The article mentioned above has been submitted to the Electronic
Transactions on Artificial Intelligence, and the present page
contains the review discussion. Click for
more
explanations and for the webpage of theauthor, Erik Sandewall.
Overview of interactions
Q1. Rob Miller (13.4):
Dear Erik,
I'm confused about axioms S4, S5 and S8 involving the action
test(p) on page 7 of your paper:
S4 seems to state that it is always possible to perform a test to
see if a given property is true. But I would have thought that
the opposite is nearly always the case - that in most commonsense
or robot environments we could almost assume by default that the
agent is not in a position to directly test the truth of a given
property of the environment. (This is certainly true for me as I
type this question at home. I can't check the condition of
anything in my office, in the other rooms in my house, etc. without
first performing some other actions.) So what is the rationale
behind axiom S4? Is the agent perhaps "testing" it's own knowledge,
rather than the real environment?
S5 states that test actions are always instantaneous. Why should
this be so, at least in a framework where other actions are not
instantaneous?
S8 says that, once executed, a test action fails if and only if
the corresponding property is false. But this seems to go against
the commonsense notion of "testing". For example, when I test to
see if I have any new emails (actually by clicking on the "?"
button on Netscape) I count this action as successful if the system
reports "no new messages on server". I count the action as failed
if (as frequently happens with my faulty modem here at home),
clicking on "?" crashes my computer. I'm then left with no
information as to whether I have new emails or not. So is this
not a test action in the sense that you intended?
Regards,
Rob
A1. Erik Sandewall (13.4):
Dear Rob,
The "action" test(p) is classified as an action in the formal sense
that it can be combined with other actions using, for example, the
sequential operator. In those cases that you describe, where the
actual performance of the test takes a nontrivial amount of time
compared to other events, I imagine that one would use test(p) merely
for the internal decision within the robot and using knowledge that
it has already acquired. The corresponding, external action of finding
out what is the case and then succeeding or failing would then be
represented with something along the lines of findout(p) ; test(p) ,
where findout(p) is non-instantaneous.
Will test(p) always be immediately preceded by findout(p) in practice?
I think of at least two kinds of situations where this will not be the
case. When some fluent is being monitored continuously by a lower
software level, then the current value of p can safely be assumed
to always be available. Also, in those cases where the agent has to
plan ahead and make sure in advance that it acquires important
information, so that it is there without delay when needed, then
again test(p) will not
be directly preceded by and tied to findout(p) .
The axioms assume that the argument of test(p) is either true or
false. The case where incomplete knowledge is allowed may be handled
by any of the well-known methods, for example by having a pair of two
propositional fluents p and p' , and where lack of information is
represented by making both of them false.
The mnemonic "test" was inspired by an opcode in an assembly language
that I learned a long time ago.
Regards,
Erik
Q2. Anonymous referee 1:
Generally, the paper has the flavor of a progress report rather than
a well-knit article. My understanding is that this perfectly complies
with the publication policy of ETAI. However, sometimes such a
status of a paper is indicated by adding the qualification "preliminary
report" to the title, which the author might consider in the present case
as well. The author himself admits that there is still a lot of work to
be done. In particular, a number of rather complex axioms are proposed,
of which it is claimed that they characterize "obvious properties" (p.5)
of relation symbols which have been introduced with a certain meaning in
mind. Past experience taught us that it can be dangerous to propose
axiomatizations which seem most natural at first glance. I therefore strongly
support the author's remark on the need for an "underlying semantics, and
a validation of the present approach with respect to that semantics..."
(p.16). An essential, most basic property of any useful axiomatization is
consistency. Maybe the author could add a result in that direction.
p.7: The purpose of Section 2.6 is not clear. Composite fluents aren't
used elsewhere in the paper, and so one wonders, for instance, why
logically equivalent composite fluents cannot be treated as equal.
p.8: The operators G and D_s have been introduced as abbreviations for
formulas, e.g., G(s, a) <-> H(s, inv(a)) . Why is it, then, that they
cannot
serve as part of axioms, provided the axiomatization includes the
respective definitional formulas?
p.8: The predicate Composite is introduced but (as far as I could see) not
used elsewhere in the paper.
A2. Erik Sandewall (17.7):
| | Generally, the paper has the flavor of a progress report rather than
a well-knit article. My understanding is that this perfectly complies
with the publication policy of ETAI. However, sometimes such a
status of a paper is indicated by adding the qualification "preliminary
report" to the title, which the author might consider in the present case
as well.
|
My understanding is that the subtitle "preliminary report" is used
in conference publications in order to distinguish an article from a
later, revised version of the same article that is to be published
elsewhere. The present version of the article is intended to be the
final one, except for the corrections that follow from the review comments.
| | The author himself admits that there is still a lot of work to
be done. In particular, a number of rather complex axioms are proposed,
of which it is claimed that they characterize "obvious properties" (p.5)
of relation symbols which have been introduced with a certain meaning in
mind. Past experience taught us that it can be dangerous to propose
axiomatizations which seem most natural at first glance. I therefore strongly
support the author's remark on the need for an "underlying semantics, and
a validation of the present approach with respect to that semantics..."
(p.16).
|
See the first item in the answer to Anonymous Referee 3.
| | An essential, most basic property of any useful axiomatization is
consistency. Maybe the author could add a result in that direction.
|
I guess this will be a natural corollary of validation results relative
to an underlying semantics.
| | p.7: The purpose of Section 2.6 is not clear. Composite fluents aren't
used elsewhere in the paper, and so one wonders, for instance, why
logically equivalent composite fluents cannot be treated as equal.
|
Composite fluents are used in the examples in section 2.5 (although it's
possible that order between those two sections ought to be reversed).
Treating logically equivalent composite fluents as equal does not have
any obvious advantage, and it will complicate things considerably for
the occlusion predicate.
| | p.8: The operators G and Ds
have been introduced as abbreviations for
formulas, e.g., G(s, a) <-> H(s, inv(a)) . Why is it, then, that they
cannot serve as part of axioms, provided the axiomatization includes
the respective definitional formulas?
|
This is for reasons of convenience rather than logical necessity. The
tentative specifications in question are easy to follow when they are
written in terms of the abbreviations, but not when the abbreviations
are expanded. Furthermore, verifying the important properties of the
specifications becomes quite messy. All of this becomes clearer if
the specifications are written without the use of the abbreviations.
| | p.8: The predicate Composite is introduced but (as far as I could see) not
used elsewhere in the paper.
|
It is used in axiom S2 on page 5, where it indicates one of the cases
where an action does not start executing from the time it is invoked.
The reason for making this exception is that an action of the form
a;b can not be allowed to start executing at a time when the action a
is already executing. Therefore, it is not sufficient to say that an
invoked action starts executing unless the same action is already
in the midst of execution.
Q3. Anonymous referee 2:
Overall
This is a well-motivated and timely contribution to the field, and,
perhaps with some presentational improvements, should be accepted for
publication in ETAI. The paper's main original contribution is an
axiom-based account of control, focussing on the issue of action
failure, retry and replanning. It also addresses the issue of how these
axioms can be integrated with logical theories of action.
There follow a number of general questions I would like to raise, some
presentational suggestions, and a list of typos.
General questions
Although I'm attracted to the author's work, I am tempted to ask why we
should want an axiomatic account of goal-directed behaviour. For
example, Axioms G1 to G4 really constitute an algorithm, and perhaps
make better sense presented as an algorithm. From my point-of-view, the
role of logic in cognitive robotics is to represent the world, not to
represent the internal workings of the agent. Perhaps the author would
like to address this question, in an electronic discussion and/or in the
final version of the paper.
In Section 2.5, the third formula on page 7 entails that the
postcondition of an action is false until the action is finished. But
consider the example of a compound action WashDishes , which has the
effect of making CutleryClean true and CrockeryClean true. Now, it's
bound to be the case, assuming one item is washed at a time, that either
CutleryClean becomes true before CrockeryClean or the other way around.
Either way, one of the action's postconditions becomes true before the
whole action is finished.
It's not clear to me what it means for the robot to "state" a formula on
page 9. Does this mean it passes that formula to a control module?
Presentational suggestions
I have one serious presentational objection to the paper. I think it
would be very much improved if there were some concrete examples showing
what inferences can be drawn from the axioms. (By a concrete example, I
mean one with meaningful fluent names.) Even a single concrete example
illustrating some of the main ideas would be of enormous benefit to the
reader's intuition. Otherwise, a hostile reader might think this is all
just empty formalism.
Here are some more minor presentational suggestions. At the start of
Section 2.6, the author introduces logical connectives for composing
fluents. But these have already been used in Section 2.5. Perhaps this
material could be reshuffled. Similarly, on page 10, the author declares
how the variable symbols a and g will be used, although they have
already appeared many times in the paper.
A3. Erik Sandewall (17.7):
| | Although I'm attracted to the author's work, I am tempted to ask why we
should want an axiomatic account of goal-directed behaviour. For
example, Axioms G1 to G4 really constitute an algorithm, and perhaps
make better sense presented as an algorithm. From my point-of-view, the
role of logic in cognitive robotics is to represent the world, not to
represent the internal workings of the agent. Perhaps the author would
like to address this question, in an electronic discussion and/or in the
final version of the paper.
|
My argument goes in two steps:
- Rational agent behavior in a robot needs a precise specification,
using logic
- Such a specification can gain considerably by being integrated with
a logic of actions and change.
First, rational agent behavior is fairly complex in the case of a robot
that interacts with the real world. It requires pursuing goals, choosing
plans, making appropriate reactions to new information, dealing with
uncertainty and temporal constraints, and so on. Even though in the end
this behavior is going to be realized by software, it is clear that a
high-level specification of that software will be necessary for the
actual software engineering as well as for making it possible to validate
that software and to prove its properties.
Furthermore, if this software is described in a purely algorithmic style,
it is difficult to avoid introducing a lot of administrative machinery.
This is exemplified by the article "A Formal Specification of dMARS"
by Mark d'Inverno et al. (Proceedings of the ATAL-97 workshop, pages
155-176), where a variant of PRS is specified in the Z notation (which is
a software specification language). In my approach, the agent's rational
behavior is specified in terms of restrictions: for each scenario, the
set of models for the formalization is intended to equal the set of
rational behaviors, each interpretation being one possible history in
the world. Such a constraint-oriented approach has chances of being
much more concise and to the point.
Finally, once we decide that it is appropriate to specify rational robotic
behavior in logic, we also have to deal with actions. The robotic
behavior consists of actions, so this already defines a connection point.
Also, when several agents are involved, the actions of one need to be
observed and understood by the others. In the longer perspective, I think
we will see a lot more integration between theories for reasoning about
actions and for characterizing agent behavior.
| | In Section 2.5, the third formula on page 7 entails that the
postcondition of an action is false until the action is finished. But
consider the example of a compound action WashDishes , which has the
effect of making CutleryClean true and CrockeryClean true. Now, it's
bound to be the case, assuming one item is washed at a time, that either
CutleryClean becomes true before CrockeryClean or the other way around.
Either way, one of the action's postconditions becomes true before the
whole action is finished.
|
The text preceding the formula was:
| | As another simple example, consider the case of actions which are
described in terms of a precondition, a prevail condition, and a
postcondition, where the postcondition is at the same time the
termination condition for the action...
|
The formula in question therefore refers to a limited class of actions,
rather than to my approach as a whole. (Besides, in the case you mention,
the postcondition of the compound action ought to be the conjunction
of the two conditions, that is, CutleryClean ^ CrockeryClean .
Each action is assumed to have a postcondition, in the singular, in
the example).
| | It's not clear to me what it means for the robot to "state" a formula on
page 9. Does this mean it passes that formula to a control module?
|
Yes. This deductive process, which one may think of as a control module,
is modelled as receiving formulae from two sources: both from a higher
software layer of the robot itself ("decisions") and from the
surrounding world via the sensors ("observations"). Both kinds of
"signals" may influence actions of the agent. This is discussed
in section 3.5, the last paragraph on page 12.
| | I have one serious presentational objection to the paper. I think it
would be very much improved if there were some concrete examples showing
what inferences can be drawn from the axioms. (By a concrete example, I
mean one with meaningful fluent names.) Even a single concrete example
illustrating some of the main ideas would be of enormous benefit to the
reader's intuition. Otherwise, a hostile reader might think this is all
just empty formalism.
|
Such an example is forthcoming.
| | Here are some more minor presentational suggestions. At the start of
Section 2.6, the author introduces logical connectives for composing
fluents. But these have already been used in Section 2.5. Perhaps this
material could be reshuffled. Similarly, on page 10, the author declares
how the variable symbols a and g will be used, although they have
already appeared many times in the paper.
|
This is easily arranged (although there were in fact good reasons for
the order in which this material is presently presented).
Q4. Anonymous referee 3:
The paper relates the concept of a "deliberated retry" to the author's
earlier work on the logic of actions and change. It is intended for
use in an applied project related to controlling an intelligent
airborne vehicle. The problems discussed in the paper are important,
and its ideas are interesting and original.
On the negative side, the paper does not really prove that its formalism
is good for any specific purpose. It does not even make any mathematically
precise claim of this kind. It would be good to include a description of
goal-directed behavior in a toy domain and prove that some intuitively
expected conclusions abour goal-directedness do indeed follow from the
given axioms using the entailment methods proposed by the author. This
would be more convincing than the "hand-waving" arguments in favor of
the proposed approach given in Sec. 4. In the absence of such an
example, the paper is reminiscent of the work on actions done in the early
days of AI, such as the "frame default" in Reiter's 1980 paper on default
logic, or the formalization of the blocks world in McCarthy's 1986 paper
on circumscription. The ideas were interesting, but their authors were
unable to prove anything about them. As the familiar shooting scenario
demonstrated, a nonmonotonic formalization that looks plausible may turn
out to be unsatisfactory after all. If the author of this paper tries to
check that his theory works for one or two toy examples, he may very well
discover bugs that need to be fixed.
It seems to me that Rob Miller was right when he suggested in his message
to the author that test(p) is the action of testing the agent's knowledge
rather the real environment, and that otherwise the axioms for testing
are not convincing. The notation proposed in the paper uses the same
symbol p to represent the fluent itself and the agent's knowledge about
it, which looks peculiar. Regarding the author's suggestion that the
incompleteness of knowledge be represented by distinguishing between p
and p' "where the lack of information is represented by making both of
them false". I have this question: How would you represent the assertion
that p is true but this fact is not known to the agent?
Re Theorem 1: There seems to be an implicit assumption here that the
set of intervals in question is finite. Shouldn't it be included in
the statement of the theorem?
Re Theorem 2: I am puzzled by the use of the word "conversely" here. It
seems to me that both parts say more or less the same thing.
In the 3rd displayed formula on p. 7, conjunction is applied to fluents,
which is only explained in the next section, and an interval is used as
the first argument of H which, as far as I can see, is not defined at all.
My recommendation is that the paper be accepted for publication in the
ETAI after the author makes the changes that he deems appropriate.
A4. Erik Sandewall (17.7):
| | On the negative side, the paper does not really prove that its formalism
is good for any specific purpose. It does not even make any mathematically
precise claim of this kind. It would be good to include a description of
goal-directed behavior in a toy domain and prove that some intuitively
expected conclusions abour goal-directedness do indeed follow from the
given axioms using the entailment methods proposed by the author. This
would be more convincing than the "hand-waving" arguments in favor of
the proposed approach given in Sec. 4.
|
A proof that correct conclusions are obtained for one or two toy domains
does not prove that the formalism is good for any interesting purpose
either. As indicated in subsection 5.1 ("Limitations of these results"),
it remains to validate the proposed approach using a plausible underlying
semantics. This is in line with the methodology for research in this area
that I have defended at a number of occasions, beginning in my IJCAI-93
paper. Only so can one identify the range of applicability of the approach
in a reliable way.
You might say that the paper ought not to be published until such a
validation exists and can be included. This would be an excellent position
to take, provided that it were shared by the present community. However,
even a quick look at the literature in our field will show that that's
not the way things work: Citations to earlier work refer almost exclusively
to the approaches proposed by the earlier author, and quite rarely
to the theorems that were proved in the earlier paper.
Besides the formal validation, it's the applications that will prove what
the formalism is good for, but this would also take too long in the
present paper.
| | In the absence of such an
example, the paper is reminiscent of the work on actions done in the early
days of AI, such as the "frame default" in Reiter's 1980 paper on default
logic, or the formalization of the blocks world in McCarthy's 1986 paper
on circumscription. The ideas were interesting, but their authors were
unable to prove anything about them. As the familiar shooting scenario
demonstrated, a nonmonotonic formalization that looks plausible may turn
out to be unsatisfactory after all. If the author of this paper tries to
check that his theory works for one or two toy examples, he may very well
discover bugs that need to be fixed.
|
I have of course done a few toy examples for my own sake; the details are
too long and boring to merit going into the paper. With respect to the
historical comparison: the bugs in those cases were in the entailment
method rather than the axiomatization. The approach described here is
not dependent on the exact formulation of the axioms, and would not
collapse if some of the axioms were to require debugging. Compare
subsection 5.1.
Another comparison with the work on the frame problem in the 1980's is
more appropriate: those were the days of first exploration of the problem
(besides for a small number of articles in the 1970's), and it is
quite natural and respectable that one started by looking for approaches
that were at least intuitively plausible. After that start it was
natural to look for precise and proven properties of those approaches.
Ramification and causality have followed suit, and qualification is in its
early stages. The characterization of rational robotic behavior is just
in its very first stage of development, that is all.
| | It seems to me that Rob Miller was right when he suggested in his message
to the author that test(p) is the action of testing the agent's knowledge
rather the real environment, and that otherwise the axioms for testing
are not convincing. The notation proposed in the paper uses the same
symbol p to represent the fluent itself and the agent's knowledge about
it, which looks peculiar.
|
Well, it wasn't Rob who suggested it; you refer to my answer to his question.
Anyway, the full characterization of a rational agent is bound to be fairly
extensive, and the distinction between the actual and the believed value
of a fluent is one of the aspects of the full problem. I believe it is best
to address this complex problem by divide-and-conquer, so several other
papers including references [11] and [12] "complement the work
reported here", as stated in the second paragraph of section 1.2.
Those articles use distinct predicates for actual and estimated feature
values, so the problem you mention has indeed been addressed in the context
of the present approach and we have shown how to deal with it.
The present paper works with the simplifying assumption that the agent
has perfect knowledge of the fluents. This is in particular in the interest
of the reader, since it makes for heavy reading to address all problems
at once.
| | Regarding the author's suggestion that the
incompleteness of knowledge be represented by distinguishing between p
and p' "where the lack of information is represented by making both of
them false". I have this question: How would you represent the assertion
that p is true but this fact is not known to the agent?
|
By making both p and p' false; this is a standard technique. However,
I don't recognize having mentioned it in this paper?
| | Re Theorem 1: There seems to be an implicit assumption here that the
set of intervals in question is finite. Shouldn't it be included in
the statement of the theorem?
|
No, the proof does not require that assumption.
| | Re Theorem 2: I am puzzled by the use of the word "conversely" here. It
seems to me that both parts say more or less the same thing.
|
The theorem has the form "In all the models for the axioms, P. Conversely, Q".
It is correct that Q follows from P even without the use of those axioms,
and the second part of the theorem is merely for showing the
conclusion from another point of view. Maybe it would be better to
write it as a separate comment.
| | In the 3rd displayed formula on p. 7, conjunction is applied to fluents,
which is only explained in the next section, and an interval is used as
the first argument of H which, as far as I can see, is not defined at all.
|
These bugs will be corrected.
C4-1. Anonymous referee 3 (19.8):
Thank you for your reply to my comments. One point is still not clear
to me. You claim that, in Theorem 1, there is no need to assume that the
set of intervals is finite. The following seems to be a counterexample:
| |
si = 1/(2*i+1), ti = 1/(2*i)
| |
where i=1,2,... Please explain.
C4-2. Erik Sandewall (19.8):
Theorem 1 states that under the axioms and for some ordering of the
intervals, si < si+1 and ti < si+1 for all i .
In your example, there is an infinite sequence of intervals that has
a Zeno property and proceeds to the limit from above. This infinite
sequence of intervals therefore has to be renumbered so that
| |
s-i = 1/(2*i+1), t-i = 1/(2*i)
| |
In other words, the numbering is reversed and you have to consider
i = -1, -2, ... With this ordering the consequent of the
theorem holds.
Your example also shows that if there is an infinite sequence of
intervals, the theorem does not hold in the limit as i tends to
infinity. However, this is also not claimed.
Your example does however remind me that if one is going to be very
technical, it might be better to phrase the theorem so that it states
that if interval i precedes interval j under the ordering, then
si < sj and ti < sj . In this way one
does not give the impression that a numbering of the intervals always
exists using natural numbers. Such a numbering does exist in your
example, but if one combines several Zeno sequences then it doesn't.
Of course all of this is very remote from the situations that arise
in the context we're addressing.
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