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, Murray Shanahan.
Overview of interactions
Q1. Paulo Eduoardo Santos (1.8):
1- In section 1, when defining the assimilation of sensor data, it is
proposed a background theory SigmaB comprising axioms for change,
actions, space and shape. However along the paper I did not see any other
mention of such a theory, my question is whether SigmaB is
represented by the last formula of section 4?
2- If so, why include in the theory SigmaE (section 5) again the
axioms for actions and change, space and shape already included in
SigmaB , since it is considered the conjunction of SigmaB and
SigmaE for the abduction process?
3- All along the paper, Circumscription is done in parts of theories
(rather than in the whole theory). I understand it is done 'by
construction' since the chosen version of Event Calculus considered, is
the one defined using forced separation (as presented in Shanahan's book
"Solving the Frame Problem" [b-Shanahan-97]. My question is why do we
have to circumscribe parts of the theories in the way presented, and not
in any other way? Is there any formal justification for using forced
separation ?
4- At the beginning of section 9 we read:
| |
An alternative approach is to tailor make algorithms for specific
tasks, such as sensor data assimilation, whose correctness with respect
to the logical account can be demonstrated. This is the methodology I
will adopt here, and the logic programming approach is left for further
research.
|
In another paper by Shanahan "What Sort of Computation Mediates Best
between Perception and Action" [Shanahan-96] we read:
| |
It is important to note that the logicist prescription does not
demand a one to one correspondence between the data structures in the
machine and the sentences of the chosen formal language. (...). In other
words, the machine does not have to implement a theorem prover directly.
Between the abstract description of a logic-based AI program and the
actual implementation can come many steps of transformation,
compilation, and optimisation.
|
I have two questions about these statements: first, by assuming a logic
programming approach, aren't we contradicting the last statement above?
and, if it is not to have a theorem prover implementing the
logic-based description of the system, what is exactly the role of logic
in this framework?
My last question is about computational complexity:
In the framework presented in the paper under discussion two important
points are 'explanation by adbuction' and 'circumscribing theories'. As
presented in [c-stacs-93-Eiter] the complexity of logic-based abduction is
NP-hard (for the problem of finding an abductive explanation with the
additional constraint that it has to contain a predefined letter p); the
results about complexity of Circumscription are not much more impressive
(as can be seen in [j-jlp-17-127].
My question is, taking into account these complexity results, can we
still apply this framework in robotics ?
Yours,
Paulo Eduardo Santos
Unpublished reference
[Shanahan-96] Murray Shanahan,
What Sort of Computation Mediates Between Perception and Action?,
Working notes of the AAAI Fall Symposium on Embodied Cognition,
1996.
References:
| c-stacs-93-au/Eiter | T. Eiter and G. Gottlob.
The Complexity of Logic Based Abduction.
Proc. Symposium of Theoretical Aspects of Computer Science, 1993, pp. .
|
| j-jlp-17-127 | Marco Cadoli and Marco Schaerf.
A Survey of Complexity Results for Non-monotonic Logics.
Journal of Logic Programming, vol. 17 (1993), pp. 127-160. |
A1. Murray Shanahan (25.8):
Many thanks for the questions.
| | 1- In section 1, when defining the assimilation of sensor data, it is
proposed a background theory SigmaB
comprising axioms for change,
actions, space and shape. However along the paper I did not see anyother
mention of such a theory, my question is whether is SigmaB
represented by the last formula of section 4?
|
The description in Section 1 is supposed to give just an impression of
the way the abduction works. It's just a caricature of the real
formalisation, intended to help the reader. The actual formalisation we
see later is very complex, and I thought it would be hard to understand
without a gentle introduction. The axioms for change, actions, space and
shape in SigmaB
are actually the event calculus axioms CEC plus the
spatial axioms (Sp1) to (Sp8).
| | 2- If so, why include in the theory SigmaE
(section 5) again the
axioms for actions and change, space and shape already included in
SigmaB , since it is considered the conjunction of
SigmaB and
SigmaE for the abduction process?
|
I guess this question is irrelevant in the light of the last answer.
| | 3- All along the paper, Circumscription is done in parts of theories
(rather than in the whole theory). I understand it is done 'by
construction' since the chosen version of Event Calculus considered, is
the one defined using forced separation (as presented in Shanahan's book
"Solving the Frame Problem" cite{Shan:97}). My question is why do we
have to circumscribe parts of the theories in the way presented, and not
in any other way? Is there any formal justification for using forced
separation ?
|
By splitting the circumscription into parts, we get a more managable
theory, one whose consequences are easier to work out. In fact, the role
of circumscription here is mainly to complete certain predicates,
specifically Initiates, Terminates and Happens. If we circumscribe
everything together, we have to do a lot more work to avoid difficulties
like the Hanks-McDermott problem.
The technique is similar to what Erik Sandewall calls filtered
preferential entailment. I think I've seen Erik provide a carefully
argued justification of this technique in one of his papers. Perhaps he
will remind us where to find it.
| | 4- At the beginning of section 9 we read:
|
| |
An alternative approach is to tailor made algorithms for specific
tasks, such as sensor data assimilation, whose correctness with respect
to the logical account can be demonstrated. This is the methodology I
will adopt here, and the logic programming approach is left for further
research.
|
| | In another paper by Shanahan ("What Sort of Computation Mediates Best
between Perception and Action" cite{Shan:96} we read:
|
| |
It is important to note that the logiscist prescription does not
demand a one to one correspondence between the data structures in the
machine and the sentences of the chosen formal language. (...). In other
words, the machine does not have to implement a theorem prover directly.
Between the abstract description of a logic-based AI program and the
actual implementation can come many steps of transformation,
compilation, and optimisation.
|
| | I have two questions about these statements: first, by assuming a logic
programming approach, aren't we contradicting the last statement above?
and, if it is not to have a theorem prover implementing the
logic-based description of the system, what is exactly the role of logic
in this framework?
|
I don't think there's a contradiction here. As both these quotes
emphasise, the role of logic in the implementation can be more or less
direct. The implementation described in the paper under discussion
doesn't use a theorem proving approach, so the role of the logic with
respect to that implementation is solely as a specification. (I regard
the logic, not the implementation, as the main contribution of the
paper, by the way.)
On the whole, as I argue in the other paper you quote from, I think it's
preferable to take a more theorem proving approach, in which case the
logic is more intimately related to the implementation. But this
approach is hard when we're dealing with difficult mathematical objects
like the plane, as in this paper. In my current work, however, I have a
simpler description of the robot's environment, and a logic programming
implementation of sensor data assimilation is more feasible.
| | In the framework presented in the paper under discussion two important
points are 'explanation by adbuction' and 'circumscribing theories'. As
presented in cite{EG:92} the complexity of logic-based abduction is
NP-hard (for the problem of finding an abductive explanation with the
additional constraint that it has to contain a predefined letter p); the
results about complexity of Circumscription are not much more impressive
(as can be seen in cite{CS:93}).
My question is, taking into account these complexity results, can we
still apply this framework in robotics ?
|
This is a difficult issue.
My feeling is that complexity results should be used only as a
guideline, and a disappointing complexity result rarely justifies the
wholesale rejection of an approach. This is because the complexity
results are worst-case, while in actual usage, a technique is often
confined to a narrow, tractable sub-class of problems that no-one has
pinned down yet.
In fact the use of circumscription to overcome the frame problem here is
a case in point. The form of the theories we're interested in guarantees
that the circumscriptions always reduce to predicate completions, which
can be handled efficiently by Prolog.
Moreover, in the context of robotics, I think there's another argument
that worst-case complexity results are misleading. No robot should be
allowed unlimited computation time for any reasoning task before that
task is suspended to sense the world and respond reactively to it. And
ultimately, the world always moves on and renders old, unfinished
reasoning tasks irrelevant. (I used to spend a lot of time thinking
about the mind-body problem in philosophy, no doubt a "computationally
intractable problem". Now I have children, and don't have time for such
luxuries.) A robot's designer needs to organise things so that most
reasoning tasks the robot sets out to perform can be completed in a
short time. And if, once in a while, the robot is unfortunate enough to
hit on one that would take the lifetime of the universe to solve, who
cares? It'll soon give up on it when it has to dodge a falling rock or
grab a passing robot of the opposite sex :-)
I hope this answers your questions, and thanks for taking the time to
read my paper.
Murray Shanahan
Q2. Chitta Baral (19.8):
Dear Murray:
It was nice (but a little exhaustive :-) ) reading your paper. I hope
the following feedback will be useful.
In this paper you have initially (Section 2-5) expressed using logic:
actions and their effects, occurrences of robots actions, initial value
of fluents, event calculus axioms, domain constraints, formulation of
continuous change using the release predicate, representation of space
and shape, and axioms about triggered events.
Given information on occupies (at the initial situation) the formulation can
predict occurrence of triggered events. You rightly argue that an abductive
method can make conclusions about occupies when told about (or when it
senses) triggered events. This is the basic essence of the first part of
the paper I like the detailed logical formulation.
Some of the questions and suggestions that I have about this part are
as follows:
(i) I think that in general a robot does not really sense events,
rather it notices changes in certain fluent values (in say resistors
linked to the sensors) from which it abduces the occurrences of triggered
events. Nevertheless, it is ok with me to skip this part and directly
talk about robots observing triggered events. But a clarification would
help.
(ii) Since you mention several times (abstract, Section 2, etc.)
that you use a novel solution to the frame problem using `Releases'
it will be nice if you say about it a little more than what is said in
Section 2 (just after EC 5). (You do use it in axioms in later sections,
but you don't discuss them.)
Although from the illustrations I can appreciate the use of `Releases'
in formulating continuous change, its utility in formulating constraints
is not clear to me. For example, why not eliminate B4 and instead of
`Releases' have `Terminates' in the head of rule E2.
To me the advantage of having constraints such as B4 is that by having
it we avoid explicit compilation of it to effect axioms. I.e. we can
use constraints for automatically deducing effects indirectly. But if
we have both B4 and E2 then we are not really avoiding the compilation,
as E2 is like an effect axiom.
(iii) I am not sure if `Bearing' is a standard geometrical notion.
Perhaps an intuitive meaning of it will help. Or may you can use the
more familiar notion of `slope'.
(iv) You say (just after Sp3): ``the term Line(p1, p2) denotes the
straight line whose ...''. Perhaps it is more appropriate to say ``straight
line segment'' instead of ``straight line''.
(v) I think in axiom (B3) you are assuming velocity to be one. If you do
please mention it.
(vi) The sentence after (B6). In it you explain Blocked(w1, w2, r) by
`if object w1 cannot move any distance at all in direction r without
overlapping with another object'. Perhaps you should say: ``if object w1
cannot move any distance at all because of w2 in direction r without
overlapping with another object'.
(vii) When defining HoldsAt(Touching(w1, w2, p), t) are you making some
assumptions about the shape of w1 and w2 . Imagine two triangles which
touch at a point, you can align them such that they touch but yet do not
satisfy the conditions you have in B6.
(viii) I am not clear about the intuition behind the notion of partial
completion in Section 5; especially in the text after (5.7).
For example in proposition 5.8, I would encode the intuition ``bump
switches are not tripped at any other time'' by
| |
Happens(Switch1, t) ·-> t = T {bump}
| |
and
| |
Happens(Switch2, t) ·-> t = T {bump}
| |
I am not clear about the intuition behind your formulation.
Also, why not use the standard Clark's completion and explain the
Clark's completion of Psi , where Psi is as mentioned in
Definition 5.9 and the paragraph before. I.e, have the Clark's
completion of Psi in the right hand side of the turnstyle in
Proposition 5.8
(ix) In section 6 you logically express a region as a list of straight
lines. (You say it just before Bo3.) Is there any particular reason you
use lists instead of sets. If not, since you already use set notation in
the rest of your formulation, by using sets here also, you might avoid
additional axioms such as Bo3 and Bo4
(x) Also (Bo3) is a fixpoint expression and you probably need
(as needed when defining transitive closure) to minimize `Members'
to get the right models.
(Recall that the logic program
| |
anc(X, Y) <- par(X, Y)
| |
| |
anc(X, Y) <- par(X, Z), anc(Z, Y)
| |
is not equivalent to the formula
| |
anc(X, Y) <-> par(X, Y) v (par(X, Z) ^ anc(Z, Y))
| |
You are not minimizing `Members' in Proposition 6.2. Or perhaps I am
missing something.
(xi) In Section 7 you first take into account noise and formulate it
and later define preferred explanations.
From Section 2-7 your formulation is in logic. It seems to me in
Section 8 you give an independent formulation and relate it to the
logical formulation with necessary and partially sufficient conditions.
Your algorithms in section 9 are justified based on the formulation and
results in Section 8.
(xi) Although I can appreciate the usefulness of the logical formulation
in Section 2-7, some may pose the following question: Why not just
formulate as in Section 8 (with some extensions perhaps) and then have
the correctness of the algorithm in Section 9 proven with respect to the
formulation in Section 8. Why go through the formulation in Section 2-7?
I think it will be a good idea to address this or say a few lines about
this to preempt such questions/attacks on logical formulation.
These are some of the questions and/or suggestions I have so far.
I am reading the proofs now. If I have additional questions I will
take the opportunity provided by this wonderful forum.
Best regards
Chitta
A2. Murray Shanahan (11.9):
Chitta,
Many thanks for your comments and questions.
| | (i) I think that in general a robot does not really sense events,
rather it notices changes in certain fluent values (in say resistors
linked to the sensors) from which it abduces the occurrences of triggered
events. Nevertheless, it is ok with me to skip this part and directly
talk about robots observing triggered events. But a clarification would
help.
|
But isn't a change in the voltage passing through a sensor an event?
Especially if we consider that voltage passing through a threshold
value.
| | (ii) Since you mention several times (abstract, Section 2, etc.)
that you use a novel solution to the frame problem using `Releases'
it will be nice if you say about it a little more than what is said in
Section 2 (just after EC 5). (You do use it in axioms in later sections,
but you don't discuss them.)
|
The use of "Releases" isn't really a big feature of the solution. More
important is the division of the theory into parts which are
circumscribed separately. This is what I call "forced separation" in my
book, "Solving the Frame Problem" (MIT Press, 1997). There's a lot of
detail about this solution to the frame problem in that book, which
makes me a bit reluctant to duplicate it here, as it really is a
side-issue. Maybe I should add a few sentences if things aren't clear.
But perhaps the following answers will suffice.
| | Although from the illustrations I can appreciate the use of `Releases'
in formulating continuous change, its utility in formulating constraints
is not clear to me. For example, why not eliminate B4 and instead of
`Releases' have `Terminates' in the head of rule E2.
|
Yes we could do that. But only because I've abstracted away the
continuous motion in the Rotate action, and made it instantaneous. If
the Rotate action initiated a period of continuous motion, then we would
have to use Releases, as in the case of the Occupies fluent. This is
because the axioms enforce the following rule:once a fluent has been
initiated (terminated) directly by an event, only another event that
directly terminates (initiates) it can change its value.
| | To me the advantage of having constraints such as B4 is that by having
it we avoid explicit compilation of it to effect axioms. I.e. we can
use constraints for automatically deducing effects indirectly. But if
we have both B4 and E2 then we are not really avoiding the compilation,
as E2 is like an effect axiom.
|
Actually the purpose of (B4) here is to cut out spurious models. (But
again, this only applies if we represent the continuous motion properly,
instead of abstracting it away as I have done here.) Without (B4),
during the period of continuous rotation of the robot, it could be
facing in many different directions at once.
| | (iii) I am not sure if `Bearing' is a standard geometrical notion.
Perhaps an intuitive meaning of it will help. Or may you can use the
more familiar notion of `slope'.
|
The word "bearing" is used in navigation. That's why I chose it. Maybe
it's not the mathematically most appropriate term.
| | (iv) You say (just after Sp3): ``the term Line(p1, p2) denotes the
straight line whose ...''. Perhaps it is more appropriate to say
``straight line segment'' instead of ``straight line''.
(v) I think in axiom (B3) you are assuming velocity to be one. If you do
please mention it.
(vi) The sentence after (B6). In it you explain Blocked(w1,w2,r) by
`if object w1 cannot move any distance at all in direction r without
overlapping with another object'. Perhaps you should say: ``if object w1
cannot move any distance at all because of w2 in direction r without
overlapping with another object'.
|
I'll make the changes you suggest. Thanks.
| | (vii) When defining HoldsAt(Touching(w1,w2,p),t) are you making some
assumptions about the shape of w1 and w2. Imagine two triangles which
touch at a point, you can align them such that they touch but yet do not
satisfy the conditions you have in B6.
|
Yes, I think you're right. But the definition in (B6) is correct for the
sense of touching required here, which excludes cases like the one you
mention. I should probably add a sentence on this.
| |
(viii) I am not clear about the intuition behind the notion of partial
completion in Section 5; especially in the text after (5.7).
For example in proposition 5.8, I would encode the intuition ``bump
switches are not tripped at any other time'' by
| |
Happens(Switch1, t) ·-> t = ind(T, bump)
| |
| |
Happens(Switch2, t) ·-> t = T_{bump}
| |
I am not clear about the intuition behind your formulation.
|
I think your formulation is equivalent to mine. I just elected to
separate the if and the only-if halves of the completion.
| | Also, why not use the standard Clark's completion and explain the
Clark's completion of Psi , where Psi is as mentioned in
Definition 5.9 and the paragraph before. I.e, have the Clark's
completion of Psi in the right hand side of the turnstyle in
Proposition 5.8
|
I can't use the Clark completion, because I only want to complete the
Happens predicate for sensor events. I might have incomplete knowledge
about other events.
| | (ix) In section 6 you logically express a region as a list of straight
lines. (You say it just before Bo3.) Is there any particular reason you
use lists instead of sets. If not, since you already use set notation in
the rest of your formulation, by using sets here also, you might avoid
additional axioms such as Bo3 and Bo4
|
I don't have a good answer to this. I guess I could have used sets, and
the result would have been slightly more succinct.
(x) Also (Bo3) is a fixpoint expression and you probably need
(as needed when defining transitive closure) to minimize `Members'
to get the right models.
| |
(Recall that the logic program
| |
anc(X, Y) <- (X, Y)
| |
| |
anc(X, Y) <- (X, Z) , anc(Z, Y)
| |
is not equivalent to the formula
| |
anc(X, Y) <-> (X, Y) v ( (X, Z) ^ anc(Z, Y))
| |
)
You are not minimizing `Members' in Proposition 6.2.
Or perhaps I am missing something.
|
There is an axiom missing, which says that nothing is a member of Nil.
I'll put this in the final draft.
But given that, I don't think there's a problem here. It's easy to
prove, for example, that ¬ Member(A, Cons(B, Cons(C, Nil))) , just by
recursing down the list (assuming A, B, and C are distinct). It's not
the same as the transitive closure case.
| | (xi) Although I can appreciate the usefulness of the logical formulation
in Section 2-7, some may pose the following question: Why not just
formulate as in Section 8 (with some extensions perhaps) and then have
the correctness of the algorithm in Section 9 proven with respect to the
formulation in Section 8. Why go through the formulation in Section 2-7?
I think it will be a good idea to address this or say a few lines about
this to preempt such questions/attacks on logical formulation.
|
This is a very good question, and the issue is fundamental to our
community's approach to AI. I don't think I can answer it fully here.
But one argument would appeal to the fact that perception is a process
which involves knowledge and reasoning, and if we're going to use logic
for knowledge representation and reasoning in "higher level" cognitive
processes, then we should use it throughout. I think this argument
becomes more forceful when we consider less trivial sensors than the
bump switches used here.
I hope that answers all your questions. Many thanks for taking so much
trouble over my paper.
Murray
C2-1. Murray Shanahan (31.1):
In the newsletter of 11.9, in answer to one of Chitta Baral's questions of
19.8, I wrote: "There is an axiom missing, which says that nothing is a member
of Nil. I'll put this in the final draft". In fact, this axiom is unnecessary,
as it follows from Axioms (Bo3) and (Bo4) of my formalisation.
Murray
Q3. Paulo Eduoardo Santos (11.9):
Thank you very much for answering my first questions. I really think it
is a very interesting paper.
The second bunch of questions follows:
1. In the last answer set we read:
| | By splitting the circumscription into parts, we get a more managable
theory, one whose consequences are easier to work out. In fact, the role
of circumscription here is mainly to complete certain predicates,
specifically Initiates, Terminates and Happens. If we circumscribe
everything together, we have to do a lot more work to avoid difficulties
like the
|
I agree that Separation avoids the Hanks-McDermott problem , but doing
so you get a restriction in the theory, since you are not able to write
formulae using Initiates (or Terminates) and Happens together (on the
contrary it won't be clear where to place such formulae in the
circumscriptions). Thus, we are not able to express (and infer) some
facts.
Then, why do not use negation-as-failure instead, since, for the
particular case of circumscription we are interested in, the former is
equivalent to the later (as proved in [j-aij-38-75]).
In which sense circumscription is more powerful than negation-as-failure
in this framework?
2. I could not understand the last formula of page 14. There a
biimplication is used defining the region g with the formula Pi . My
interpretation of this is that Pi is not an approximation of g but
it describes exactly g . Is that what it means?
3-
In the beginning of page 15 it is considered, as a solution to the
abduction process, "conjunctions M2 of formulae" such that a given
sensor data ( Psi ) is logical consequence (considering the background
theory).
My question is: what do you do if there is no M2 that explains Psi ?
(I'm not considering the case where M2 follows from the background
theory).
Many thanks for this opportunity,
Paulo Eduardo Santos
References:
| j-aij-38-75 | Michael Gelfond, Halina Przymusinska, and Teodor Przymusinski.
On the Relationship between Circumscription and Negation as Failure.
Artificial Intelligence Journal, vol. 38 (1989), pp. 75-94. |
A3. Murray Shanahan (9.10):
| | I agree that Separation avoids the Hanks-McDermott problem , but doing
so you get a restriction in the theory, since you are not able to write
formulae using Initiates (or Terminates) and Happens together (on the
contrary it won't be clear where to place such formulae in the
circumscriptions). Thus, we are not able to
express (and infer) some facts.
|
It's true that there are some (very few) kinds of formulae that we cannot
write using this method. For example, if we wanted to express the fact that
either flicking the switch terminates the light being on
or it was initially
dark, then there's no obvious way to do it. (This is Tom Costello's example.)
However, I'm a little sceptical that we do ever want to mix these different
kinds of information in this way. In this example, I suspect that another
layer of reasoning is called for, which explains observations (such as the
fact that it is dark), and this may update the Initiates/Terminates part of
the theory, or may update the initial situation description.
On the other hand we can, and often do, write other sorts of formulae that mix
Initiates , Terminates and Happens
predicates. In particular, triggered events
can be described using formulae of the form:
| |
Happens(a, t) if Initiates(a, f, t)
| |
These formulae can be included in the circumscription of Happens , and this
doesn't cause a problem, since the assumption is that the meaning of
Initiates
is already fixed by separate the circumscription of the Initiates and
Terminates part of the theory, and that this formula is, so to speak, just a
"consumer" of the Initiates predicate.
| | Then, why do not use negation-as-failure instead, since, for the
particular case of circumscription we are
interested in, the former is equivalent to the later
In which sense circumscription is more powerful than negation-as-failure
in this framework?
|
We could use negation-as-failure (or rather, say, predicate completion). Using
circumscription does allow for the addition of, for example, disjunctive
facts, however. Predicate completion is only defined for a certain class of
theories. Event though this class encompasses most of what we're interested
in, there doesn't seem any point in ruling out exceptions.
| | I could not understand the last formula of page 14. There a
biimplication is used defining the region g
with the formula Pi . My interpretation of this is that Pi is not an
approximation of g but it describes
exactly g . Is that what it means?
|
This is exactly what it means. Formula (5.7) on the same page is an example.
| | My question is: what do you do if there is no M2 that explains Psi ?
|
Then there really is no explanation. The robot is stuck.
Murray Shanahan
Q4. Paulo Eduoardo Santos (17.9):
Dear Murray Shanahan,
As you suggested, I am sending those questions to ETAI:
1. On page 5 we read the definition of the following circumscription
policy:
| |
Given a conjunction of Happens and Initially formulae N , a conjunction
of Initiates , Terminates and Releases formulae E (...), we are
interested in:
| |
CIRC [N;Happens] ^ CIRC [E;Initiates, Terminate, Releases] ^ U ^ EC
| |
|
My question is: Why didn't you circumscribe Initially and Happens in
parallel in the first conjunctive term of the expression above (since we
should expect to have, as true in the time 0, only the explicitly stated
facts and nothing else.)?
2. The second question concerns the same subject.
On page 9 we have the predicate AbSpace defined in terms of Initially :
| |
AbSpace(w) <- Initially(Occupies(w, g))
| |
Further on we read:
| |
The predicate AbSpace needs to be minimised, with Initially allowed to
vary.
|
The circumscription policy w.r.t. this idea is described
on the top of page 10 :
| |
CIRC [O ^ M;AbSpace;Initially] ^ ...
| |
Question: Why do we have to circumscribe Abspace letting Initially
vary, and not circumscribe only Initially (or both Initially and
Abspace )?
Cheers,
Paulo
A4. Murray Shanahan (9.10):
| | Why didn't you circumscribe Initially and Happens in parallel in the
first conjunctive term of the expression?
Why do we have to circumscribe Abspace letting Initially vary, and
not circumscribe only Initially (or both Initially and Abspace )?
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Well, it may be possible to do things that way. I was trying to follow as
closely as possible the approach I'd taken in my AIJ paper "Default Reasoning
about Spatial Occupancy", where I introduced a predicate similar to
AbSpace .
But anyway, I think you may have uncovered a bug in my formalisation. As
you'll see in other papers and in Chapter 15 of my book, usually when I
present the event calculus I use two Initially predicates: Initiallyp
to say
that a fluent holds and Initiallyn to say that it doesn't hold. A counterpart
to axiom (EC1) for ¬ HoldsAt and Initiallyn is also included. (Using two
predicates like this allows us to distinguish fluents that (1) are inertial
and true from time 0, (2) are inertial and false from time 0, and (3) are
non-inertial from time 0.) I tried to get away with just one predicate here,
because I thought the examples didn't need the Initiallyn
predicate. I need to
look into it properly, but I suspect that I need to reintroduce
Initiallyn to
get the minimisation of AbSpace right. It's only a minor modification, but at
the moment I don't think it works.
Murray Shanahan
Q5. Anonymous referee 1 (27.3):
Much of the work in the paper has already been published. That's not a
criticism, since it is signaled by the author himself, but the paper seems
to initiate a third kind of article in the ETAI, between reference papers
and crisp new results. I took a real interest reading it, because it
collects a bunch of results into a single framework. Showing how those
fragments, considered as specifying pieces of a common task, can
consistently work together and can help mastering the architecture of a
reasoning robot is, according to me, a real contribution worthy of
publication in the ETAI (parenthetically, this contribution could be more
neatly stated in the abstract).
The discussion with Paolo Eduardo Santos and Chitta Baral has been
extensive and several points have been improved. Here under are some more
suggestions, which are not conditions to the publication, but that Murray
Shanahan can follow if he feels they are improvements.
- In part 4, I suggest: "a region is an open (path)-connected subset of
R × R ... Objects occupy regions". That's a more standard definition of
region, which is not a synonymous of subset in standard math. Moreover,
with the present definition, according to (Bo1) p16, a closed set has an
empty boundary.
- while the reader can understand what is meant by a direction, the
definitions could be more precise. In (SP3), since Bearing is
real-valued, it is not a function (it is only defined modulo 360) and is
not defined if P1 = P2 . It is then unclear in (SP4) if P1 belongs to
line(P1, P2) , while P2 does. On the other hand, in axioms (H1)...(H3) p12,
the modulo arithmetic is implicit, and e.g. the bearing value -10 can not
be replaced by +350 in the inequalities.
I suggest to point that a bearing is in fact an equivalence class which
may be represented by any of its members, without further
developments. (SP3) could then be simplified to :
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Bearing(P1, P)-Bearing(P2, P) = 180 [mod 360]
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(and including the end points if prefered). Also, the definition
of intervals in (H1)...(H3) could be left to the reader's background
knowledge.
- The question raised by Chita Baral about touching triangles in (B6) can
be solved if P belongs Line(P1, P2) is omitted in the third line of this
axiom.
- (Bo5) could be simplified:
Connect(c) is the region g such that
forall P2, l [Boundary...] , if such
a region exist, then empty set else...
I suppose the definition of c is meant to exclude crossed polygons (two
lines of c having a common point appart from common end points mentined
in the list)
Also in paragraph 3, line 3 of 6., change Boundary(g, l) and in the last
line of (Bo5) exist P3, z forall p2...
- p18, just above (B8): I doubt that the condition for the robot
leaping over an obstacle is this one, which does not depend on the size
of the robot (if I do not misunderstand the sentence). Could it be
clarified which location/circle of uncertainty is relevant ?
- p22 def 7.11 I suggest clarifying that MIN is a parameter of the
definition.
Q6. Anonymous referee 2 (27.3):
The paper describes interesting results, which have been
originally presented at ECAI-96, that researchers working in
the area of reasoning on actions and change ought to know
about. It is well-written and clear. At some points, where
rather natural solutions to specific problems are proposed,
the presentation is too turgid.
The following are my answers to the standard referee questions:
1./2. There is a short (10 lines) abstract, but there is
not a summary where the main results are specified. I would
ask the author to provide it.
3. No.
4. Even though the paper is basically well organized, it can
be shorthened. Some general discussions as well as some
straightforward proofs, e.g., the proof of Proposition 2.8,
can be omitted and/or summarized.
5. The major limitation of the paper is that it is not
up-to-date (as reported in its cover page, its last
revision dates back to April 1996).
I wish to make the following additional comments regarding policy.
One of the major advantages of an electronic journal as ETAI is
that it guarantees a rapid publication of new results. In
particular, it reduces the delay between the presentation of the
results of a research work at a conference and their publication
in a journal paper.
I believe that one cannot publish old results without putting them
in the current state-of-the-art. In the specific case, I do not
think that the proposed contribution has been invalidated by later
developments in the field, but I would ask the author to discuss
such developments in the paper. My suggestion is to provide an
additional section relating the work to what has happened elsewhere
since then as well as to its subsequent developments (e.g., the
simpler description of the robot's environment, mentioned in an
answer to Paulo Eduoardo Santos).
More precisely, I would like to ask the author whether nothing has
been published on the subject since then that deserves to be taken
into account (if this is his opinion, it must be explicitly
formulated). I just mention the subsequents developments of the
logical approach proposed by Lesperance et al. (cf. the special
issue of the Journal of Logic Programming on Reasoning about
Action and Change, as well as the Proceedings of KR'98) and
Galton's work on representation and reasoning about spatial
knowledge. Furthermore, the paper reports the results of
preliminary experimentation with the robot. Has experimentation
been systematically executed? What are its outcomes?
Another relevant point: complexity issues are completely neglected
in the paper and dealt with rather quickly (and superficially) in
one of the interactions with Paulo Eduoardo Santos. I ask the
author to briefly discuss them in the paper. In particular, he
should at least summarize the known existing results about the
(worst-case) complexity of logic-based abduction and
circumscription, and explain his opinion about the impact of
these complexity results on research in logic-based/cognitive
robotics.
Minor point: I would remove from the abstract the sentence about
the novel solution to the frame problem (inspired by the work of
Kartha and Lifschitz). It seems to me a rather specific technical
point (as the author explicitly recognizes in his answer to Chitta
Baral), mainly concerned with the adopted formalims rather than
with the considered problem. Moreover, if the form of the
considered theories actually guarantees that the circumscriptions
(almost) always reduce to predicate completions, then I believe
that this fact should be explicitly stated.
References: please check/integrate [Charniak & McDermott,
1985], [Miller, 1996], and [Shanahan, 1996].
C6-1. Area Editor (30.3):
The second part of the comments by Anonymous Referee 2 raises an
interesting policy question for the ETAI, namely to what extent shall
commentary material be placed in the article itself, and to what
extent is it better placed in the article's discussion session.
With 'commentary' material I include comparison to related work
that occurred concurrently with or after then work being reported
in the article; discussions of alternative ways of realizing
subsystems of a largeer system being presented in the article;
discussion of intrinsic theoretical limitations of the proposed approach;
and so forth.
The A I literature has traditionally required fairly extensive
consideration of commentary material. This is clear in comparison with
other fields, such as physics, where articles usually seem to be
much more focussed on a single mission: define the problem, discuss
the state of the art relating to this problem, present the new solution,
done.
The emergence through ETAI of a systematically maintained dialogue connected
to each article offers an alternative approach: instead of the author
trying to answer all questions about the topic that some readers might ask,
he or she could focus on the main problem that's being addressed and
on its solution, and leave the rest to the question period. A change in
this direction would have its pros and cons. The advantages are in
the increased flexiblity and the possibility of adding material over
time, even after the date the article appeared in the journal. The
disadvantage might lie in a possible loss of systematicity, and in
the resistance among readers against changing old habits.
As the second half of the statement by Anonymous Referee 2 is a
suggestion for including several types of commentary into the article,
it would be possible syntactically to rephrase most of these
suggestions into questions that the author could answer in the
discussion page. Whether it is better to answer the questions this way
or by amendments in the article itself may be a matter of debate, and
it would be useful to have a decision about a recommended policy in
this respect.
Since the same question is likely to come up at other times, I will ask
the ETAI policy committee and our area editorial committee to study it
and to make a recommendation. Comments by subscribers are invited.
For the time being and for the present article, I will ask the author,
Murray Shanahan, to consider the second half of the referee statement
as a set of questions that can be answered either by amendments to the
article, or through the review dialogue. Based on the referee reports,
the article is accepted for the ETAI while giving the author an option
of minor modifications in response to the suggestions by both the
anonymous referees.
Background: Review Protocol Pages and the ETAI
This Review Protocol Page (RPP) is a part of the webpage structure
for the Electronic Transactions on Artificial Intelligence, or
ETAI. The ETAI is an electronic journal that uses the Internet
medium not merely for distributing the articles, but also for a
novel, two-stage review procedure. The first review phase is open
and allows the peer community to ask questions to the author and
to create a discussion about the contribution. The second phase -
called refereeing in the ETAI - is like conventional journal
refereeing except that the major part of the required feedback
is supposed to have occurred already in the first, 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).
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