kills birds. However, my whistle frightened the birds away).
So what assumptions must a person on the street be making, when asked to judge if an axion is plausible or not?
Here is a suggestion (for transitivity). Our person-on-the-street interprets transitivity to mean: If
The suggestion is that questions about transitivity bring to mind
chain-like processes, where
Conclusion: testing axioms against intuition is a dangerous enterprise; formal semantics is safer.
PS. Structural semantics of cause and counterfactuals is proposed
in my IJCAI-99 paper; posted on
Thank you for your remarks on my paper.
I am not sure that in my paper I have been sufficiently clear. I do not think that I discussed axioms, but something weaker: postulates, or just criteria, i.e. properties of a causal relation. I find this approach useful for studying different theories for causality and actions and I beliefe that it is useful to question whether a theory for causal reasoning has these properties or not. As I have shown in my paper, and partly in my answer to Fangzhen Lin, this study allows to exhibit general properties for actions and causality and to show the advantages and limits of several approaches.
In more detail:
I do not agree with your counter-example concerning right weakening.
I have not advanced a special opinion on transitivity. As I pointed out, I think there are arguments for having transitivity as well as for not having transitivity. I think your example is interesting, because it illustrates, that the presence of transitivity may relate in some way to two different readings of causality:
C3-1. Judea Pearl (28.9):
Perhaps, we can better study the problem with Right-Weakening if we replace C by any tautology, say C = "2+1 = 3". C is true in all worlds, hence it logically follows from B = smoke, which is caused by A=fire. We do not wish to conclude that fire causes the equality 2+1 = 3.
"2+1 = 3" is not a tautology neither. "+" is a function and its semantics in natural number arithmetic is such that it is true in this particular world! We can of course find a world and a meaning for "+" (and for the 0-ary finction symbols "2", "3" and "1") such that "2+1 = 3" is not true.
But take the tautology "C = it rains or it does not rain". C follows from B = smoke which is caused by A = fire. Hence we conclude that fire causes the tautology "it rains or it does not rain". For me this is ok.
More generally, every sentence can cause every tautology!
C3-3. Judea Pearl (28.9):
Glad this discussion has led to such crisp summary of the difference between the postulate-based and the semantical approaches to causation.
To students of the latter, only propositions that can be false (in at least some imaginable worlds) can be caused by other things (events or actions).
(For my postulates, it would be sufficient to skip or to weaken RW).
But I want to point out that therre is an enormous misunderstanding. The focus of my paper is not to present postulates for causation, neither to present a particular approach to causation. I have used criteria in order to compare and to study different approaches to action and causation!
C3-5. Judea Pearl (28.9):
I believe Hector Geffner expressed the same kind of concerns.
The referees make a recommendation whether the article is to be
accepted or declined, as usual. The article and the discussion
remain on-line regardless of whether the article was accepted or
not. Additional questions and discussion after the acceptance decision
The Review Protocol Page is used as a working structure for the entire
reviewing process. During the first (review) phase it accumulates the
successive debate contributions. If the referees make specific
comments about the article in the refereeing phase, then those comments
are posted on the RPP as well, but without indicating the identity
of the referee. (In many cases the referees may return simply an
" accept" or " decline" recommendation, namely if sufficient feedback
has been obtained already in the review phase).
The referees make a recommendation whether the article is to be accepted or declined, as usual. The article and the discussion remain on-line regardless of whether the article was accepted or not. Additional questions and discussion after the acceptance decision are welcomed.
The Review Protocol Page is used as a working structure for the entire reviewing process. During the first (review) phase it accumulates the successive debate contributions. If the referees make specific comments about the article in the refereeing phase, then those comments are posted on the RPP as well, but without indicating the identity of the referee. (In many cases the referees may return simply an " accept" or " decline" recommendation, namely if sufficient feedback has been obtained already in the review phase).